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The numbers of students in the 7 schools in a district are given below.(Note that these are already ordered from least to greatest.)193, 244, 252, 263, 277, 335, 389Suppose that the number 389 from this list changes to 340. Answer the following.(a)   What happens to the median? It decreases by.It increases by.It stays the same.(b)   What happens to the mean? It decreases by.It increases by.It stays the same.

Question

The numbers of students in the 7 schools in a district are given below.(Note that these are already ordered from least to greatest.)193, 244, 252, 263, 277, 335, 389Suppose that the number 389 from this list changes to 340. Answer the following.(a)   What happens to the median? It decreases by.It increases by.It stays the same.(b)   What happens to the mean? It decreases by.It increases by.It stays the same.

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Solution

(a) The median of a set of numbers is the middle number when the numbers are arranged in order. In this case, the median is the 4th number, which is 263. If the number 389 changes to 340, the median does not change because it is still the 4th number. So, the median stays the same.

(b) The mean of a set of numbers is the sum of the numbers divided by the number of numbers. The original sum of the numbers is 1953. If the number 389 changes to 340, the new sum is 1904. The original mean is 1953/7 = 279. The new mean is 1904/7 = 272. So, the mean decreases by 7.

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