Question

the numbers of trading cards owned by 9 middle - school students are given below. (note that these are already ordered from least to greatest.) 318, 473, 478, 483, 501, 514, 613, 632, 668 send data to calculator suppose that the number 668 from this list changes to 767. 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.

Explanation:

Step1: Analyze the Mean

The mean is the sum of all values divided by the number of values. Originally, the sum includes 668. After changing to 767, the new sum is original sum - 668 + 767 = original sum + 99. There are 9 values, so the mean increases by $\frac{99}{9} = 11$. So the mean increases by 11.

Step2: Analyze the Median

The median of 9 ordered values is the 5th value. The original data is ordered: 318, 473, 478, 483, 501, 514, 613, 632, 668. The 5th value is 501. After changing 668 to 767, the ordered data becomes: 318, 473, 478, 483, 501, 514, 613, 632, 767. The 5th value is still 501. So the median stays the same.

Answer:

(a) It increases by 11.
(b) It stays the same.