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1. For a particular sample of 68 scores on a psychology exam, the following results were obtained.

First quartile = 57 Third quartile = 89 Standard deviation = 7 Range = 60

Mean = 70 Median = 73 Mode = 74 Midrange = 68

Answer each of the following:

I. What score was earned by more students than any other score? Why?

II. What was the highest score earned on the exam?

III. What was the lowest score earned on the exam?

IV. According to Chebyshev's Theorem, how many students scored between 42 and 98?

V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 63 and 77?

Please show all of your work.

2. Find the range, standard deviation, and variance for the following sample data:

32, 11, 11, 64, 67, 68, 46, 5, 31, 2, 92, 40, 20, 82, 27, 39

3. In terms of the mean and standard deviation:

- What does it mean to say that a particular value of x has a standard score of +1.5?

- What does it mean to say that a particular value of x has a z-score of -2.6?

4. A student scored 92 percent on a test, and was in the 85th percentile. Explain these two numbers.

5. In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent.

I. Taxi fare; Length of ride

II. Geographic location; Average annual snowfall

III. Monthly commission; Monthly sales

IV. Rainfall; Crop yield

6. A sample of purchases at the local convenience store has resulted in the following sample data, where x = the number of items purchased per customer and f = the number of customers.

x 1 2 3 4 5

f 7 17 8 8 7

•What does the 17 stand for in the above table?

•Find the midrange of items purchased.

•How many items were purchased by the customers in this sample?

7. Suppose we have a set of blood pressures with a mean of 80 Diastolic, and a sample standard deviation of 10 points. Assuming a normal distribution of Diastolic blood pressures, between what two values should 95% of all Diastolic blood pressures lie? Show all work.

8. SAT I scores around the nation tend to have a mean scale score around 500, a standard deviation of about 100 points, and are approximately normally distributed. What SAT I score within the population would have a percentile rank of approximately 97.5? Show all work as to how this is obtained.

First quartile = 57 Third quartile = 89 Standard deviation = 7 Range = 60

Mean = 70 Median = 73 Mode = 74 Midrange = 68

Answer each of the following:

I. What score was earned by more students than any other score? Why?

II. What was the highest score earned on the exam?

III. What was the lowest score earned on the exam?

IV. According to Chebyshev's Theorem, how many students scored between 42 and 98?

V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 63 and 77?

Please show all of your work.

2. Find the range, standard deviation, and variance for the following sample data:

32, 11, 11, 64, 67, 68, 46, 5, 31, 2, 92, 40, 20, 82, 27, 39

3. In terms of the mean and standard deviation:

- What does it mean to say that a particular value of x has a standard score of +1.5?

- What does it mean to say that a particular value of x has a z-score of -2.6?

4. A student scored 92 percent on a test, and was in the 85th percentile. Explain these two numbers.

5. In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent.

I. Taxi fare; Length of ride

II. Geographic location; Average annual snowfall

III. Monthly commission; Monthly sales

IV. Rainfall; Crop yield

6. A sample of purchases at the local convenience store has resulted in the following sample data, where x = the number of items purchased per customer and f = the number of customers.

x 1 2 3 4 5

f 7 17 8 8 7

•What does the 17 stand for in the above table?

•Find the midrange of items purchased.

•How many items were purchased by the customers in this sample?

7. Suppose we have a set of blood pressures with a mean of 80 Diastolic, and a sample standard deviation of 10 points. Assuming a normal distribution of Diastolic blood pressures, between what two values should 95% of all Diastolic blood pressures lie? Show all work.

8. SAT I scores around the nation tend to have a mean scale score around 500, a standard deviation of about 100 points, and are approximately normally distributed. What SAT I score within the population would have a percentile rank of approximately 97.5? Show all work as to how this is obtained.

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