Question

the stemplot below displays the times, in seconds, for 25 students to run 100 meters. which of the following is the correct five - number summary? 100 - meter times (sec) 2|2 3 3 4 4 4 2|5 5 5 5 6 6 6 6 6 7 7 7 8 8 8 8 9 9 3|0 key: 1|6 = 16 seconds taken to run 100 meters

Explanation:

Step1: Find the minimum value

The minimum value in the stemplot is 22.

Step2: Find the first - quartile ($Q_1$)

There are $n = 25$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{25+1}{4}=6.5$. The 6th and 7th ordered data values are 24 and 25. So, $Q_1=\frac{24 + 25}{2}=24.5$.

Step3: Find the median

The position of the median for $n = 25$ data points is $\frac{n + 1}{2}=\frac{25+1}{2}=13$th value. The 13th value is 26.

Step4: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(25 + 1)}{4}=19.5$. The 19th and 20th ordered data values are 28 and 28. So, $Q_3 = 28$.

Step5: Find the maximum value

The maximum value is 30.

Answer:

22, 24.5, 26, 28, 30