Question

The following data shows the scores Gina obtained on 12 IQ tests

Answer 1

To solve the exercise it is advisable to first order the data from smallest to largest. So,

`74,74,83,83,83,86,87,90,92,93,93,94`

The median is found like this

`\begin{gathered} \text{ If the number of observations (n) is even} \\ Me=\frac{x_{(n)/(2)}+x_{(n)/(2)+1}}{2} \end{gathered}`

In this case, the median will be the average of the sixth and seventh data

`\begin{gathered} Me=(x_6+x_7)/(2) \\ Me=(86+87)/(2) \\ Me=86.5 \end{gathered}`

On the other hand, in a box plot you have

In other words, the boxplot of the statement shows that the median of the data set is 88.5 and that is false because doing the calculation we get that the median of the data set 86.5.

Therefore, the correct answer is 1) Median, because it is shown incorrectly in the box plot.