Question

The numbers trading cards owned by 10 middle-school students are given below.(NOTE THAT THESE ARE ALREADY ORDERED FROM LEAST TO GREATEST)Suppose that the number 355 from the list changes to 415. Answer the following.

Answer 1

(a) It increases by 8

(b) It stays the same

Step-by-step explanation:

First, we need to calculate the mean and median of the original data. This data is

335, 393, 425, 453, 489, 542, 556, 563, 623, 661

Then, the mean is the sum of all the values divided by the number of values, so

`\begin{gathered} \text{ mean = }(335+393+425+453+489+542+556+563+623+661)/(10) \\ \\ \text{ mean = }(5040)/(10) \\ \\ \text{ mean=504} \end{gathered}`

The median is the value that divides the set into two sets of equal sizes. In this case, these numbers are 489 and 542 because there are 4 numbers before 489 and 4 numbers after 542

335, 393, 425, 453, 489, 542, 556, 563, 623, 661

Then, the median is

`\begin{gathered} \text{ median = }(489+542)/(2) \\ \\ \text{ median=}(1031)/(2) \\ \\ \text{ median=515.5} \end{gathered}`

Now, we need to calculate the mean and median when 335 is changed to 415. So, the new data set is

393, 415, 425, 453, 489, 542, 556, 563, 623, 661

Then, the mean is

`\begin{gathered} \text{ mean = }(393+415+425+453+489+542+556+563+623+661)/(10) \\ \\ \text{ mean =}(5120)/(10) \\ \\ \text{ mean = 512} \end{gathered}`

And the median is 515.5 because the numbers in the middle are the 489 and 542

393, 415, 425, 453, 489, 542, 556, 563, 623, 661

Therefore, we can say that:

The mean increased by 8 because 512 - 504 = 8

The median stays the same

So, the answers are

(a) It increases by 8

(b) It stays the same