the numbers of students in the 7 schools in a district are given below. (note that these are already ordered…

the numbers of students in the 7 schools in a district are given below. (note that these are already ordered from least to greatest.) 179, 234, 241, 255, 302, 343, 392 suppose that the number 392 from this list changes to 238. answer the following. (a) what happens to the mean? it decreases by it increases by it stays the same. (b) what happens to the median? it decreases by it increases by it stays the same.

the numbers of students in the 7 schools in a district are given below. (note that these are already ordered from least to greatest.) 179, 234, 241, 255, 302, 343, 392 suppose that the number 392 from this list changes to 238. answer the following. (a) what happens to the mean? it decreases by it increases by it stays the same. (b) what happens to the median? it decreases by it increases by it stays the same.

Answer

Answer:

(a) It decreases by 22 (b) It stays the same

Explanation:

Step1: Calculate original mean

The original sum of numbers is (179 + 234+241 + 255+302+343+392=1946). The original mean is (\frac{1946}{7}\approx278).

Step2: Calculate new mean

The new sum of numbers is (179 + 234+241 + 255+302+343+238=1792). The new mean is (\frac{1792}{7}=256). The change in mean is (278 - 256=22), so the mean decreases by 22.

Step3: Analyze the median

The original data - set has 7 numbers. The median is the 4 - th number when ordered, which is 255. After changing 392 to 238, the data - set is still ordered as (179,234,241,255,302,343,238). Re - ordering it gives (179,234,238,241,255,302,343). The median is still the 4 - th number, which is 255. So the median stays the same.