Question

1. what is the mode of the data set? data set: 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 11, 12 (a) 4 (b) 5 (c) 6 4. what explains the large difference in the mean and median of the data set? data set: 10, 12, 14, 16, 21, 22, 66 median: 16 mean: 23 (a) there is an odd number of data values in the set. (b) the data set contains an extreme data value. (c) there are enough numbers in the set. 5. what is the range for the data set? data set: 1, 2, 2, 3, 4, 7, 8, 12, 12, 12, 12, 13, 17 (a) 16 (b) 17 (c) 18

Explanation:

Step1: Recall mode definition

The mode is the number that appears most frequently in a data - set.

Step2: Count frequencies in first data set

In the data set 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 11, 12, the number 4 appears 4 times, which is more frequently than any other number. So the answer to question 3 is 4.

Step3: Recall mean and median sensitivity

The mean is affected by extreme values, while the median is not. In the data set 10, 12, 14, 16, 21, 22, 66, 66 is an extreme value. It pulls the mean up, while the median is the middle - value (16 for this odd - numbered data set). So the answer to question 4 is that the data set contains an extreme data value.

Step4: Recall range definition

The range of a data set is the difference between the largest and the smallest values. In the data set 1, 2, 2, 3, 4, 7, 8, 12, 12, 12, 12, 13, 17, the largest value is 17 and the smallest value is 1. Range = 17 - 1=16.

Answer:

1. a. 4
2. b. The data set contains an extreme data value.
3. a. 16