Chapter 15 – Frequencies and distributions
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 reading score does a person get who has a z score of 1.5?
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55
2. If a person has a raw score of 35 what is their z score?
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0.5
3. How many standard deviations from the mean is a person achieving a z score of 2.5?
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2.5 above the mean
4. What percentage of people score above 50 on the test?
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15.87%
5. What percentage of people score below 27?
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9.68%
6. What is the z score and raw score of someone on the 68th percentile?
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z is where 18% (or .18) are above the mean. z is .47 and this is 4.7 above 40 = 44.7
7. At what percentile is a person who has a raw score of 33?
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24th (24.2%)
Exercise 15.2
Standard error
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?
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0.82
2. Using the result of question 1, find the 95% confidence interval for the population mean.
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15.39 to 18.61
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 ± 1.61
Exercise 15.3
Have a go at this short quiz to test your understanding of frequencies and distributions and identify any gaps in your knowledge.
Weblinks
Frequencies and Distributions
All about the normal distribution. Try the Quincunx – shows you how a normal distribution is created by random events’. There are other useful statistics pages at this site. Click ‘home’ and then click ‘data’: