Question

1. refer to the data for ms. susie’s class in problem #6 above. a new student with a height of 36\ joined ms. susie’s class. which of the following describes how the mean, median, and mode were affected? a) all decrease b) mean increases, median decreases, mode is unchanged c) mean and median decrease, mode is unchanged d) mode and median decrease, mean is unchanged

Explanation:

Step1: Recall mean formula

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. If a new value that is less than the original mean is added, the sum of values increases by a smaller - amount relative to the increase in the number of data - points. So the mean will decrease.

Step2: Recall median concept

The median is the middle value when the data is ordered. If the original number of data - points is $n$ and a new value is added (so the new number of data - points is $n + 1$), and the new value is less than the original median, the median will shift towards the lower values, thus decreasing.

Step3: Recall mode concept

The mode is the most frequently occurring value. Since the new value ($36$) does not change the most frequently occurring value in the original data set (assuming the original mode was $36$ or another value that is not affected by adding a single $36$), the mode remains unchanged.

Answer:

c) mean and median decrease, mode is unchanged