Читать книгу Student Study Guide to Accompany Statistics Alive! - Wendy J. Steinberg - Страница 24

The following are the test grades for students in your European History class after the first test.

1 Find the deviation score for each test grade. What is the sum of these deviations?

2 Find the variance for the grades. Find the standard deviation for the grades.

3 How many standard deviations from the mean is the person with the highest grade? The person with the lowest score?

4 One of those who received a 99 is an exceptional student who turned in an extra-credit project that was worth an additional 10 points on the test. What would the variance and standard deviation be with this person’s correct grade? (Recalculate the measures of dispersion using this new high score.)

5 Reflecting back on your response to Question 4, which measure of dispersion had the largest change in absolute units?

6 How many of the original grades are between 1 and 2 SD above the mean?

The manager of a shoe store is interested in determining how many of each shoe size were sold the previous day. The store has made 10 sales of shoes with the following sizes:

 7. Find the variance and standard deviation for these shoe sizes.

 8. In the last few minutes of the store’s business hours, three people run in, stating that they are in a shoe emergency, and ask to purchase shoes. The shoe sizes of these three new customers are 8, 6, and 10. If they each purchase a pair of shoes, what will be the new standard deviation?

 9. How many of these 13 (including those added in Question 8) people fall within 1 SD of the mean?

 10. What is the mean absolute deviation of the original shoe sizes? How does this compare with the standard deviation?

 11. If you were to estimate the population variance in the shoe sizes of people who shop at this store from this sample, what formula would you use (using the original 10 scores)? What would be the population variance estimated from this sample?

 12. The store manager collects similar data for the following day and finds that the mean is substantially higher but the standard deviation is now 7.9. Which mean is more representative of the average shoe size of those who shop at this store?