a data set of video game scores has a mean of 35 and a range of 10. which situation will result in the…

a data set of video game scores has a mean of 35 and a range of 10. which situation will result in the greatest increase in the variance of the data set? (a) adding a value of 0 to the data set (b) adding a value of 90 to the data set (c) adding values of 30 and 40 to the data set (d) adding values of 35, 35, 35, and 35 to the data set

a data set of video game scores has a mean of 35 and a range of 10. which situation will result in the greatest increase in the variance of the data set? (a) adding a value of 0 to the data set (b) adding a value of 90 to the data set (c) adding values of 30 and 40 to the data set (d) adding values of 35, 35, 35, and 35 to the data set

Answer

Explanation:

Step1: Recall variance concept

Variance measures how far a set of numbers is spread out. Values far from the mean increase variance more.

Step2: Analyze option a

The mean is 35. Adding 0 which is $|35 - 0|=35$ away from the mean.

Step3: Analyze option b

Adding 90 which is $|90 - 35| = 55$ away from the mean.

Step4: Analyze option c

30 is $|35 - 30|=5$ away and 40 is $|40 - 35| = 5$ away from the mean.

Step5: Analyze option d

Adding 35s which have 0 distance from the mean.

Step6: Compare distances

55 (from option b) is the largest distance among all options.

Answer:

B. adding a value of 90 to the data set