Chapter 13.1, Problem 3CYU

To determine

Which measure of central tendency would change the most

Answer to Problem 3CYU

1. Mean

Explanation of Solution

Given:

The given data is

  $53,61,46,59,61,55,49$

The store sells 83 board games on eighth day

Calculation:

Mean = Sum of all observations/Total number of observations

  $\begin{array}{l}=\frac{53+61+46+59+61+55+49}{7}\\ =\frac{384}{7}\\ =54.86\end{array}$

Median = The exact middle value of the data when arranged from least to greatest

Order the data from least to greatest: 46, 49, 53, 55, 59, 61, 61

As, the total number of observations are 7 (odd), median will be the exact middle term.

Median = 55

Mode = The most frequent value in the given data set

So, Mode = 61

Now, we will calculate the new mean, median and mode by adding the sale of the eighth day i.e. 83.

New data is: $53,61,46,59,61,55,49,83$

New Mean = $\begin{array}{l}=\frac{53+61+46+59+61+55+49+83}{8}\\ =\frac{467}{8}\\ =58.38\end{array}$

New Median:

Order the data from least to greatest: 46, 49, 53, 55, 59, 61, 61, 83

As, the total number of observations are 8 (even), median will be 4^th term + 5^thterm/2.

So, Median = 57

New Mode = 61

Therefore, we can see that the mean has changed the most.

Hence, the answer is A. Mean