Question

Here is a set of sample data781517222531323544464753545562636876798390100Identify the 5 number summary (min, Q1, median, Q3, max) , , , ,

Answer 1

`\begin{gathered} a)\text{ Min = 7} \\ b)\text{ Q1 = 25} \\ c)\text{ Median = 47} \\ d)\text{ Q3 = 68} \\ e)\text{ Max = 100} \end{gathered}`

Step-by-step explanation:

Here, we want to identify the 5-number summary

To do this, it is best that we re-arrange the sample from the minimum to the maximum number. This has already been done for us fortunately

1) Minimum

This is the smallest number. We have this as 7

2) Q1

This is the 1st quartile or 25th percentile

To get the term that fits here, we use the following formula:

`\begin{gathered} Q_1\text{ = }((n+1))/(4)th\text{ term} \\ \\ n\text{ is the number of terms which is 23} \\ \\ Q_1\text{ = }((23+1))/(4)th\text{ term = 6th term} \end{gathered}`

Thus, the 6th term is the Q1 value which is 25

3) Median

The median is the middle number. Since the number of data points is odd. The median would be the 12th term

We have that as:

`47`

4) Q3

This is the third quartile or 75th percentile

We have the formula as:

`\begin{gathered} Q_{3\text{ }}\text{ = }(3(n+1))/(4)th\text{ term} \\ \\ n\text{ = 23} \\ Q_3\text{ = }(3(24))/(4)\text{ = 18th term} \end{gathered}`

The 18th term is 68

5) Max

This is the maximum or highest value, which is 100