{"id":106,"date":"2024-08-21T12:01:35","date_gmt":"2024-08-21T12:01:35","guid":{"rendered":"http:\/\/localhost\/researchmethods\/?post_type=content&#038;p=106"},"modified":"2026-08-26T11:38:24","modified_gmt":"2026-08-26T11:38:24","slug":"chapter-15-frequencies-and-distributions","status":"publish","type":"content","link":"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-15-frequencies-and-distributions\/","title":{"rendered":"Chapter 15 &#8211; Frequencies and distributions"},"content":{"rendered":"\n<div class=\"wp-block-group has-base-background-color has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--70);padding-bottom:var(--wp--preset--spacing--70)\">\n<div class=\"wp-block-group alignwide is-layout-flow wp-block-group-is-layout-flow\"><nav style=\"--separator: &quot;\/&quot;\" class=\"wp-block-breadcrumbs\" aria-label=\"Breadcrumbs\"><ol><li><a href=\"https:\/\/routledgelearning.com\/researchmethods\/\">Home<\/a><\/li><li><a href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/\">Student Resources<\/a><\/li><li><span aria-current=\"page\">Chapter 15 &#8211; Frequencies and distributions<\/span><\/li><\/ol><\/nav>\n\n<h1 class=\"alignwide wp-block-post-title has-large-font-size\">Chapter 15 &#8211; Frequencies and distributions<\/h1>\n\n\n<p class=\"wp-block-paragraph\">This chapter looks at how the authors deal with frequencies in sets of data and, in particular, with the properties and use of the normal distribution.<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--60);padding-bottom:var(--wp--preset--spacing--60)\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:75%\">\n<h2 id=\"aioseo-exercises\" class=\"wp-block-heading\">Exercises<\/h2>\n\n\n\n<h3 id=\"aioseo-exercise-15-1\" class=\"wp-block-heading\">Exercise 15.1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>z scores<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A reading ability scale has a mean of 40 and a standard deviation of 10 and scores on it are normally distributed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. What reading score does a person get who has a z score of 1.5?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\"><strong>55<\/strong><strong><\/strong><\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">2. If a person has a raw score of 35 what is their z score?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">0.5<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">3. How many standard deviations from the mean is a person achieving a z score of 2.5?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">2.5 above the mean<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">4. What percentage of people score above 50 on the test?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">15.87%<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">5. What percentage of people score below 27?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">9.68%<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">6. What is the z score and raw score of someone on the 68th percentile?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">z is where 18% (or .18) are above the mean. z is .47 and this is 4.7 above 40 = 44.7<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">7. At what percentile is a person who has a raw score of 33?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">24th (24.2%)<\/p>\n<\/details>\n\n\n\n<h3 id=\"aioseo-exercise-15-2\" class=\"wp-block-heading\">Exercise 15.2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Standard error<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. If a sample of 30 people produces a mean target detection score of 17 with a standard deviation of 4.5, what is our best estimate of the standard error of the sampling distribution of similar means?<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">0.82<\/p>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\">2. Using the result of question 1, find the 95% confidence interval for the population mean.<\/p>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">15.39 to 18.61<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Explanation: For 95% limits z must be -1.96 to +1.96; 1.96 x the se = 1.96 x 0.82 = 1.61. Hence we have 95% confidence that the true mean lies between 17 \u00b1 1.61<\/p>\n<\/details>\n\n\n\n<h3 id=\"aioseo-exercise-15-3\" class=\"wp-block-heading\">Exercise 15.3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Have a go at this short quiz to test your understanding of frequencies and distributions and identify any gaps in your knowledge.<\/p>\n\n\n\n<div class=\"wp-block-group has-base-element-background-color has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-0910e091 wp-block-group-is-layout-constrained\" style=\"border-width:1px;padding-top:var(--wp--preset--spacing--40);padding-right:var(--wp--preset--spacing--40);padding-bottom:var(--wp--preset--spacing--40);padding-left:var(--wp--preset--spacing--40)\">\n<div class=\"wp-block-group alignwide is-layout-flow wp-block-group-is-layout-flow\"><script>\n                            if (window.qmn_quiz_data === undefined) {\n                                    window.qmn_quiz_data = new Object();\n                            }\n                    <\/script><script>window.qmn_quiz_data[\"13\"] = {\"quiz_id\":\"13\",\"quiz_name\":\"exercise153\",\"disable_answer\":0,\"ajax_show_correct\":0,\"progress_bar\":0,\"contact_info_location\":\"0\",\"qpages\":{\"2\":{\"id\":\"2\",\"quizID\":\"13\",\"pagekey\":\"Lrey0nYW\",\"hide_prevbtn\":\"0\"}},\"skip_validation_time_expire\":0,\"timer_limit_val\":0,\"disable_scroll_next_previous_click\":0,\"disable_scroll_on_result\":0,\"disable_first_page\":\"0\",\"enable_result_after_timer_end\":0,\"enable_quick_result_mc\":0,\"end_quiz_if_wrong\":0,\"form_disable_autofill\":0,\"disable_mathjax\":0,\"enable_quick_correct_answer_info\":\"0\",\"quick_result_correct_answer_text\":\"Correct! You have selected correct answer.\",\"quick_result_wrong_answer_text\":\"Wrong! You have selected wrong answer.\",\"quiz_processing_message\":\"\",\"quiz_limit_choice\":\"Limit of choice is reached.\",\"not_allow_after_expired_time\":0,\"scheduled_time_end\":false,\"prevent_reload\":0,\"limit_email_based_submission\":0,\"total_user_tries\":0,\"is_logged_in\":false,\"pagination\":{\"amount\":1,\"section_comments\":\"\",\"total_questions\":6,\"previous_text\":\"Previous\",\"next_text\":\"Next\",\"start_quiz_survey_text\":\"Start Quiz\",\"submit_quiz_text\":\"Submit\"},\"error_messages\":{\"email_error_text\":\"Not a valid e-mail address!\",\"number_error_text\":\"This field must be a number!\",\"incorrect_error_text\":\"The entered text is not correct!\",\"empty_error_text\":\"Please complete all required fields!\",\"contact_field_required_error_text\":\"Please complete all required fields!\",\"url_error_text\":\"The entered URL is not valid!\",\"minlength_error_text\":\"Required atleast %minlength% characters.\",\"maxlength_error_text\":\"Maximum %maxlength% characters allowed.\",\"recaptcha_error_text\":\"ReCaptcha is missing\",\"phone_error_text\":\"Phone number is invalid\",\"empty_grid_radio_checkbox_text\":\"Please complete all  rows required fields!\",\"empty_audio_text\":\"Please upload audio!\"},\"question_list\":{\"88\":{\"question_id\":\"88\",\"quiz_id\":\"13\",\"question_name\":\"If a test is particularly easy, in what direction would the resulting scores skew?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:8:\\\"Positive\\\";i:1;d:0;i:2;i:0;}i:1;a:3:{i:0;s:8:\\\"Negative\\\";i:1;d:0;i:2;i:1;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Scores will mostly be high so there is more room to the left for relatively more extreme low scores which decreases the mean and extends the tail to the left = negative skew.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 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median?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:6:\\\"Higher\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:5:\\\"Lower\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"The greater number of relatively extreme scores in the tail to the right leads to an increased mean.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 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median?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:6:\\\"Higher\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:5:\\\"Lower\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"The greater number of relatively extreme scores in the tail to the left leads to a decreased mean with the median between this and the mode. Hence the mode is higher than the median.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 3\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"Higher\",0,1],[\"Lower\",0,0]]},\"91\":{\"question_id\":\"91\",\"quiz_id\":\"13\",\"question_name\":\"Which of the options below refers to the vertical shape of a histogram distribution?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:4:\\\"Skew\\\";i:1;d:0;i:2;i:0;}i:1;a:3:{i:0;s:8:\\\"Kurtosis\\\";i:1;d:0;i:2;i:1;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Kurtosis refers to the \\u201cpeakedness\\u201d of the distribution \\u2013 \\u2018leptokurtic\\u2019 with higher peak and \\u2018platykurtic\\u2019 with a plateau like middle.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 4\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"Skew\",0,0],[\"Kurtosis\",0,1]]},\"92\":{\"question_id\":\"92\",\"quiz_id\":\"13\",\"question_name\":\"Checking that skew and kurtosis do not violate normal distribution criteria is important when conducting which kind of test?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:10:\\\"Parametric\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:14:\\\"Non-parametric\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Skew and kurtosis should always meet certain criteria in a parametric test, hence the term \\u2018parametric\\u2019 which refers to parameters of the distribution. For non-parametric tests these criteria are irrelevant.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 5\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"Parametric\",0,1],[\"Non-parametric\",0,0]]},\"93\":{\"question_id\":\"93\",\"quiz_id\":\"13\",\"question_name\":\"If a distribution has a mean of 66.3, a median of 65.1 and a mode of 64 is it positively or negatively skewed?\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:8:\\\"Positive\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:8:\\\"Negative\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"The mean is most extended to the right, hence positive skew \\u2013 the direction in which mean and median are \\u2018pulled out\\u2019.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 6\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"Positive\",0,1],[\"Negative\",0,0]]}},\"first_page\":false,\"questions_settings\":[]}\n                    <\/script>\t\t<div class='qsm-quiz-container qsm-quiz-container-13 qmn_quiz_container mlw_qmn_quiz qsm_auto_pagination_enabled quiz_theme_default  '>\n\t\t\t\t\t\t\t\t<form name=\"quizForm13\" id=\"quizForm13\" action=\"\/researchmethods\/wp-json\/wp\/v2\/content\/106\/\" method=\"POST\" class=\"qsm-quiz-form qmn_quiz_form mlw_quiz_form\" novalidate enctype=\"multipart\/form-data\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_hidden_questions\" id=\"qsm_hidden_questions\" value=\"\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_nonce\" id=\"qsm_nonce_13\" value=\"2d82651929\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_unique_key\" id=\"qsm_unique_key_13\" value=\"6a8f8c8e961ff\">\n\t\t\t\t<div id=\"mlw_error_message\" class=\"qsm-error-message qmn_error_message_section\"><\/div>\n\t\t\t\t<span id=\"mlw_top_of_quiz\"><\/span>\n\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-1\" data-apid=\"1\" data-qpid=\"1\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-88 slide0 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 1 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>If a test is particularly easy, in what direction would the resulting scores skew?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question88-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question88\" id=\"question88_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question88_1\">\n\t\t\t\t\tPositive\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question88-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question88\" id=\"question88_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question88_2\">\n\t\t\t\t\tNegative\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question88_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question88\" id=\"question88_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_88\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-2\" data-apid=\"2\" data-qpid=\"2\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-89 slide1 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 2 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>In a positively skewed distribution would the mean be higher of lower than the median?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question89-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question89\" id=\"question89_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question89_1\">\n\t\t\t\t\tHigher\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question89-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question89\" id=\"question89_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question89_2\">\n\t\t\t\t\tLower\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question89_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question89\" id=\"question89_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_89\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-3\" data-apid=\"3\" data-qpid=\"3\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-90 slide2 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 3 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>In a negatively skewed distribution would the mode be higher or lower than the median?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question90-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question90\" id=\"question90_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question90_1\">\n\t\t\t\t\tHigher\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question90-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question90\" id=\"question90_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question90_2\">\n\t\t\t\t\tLower\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question90_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question90\" id=\"question90_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_90\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-4\" data-apid=\"4\" data-qpid=\"4\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-91 slide3 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 4 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Which of the options below refers to the vertical shape of a histogram distribution?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question91-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question91\" id=\"question91_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question91_1\">\n\t\t\t\t\tSkew\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question91-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question91\" id=\"question91_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question91_2\">\n\t\t\t\t\tKurtosis\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question91_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question91\" id=\"question91_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_91\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-5\" data-apid=\"5\" data-qpid=\"5\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-92 slide4 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 5 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Checking that skew and kurtosis do not violate normal distribution criteria is important when conducting which kind of test?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question92-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question92\" id=\"question92_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question92_1\">\n\t\t\t\t\tParametric\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question92-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question92\" id=\"question92_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question92_2\">\n\t\t\t\t\tNon-parametric\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question92_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question92\" id=\"question92_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_92\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-6\" data-apid=\"6\" data-qpid=\"6\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-93 slide5 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 6 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>If a distribution has a mean of 66.3, a median of 65.1 and a mode of 64 is it positively or negatively skewed?<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question93-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question93\" id=\"question93_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question93_1\">\n\t\t\t\t\tPositive\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question93-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question93\" id=\"question93_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question93_2\">\n\t\t\t\t\tNegative\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question93_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question93\" id=\"question93_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_93\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t<input type=\"hidden\" name=\"qmn_question_list\" value=\"88Q89Q90Q91Q92Q93Q\" \/>\n\t\t\t\t\t<div class=\"qsm-auto-page-row quiz_section quiz_end empty_quiz_end qsm-d-none\" >\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<div id=\"mlw_error_message_bottom\" class=\"qsm-error-message qmn_error_message_section\"><\/div>\n\t\t\t\t\t<input type=\"hidden\" name=\"qmn_all_questions_count\" id=\"qmn_all_questions_count\" value=\"6\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"total_questions\" id=\"total_questions\" value=\"6\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"timer\" id=\"timer\" value=\"0\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"timer_ms\" id=\"timer_ms\" value=\"0\"\/>\n\t\t\t\t\t<input type=\"hidden\" class=\"qmn_quiz_id\" name=\"qmn_quiz_id\" id=\"qmn_quiz_id\" value=\"13\" \/>\n\t\t\t\t\t<input type='hidden' name='complete_quiz' value='confirmation' \/>\n\t\t\t\t\t\t\t\t\t<\/form>\n\t\t\t\t\t\t<\/div>\n\t\t<div style=\"display: none;\" class=\"qsm-popup qsm-popup-slide\" id=\"modal-4\" aria-hidden=\"false\"><div class=\"qsm-popup__overlay\" tabindex=\"-1\" data-micromodal-close=\"\"><div class=\"qsm-popup__container qmn_quiz_container\" role=\"dialog\" aria-modal=\"true\"><div class=\"qsm-popup__content\"><img decoding=\"async\" src=\"https:\/\/routledgelearning.com\/researchmethods\/wp-content\/plugins\/quiz-master-next\/assets\/clock.png\" alt=\"clock.png\"\/><p class=\"qsm-time-up-text\"> Time&#8217;s up<\/p><\/div><footer class=\"qsm-popup__footer\"><button class=\"qsm-popup-secondary-button qmn_btn\" data-micromodal-close=\"\" aria-label=\"Close this dialog window\" onclick=\"location.reload();\">Cancel<\/button><\/footer><\/div><\/div><\/div><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 id=\"aioseo-weblinks\" class=\"wp-block-heading\">Weblinks<\/h2>\n\n\n\n<h3 id=\"aioseo-frequencies-and-distributions-weblinks\" class=\"wp-block-heading\">Frequencies and Distributions<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">All about the normal distribution. Try the Quincunx \u2013 shows you how a normal distribution is created by random events\u2019. There are other useful statistics pages at this site. Click \u2018home\u2019 and then click \u2018data\u2019:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/www.mathsisfun.com\/data\/standard-normal-distribution.html\">www.mathsisfun.com\/data\/standard-normal-distribution.html<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<div class=\"wp-block-group is-vertical is-nowrap is-layout-flex wp-container-core-group-is-layout-b3ff8204 wp-block-group-is-layout-flex wp-container-1 is-position-sticky\">\n<p class=\"wp-block-paragraph\"><strong>On this page<\/strong><\/p>\n\n\n\n<nav class=\"wp-block-table-of-contents\"><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-15-frequencies-and-distributions\/#aioseo-exercises\">Exercises<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-15-frequencies-and-distributions\/#aioseo-weblinks\">Weblinks<\/a><\/li><\/ol><\/nav>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This chapter looks at how the authors deal with frequencies in sets of data and, in particular, with the properties and use of the normal distribution. Exercises Exercise 15.1 z scores A reading ability scale has a mean of 40 and a standard deviation of 10 and scores on it are normally distributed. 1. What [&hellip;]<\/p>\n","protected":false},"featured_media":0,"parent":121,"menu_order":0,"template":"single-chapter","format":"standard","meta":{"_acf_changed":false},"categories":[],"class_list":["post-106","content","type-content","status-publish","format-standard","hentry"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"This chapter looks at how the authors deal with frequencies in sets of data and, in particular, with the properties and use of the normal distribution. Exercises Exercise 15.1 z scores A reading ability scale has a mean of 40 and a standard deviation of 10 and scores on it are normally distributed. 1. What\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-15-frequencies-and-distributions\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO Pro (AIOSEO) 5.0.0.1\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Research Methods and Statistics in Psychology - 8th Edition\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Chapter 15 \u2013 Frequencies and distributions - Research Methods and Statistics in Psychology\" \/>\n\t\t<meta property=\"og:description\" content=\"This chapter looks at how the authors deal with frequencies in sets of data and, in particular, with the properties and use of the normal distribution. Exercises Exercise 15.1 z scores A reading ability scale has a mean of 40 and a standard deviation of 10 and scores on it are normally distributed. 1. What\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-15-frequencies-and-distributions\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2024-08-21T12:01:35+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2026-08-26T11:38:24+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Chapter 15 \u2013 Frequencies and distributions - Research Methods and Statistics in Psychology\" \/>\n\t\t<meta name=\"twitter:description\" content=\"This chapter looks at how the authors deal with frequencies in sets of data and, in particular, with the properties and use of the normal distribution. Exercises Exercise 15.1 z scores A reading ability scale has a mean of 40 and a standard deviation of 10 and scores on it are normally distributed. 1. 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