the numbers of trading cards owned by 7 middle - school students are given below. (note that these are…
the numbers of trading cards owned by 7 middle - school students are given below. (note that these are already ordered from least to greatest.) 396, 434, 445, 467, 508, 515, 672 suppose that the number 396 from this list changes to 431. 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
Explanation:
Step1: Calculate original mean
The original data set is (396,434,445,467,508,515,672). The sum of the original data is (396 + 434+445 + 467+508+515+672=3437). The original mean (\bar{x}_1=\frac{3437}{7}=491).
Step2: Calculate new mean
The new data - set is (431,434,445,467,508,515,672). The sum of the new data is (431 + 434+445 + 467+508+515+672=3472). The new mean (\bar{x}_2=\frac{3472}{7}=496). The change in the mean is (496 - 491=5), so the mean increases by 5.
Step3: Analyze the median
The original data set has (n = 7) (odd - numbered) values. The median is the (\left(\frac{n + 1}{2}\right))-th value. For (n = 7), (\frac{7+1}{2}=4) - th value, which is (467). The new data set also has (n = 7) values, and the median is still the 4 - th value, which is (467). So the median stays the same.
Answer:
(a) It increases by 5. (b) It stays the same.