Algebra 2 question/ Help

Question

A caterer records the number of weddings he works during 5 weeks of the summer: {0,3,4,3,6}. If he caters 3 weddings the next week, in what ways do the mean and the standard deviation of the data set change?

 

A) the mean increases, the standard deviation increases

B) The mean increases, the standard deviation decreases

C) the mean decreases, the standard deviation increases

D) the mean decreases, the standard deviation decreases.

Answer 1

For the 5-week period, the mean is 3.2 and the standard deviation is 1.939. Adding a 6th week with 3 weddings changes the mean to 3.1667 and the standard deviation to 1.7717.

This makes sense because the 3 in the 6th week is lower than the 3.2 average for the 5-week period. Therefore, the mean will decrease. Similarly, the standard deviation decreases because the new 3 is quite close to the prior mean and lower than it. So the data set becomes more closely clustered around the mean.

Answer is D.