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.)346, 436, 454, 465, 483, 488, 523, 532, 647Suppose that the number 647 from this list changes to 440. Answer the following.

Answer 1

The mean of a set is given by the sum of all elements, dividing by the total amount of elements. If we change the number 647 from this list to 440, the amount of elements will remain the same, but the sum of all elements will decrease, therefore, the mean will decrease. Let's calculate both means to know the difference.

Mean of the set with 647:

`\bar{x}=(346+436+454+465+483+488+523+532+647)/(9)=486`

Mean for the set with 440 instead:

`\bar{x}=(346+436+454+465+483+488+523+532+440)/(9)=463`

The difference between those means is

`486-463=23`

The mean will decrease by 23.

In a set with an odd amount of elements, the median is the middle element. The one that stays perfectly in the middle in the set is ordered in increasing order.

In our original set, the median is

`\lbrace346,436,454,465,483,488,523,532,647\rbrace`

483.

If we change 647 by 440 and reorder in increasing order, the new median will be

`\lbrace346,436,440,454,465,483,488,523,532\rbrace`

465.

Therefore, the median will decrease by 18.