Question

data set a: 24,34,44,54,64
data set a which consists of the 5 values shown has a mean of 44 and a standard deviation of approximately 14.14. data set b consists of the 5 values from set a and one additional value k. for which of the following values of k will the standard deviation of data set b be less than the standard deviation of data set a?
a. 14
b. 49
c. 74
d. there is no value of k such that the standard deviation of data set b will be less than the standard deviation of data set a

Explanation:

Step1: Recall std - dev concept

Standard deviation measures data - spread from mean.

Step2: Analyze data set A

Mean of set A is 44.

Step3: Check each option

For k = 49, it's closer to mean 44 than other options, reducing spread.

Answer:

b. 49