{"id":106,"date":"2024-08-21T12:01:35","date_gmt":"2024-08-21T12:01:35","guid":{"rendered":"https:\/\/routledgelearning.com\/researchmethods\/?post_type=content&p=106"},"modified":"2024-09-12T09:05:41","modified_gmt":"2024-09-12T09:05:41","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 – Frequencies and distributions"},"content":{"rendered":"\n
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Chapter 15 – Frequencies and distributions<\/h1>\n\n\n

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

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Exercises<\/h2>\n\n\n\n

Exercise 15.1<\/h3>\n\n\n\n

z scores<\/strong><\/p>\n\n\n\n

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

1. What reading score does a person get who has a z score of 1.5?<\/p>\n\n\n\n

Show answer<\/summary>\n

55<\/strong><\/strong><\/p>\n<\/details>\n\n\n\n

2. If a person has a raw score of 35 what is their z score?<\/p>\n\n\n\n

Show answer<\/summary>\n

0.5<\/p>\n<\/details>\n\n\n\n

3. How many standard deviations from the mean is a person achieving a z score of 2.5?<\/p>\n\n\n\n

Show answer<\/summary>\n

2.5 above the mean<\/p>\n<\/details>\n\n\n\n

4. What percentage of people score above 50 on the test?<\/p>\n\n\n\n

Show answer<\/summary>\n

15.87%<\/p>\n<\/details>\n\n\n\n

5. What percentage of people score below 27?<\/p>\n\n\n\n

Show answer<\/summary>\n

9.68%<\/p>\n<\/details>\n\n\n\n

6. What is the z score and raw score of someone on the 68th percentile?<\/p>\n\n\n\n

Show answer<\/summary>\n

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

7. At what percentile is a person who has a raw score of 33?<\/p>\n\n\n\n

Show answer<\/summary>\n

24th (24.2%)<\/p>\n<\/details>\n\n\n\n

Exercise 15.2<\/h3>\n\n\n\n

Standard error<\/strong><\/p>\n\n\n\n

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

Show answer<\/summary>\n

0.82<\/p>\n<\/details>\n\n\n\n

2. Using the result of question 1, find the 95% confidence interval for the population mean.<\/p>\n\n\n\n

Show answer<\/summary>\n

15.39 to 18.61<\/p>\n\n\n\n

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

Exercise 15.3<\/h3>\n\n\n\n

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

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