Question

Find the 5 number summary for the data shownx1.48.39.31212.313.423.925.3

Answer 1

We need to find the minimum, first quartile, median, third quartile, and the maximum of the given data:

`\mleft\{1.4,8.3,9.3,12,12.3,13.4,23.9,25.3\mright\}`

Since the data is already presented in ascending order, we can see that:

`\begin{gathered} \text{minimum }=1.4 \\ \\ \text{maximum }=25.3 \end{gathered}`

Now, the median is the central value of the data set when the number of data is odd.

And, for an even number of data, the median is the mean of the two central values.

In this problem, there are 8 values, so the median is given by:

The first quartile Q1 is the median of the first half of the data. And the third quartile Q3 is the median of the second half of the data. So, we have:

`Q1=(8.3+9.3)/(2)=(17.6)/(2)=8.8`
`Q3=(13.4+23.9)/(2)=(37.3)/(2)=18.65`

Therefore, the 5 number summary for the given data is:

`\begin{gathered} \text{minimum: }1.4 \\ \\ Q1\colon8.8 \\ \\ \text{Median: }12.15 \\ \\ Q3\colon18.65 \\ \\ \text{Maximum: }25.3 \end{gathered}`