Answer:
[tex]\begin{gathered} a)\text{ Min = 7} \\ b)\text{ Q1 = 25} \\ c)\text{ Median = 47} \\ d)\text{ Q3 = 68} \\ e)\text{ Max = 100} \end{gathered}[/tex]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:
[tex]\begin{gathered} Q_1\text{ = }\frac{(n+1)}{4}th\text{ term} \\ \\ n\text{ is the number of terms which is 23} \\ \\ Q_1\text{ = }\frac{(23+1)}{4}th\text{ term = 6th term} \end{gathered}[/tex]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:
[tex]47[/tex]4) Q3
This is the third quartile or 75th percentile
We have the formula as:
[tex]\begin{gathered} Q_{3\text{ }}\text{ = }\frac{3(n+1)}{4}th\text{ term} \\ \\ n\text{ = 23} \\ Q_3\text{ = }\frac{3(24)}{4}\text{ = 18th term} \end{gathered}[/tex]The 18th term is 68
5) Max
This is the maximum or highest value, which is 100
