Data Analysis and Probability Unit Pre-Assessment

Math 2 Name ______Data Analysis and Probability Unit Pre-Assessment

MM2D1: Using sample data, students will make informal inferences about population means and standard deviations

1. The standard deviation of 16 measurements of people’s weights (in pounds) is computed to be 5.4 The variance of these measurements is

a) 2.24 b) 29.16 c) 52.34 d) 256

2. There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the

a) mean age will stay the same but the standard deviation will increase. b) mean age will stay the same but the standard deviation will decrease. c) mean age and standard deviation will stay the same d) mean age and standard deviation will increase

3. The five-number summary of a set of data is

a) the mean, standard deviation, first quartile, median, and third quartile b) the mean, median, mode, variance, and standard deviation c) the minimum, first quartile, median, third quartile, and maximum d) the minimum, first quartile, mean, third quartile, and maximum

4. The following is a boxplot of the birth weights (in ounces) of a sample of 160 infants born in a local hospital.

About 40 of the birth weights were below

a) 92 b) 102 c) 112 d) 122

5. The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the middle 68% of students will get a “C”, what is the lowest mark that a student can have and still be awarded a C?

a) 56.5 b) 51 c) 73 d) 40 6. In the accompanying display, which has the larger mean and which has the larger standard deviation?

a) Larger mean, A; larger standard deviation, A b) Larger mean, A; larger standard deviation, B c) Larger mean, B; larger standard deviation, B d) Larger mean, B; larger standard deviation, A

Use figure 1 to the right to answer questions 7 & 8

7. Which of the following statements is TRUE about figure 1:

a) The standard deviation of B is larger than the standard deviation of A b) The standard deviation of C is larger than the standard deviation of A c) The standard deviation of C is larger than the standard deviation of B d) The standard deviation of A is smaller than the standard deviation of C

8. Which of the following statements is NOT TRUE about figure 1:

a) The mean of C is larger than the mean of A b) The mean of B is larger than the mean of A c) The mean of A is smaller than the mean of C d) The mean of A is equal to the mean of B

9. Salaries of professional baseball players take on a right-skewed distribution. If we were to take both the mean and median of this distribution, what would be true about the relationship between these two measures?

a) Mean salary is equal to median salary b) Mean salary is less than median salary c) Mean salary is greater than median salary d) There is not enough information provided to answer.

10. Mr. Jones’ math class had an average of 86 on the first test with a standard deviation of 3.4. Mrs. Smith’s math class had an average of 86 on the first test with a standard deviation of 6.2. Which is true in comparing the performance of the two classes?

a) Both classes did equally well b) Mr. Jones’ class did better than Mrs. Smith’s class c) Mr. Jones’ class did worse than Mrs. Smith’s class d) Mr. Jones’ class had less spread in the scores than Mrs. Smith’s class 11. Calculate the mean, median, mode, standard deviation, and range for the following data set.

Test scores from the last quiz:

72 88 93 99 78 78 60 97 43

mean: ______median: ______mode: ______standard deviation: ______range: ______

12. During contract negotiations a company seeks to change the number of sick days employees may take, saying that the annual “average” is 7 days of absence per employee. The union negotiators counter that the “average” employee misses only 3 days of work each year. Explain how both sides might be correct.

13. Hotel occupancy rates often dictate how easy it might be to reserve a room at the last minute and determine the average cost of a room. Rooms are often discounted in areas with low occupancy. Occupancy rates across the United States for major cities are given below:

56 89 79 71 70 60 60 61 62 63 64 65 81 73 68 72 56 59 60 62 73 64 72 67

a) Compute the five-number summary and the interquartile range.

b) Make a boxplot.

c) What scores separate the middle 50% of the data?

14. Determine if the data set is a sample or a population. a. Ms. Smith asks 15 students her class to rate the food in the school cafeteria to publish in the school newspaper for an article about school lunches.

______

b. Mary asks every student in her class how many pets they have to compile data for a project about her classmates.

______

c. The average weight of every sixth person entering the mall within 3 hour period was 146 lb. ______

15. The heights (in inches) of 7 out of 20 students in Mr. Kelly’s 8th grade class is given in the data set below.

54, 56, 60, 52, 51, 50, 55

(a) What is the mean and standard deviation of these heights? (SHOW ALL WORK!!)

mean = ______standard deviation = ______

(b) What scores separate the middle 68% of the data?