Question

which two data sets appear to be normally distributed? a. value: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55; frequency: 10, 27, 40, 60, 75, 100, 80, 55, 35, 30, 11 b. value: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55; frequency: 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71 c. value: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55; frequency: 12, 25, 32, 41, 68, 75, 66, 52, 35, 26, 13 d. value: 5, 10, 15, 20, 25, 30, 21, 24, 27, 30, 33; frequency: 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63

Explanation:

To determine which data sets are normally distributed, we look for a bell - shaped curve pattern in the frequency distribution. A normal distribution has frequencies that increase to a peak and then decrease symmetrically around the peak.

Step 1: Analyze Data Set A

• For data set A, the frequencies start at 10, increase gradually (10, 27, 40, 60, 75, 100) until the value of 30, and then decrease (80, 55, 35, 30, 11). The frequencies are symmetric around the peak at 30.

Step 2: Analyze Data Set B

• For data set B, the frequencies are constantly increasing (11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71). This is a left - skewed or increasing distribution, not a normal distribution.

Step 3: Analyze Data Set C

• For data set C, the frequencies start at 12, increase (12, 25, 32, 41, 68, 75) until the value of 30, and then decrease (66, 52, 35, 26, 13). The frequencies are symmetric around the peak at 30.

Step 4: Analyze Data Set D

• For data set D, the values are not in a proper order (there are repeated and out - of - order values like 21, 24, 27 among the values 5, 10, 15, 20, 25, 30), and the frequencies are constantly increasing (13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63). This is not a normal distribution.

Answer:

A. The data set with values 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and frequencies 10, 27, 40, 60, 75, 100, 80, 55, 35, 30, 11
C. The data set with values 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and frequencies 12, 25, 32, 41, 68, 75, 66, 52, 35, 26, 13