Question

The numbers of students in the schools in a district are given below.

(Note that these are already ordered from least to greatest.)
168, 257, 277, 282, 335, 342, 398, 429
Suppose that the number 429 from this list changes to 341. Answer the following.
(a) What happens to the mean?

a) It decreases by
b) It increases by
c) It stays the same.

(b) What happens to the median?

a) It decreases by
b) It increases by
c) It stays the same."

Answer 1

Changing a value in a data set can affect the mean but not the median.

Step-by-step explanation:

To find the effect of changing a value in a data set on the mean and median, we need to understand the definitions of mean and median.

Mean: The mean is calculated by summing up all the values in the data set and dividing it by the total number of values. In this case, the mean is the sum of all the numbers divided by 8, the total number of students.

Median: The median is the middle value in an ordered data set. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values.

In this case, the mean will be affected by changing the value 429 to 341. Since the mean is the sum of all the numbers divided by 8, subtracting a larger number and adding a smaller number in the calculation will decrease the mean. Therefore, the mean decreases by 88.

The median, however, will not be affected by changing the value 429 to 341. Since the median is the middle value, it does not depend on the values at the extremes of the data set. Therefore, the median stays the same.