1. For a particular sample of 63 scores on a psychology exam, the following results were obtained.
First quartile = 57 Third quartile = 72 Standard deviation = 9 Range = 52
Mean = 72 Median = 68 Mode = 70 Midrange = 57
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 54 and 90?
V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 54 and 90?
2. Find the range, standard deviation, and variance for the following sample data:
87, 75, 58, 29, 21, 19, 80, 27, 61, 77, 26, 16, 79, 1, 68, 100 (Points : 6)
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 -2.3?
- What does it mean to say that a particular value of x has a z-score of +1.0?
4. A student scored 81 percent on a test, and was in the 77th 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.
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
|
10
|
18
|
8
|
8
|
7
|
• What does the 18 stand for in the above table?
• Find the midrange of items purchased.
• How many items were purchased by the customers in this sample?
7. Scores on the Stanford-Binet Intelligence scale have a mean of 100 and a standard deviation of 16, and are presumed to be normally distributed. A person who scores 84 on this scale has what percentile rank within the population? Show all work as to how this is obtained.
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 2.5? Show all work as to how this is obtained.