Question

W0 1What is the interquartile range of the data in question 51

Answer 1

For this problem, we are given the ages of 15 students in order from least to greatest. The ages are:

`6,6,6,7,8,9,9,10,11,12,12,13,14,15,18`

We need to locate the first quartile number of this data.

The first quartile is the median of the first half of the data. We can first locate the median of the whole dataset, so we can divide it in two, the median is 10 at the seventh spot, so we can divide the dataset in two halves:

`\begin{gathered} \text{ lower half}=6,6,6,7,8,9,9\\ \\ \text{ upper half}=11,12,12,13,14,15,18 \end{gathered}`

The first quartile number is the median of the lower half, so for our case, the Q1 is 7.

The third quartile number is the median of the upper half, so for our case, the Q3 is 13.

The interquartile range is the subtraction between the Q3 and Q1, so we have:

`IQR=Q3-Q1=13-7=5`

The IQR is 5.