Question

Which of the following best describes the change in the median when 1213 is included in the data set below? 34, 75, 26, 81, 65, 38, 49 A. It does not change. B. It increases by 8. O C. It increases by 12. O D. It decreases by 8. SUBT

Answer 1

Given:

The given data:

`34,\text{ 75, 26, 81, 65, 38, 49}`

Solution

The median of the original data would have to be obtained to know the change when a new value is added:

First, we re-arrange the given data:

`26,\text{ 34, 38, 49, 65, 75, 81}`

The median is the value in the middle of the dataset.

`\text{Median = 49}`

When 1213 is added to the original dataset, we have the new dataset below:

`26,\text{ 34, 38, 49, 65, 75, 81, 1213}`

The new median is the average of the two values at the center:

`\begin{gathered} \text{Median = }\frac{49\text{ + 65}}{2} \\ =\text{ 57} \end{gathered}`

The change is the difference between the new median and the original median:

`\begin{gathered} \text{Change = 57 - 49 } \\ =\text{ 8} \end{gathered}`

Answer : It increases by 8 (option B)