Question

1. a survey was conducted on the ages of teachers at a large local high school. here is the data: 2|2 3 3 4 4 4 2|5 5 5 6 6 6 7 7 8 8 9 9 9 3|0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 3 4 4 4 3|5 5 6 7 7 8 8 9 9 9 4|0 0 0 0 0 1 2 2 2 2 2 3 4 4 4|6 8 5|0 0 1 1 1 1 1 2 2 2 3 4 5|5 5 5 5 6 7 8 8 9 9 6|0 6|7 which of the following boxplots is a correct representation of the same distribution? (a) (b) (c) (d) (e)

Explanation:

Step1: Find the minimum value

The minimum value in the data - set from the stem - and - leaf plot is 22.

Step2: Find the first quartile ($Q_1$)

First, find the position of $Q_1$. Since $n$ (the number of data points) is 50. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{50+1}{4}=12.75$. The 12th and 13th ordered data points are 35 and 35, so $Q_1 = 35$.

Step3: Find the median ($Q_2$)

The position of the median for $n = 50$ (an even number of data points) is $\frac{n}{2}=25$ and $\frac{n}{2}+1 = 26$. The 25th and 26th ordered data points are 41 and 41, so $Q_2=41$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(50 + 1)}{4}=38.25$. The 38th and 39th ordered data points are 49 and 49, so $Q_3 = 49$.

Step5: Find the maximum value

The maximum value in the data - set from the stem - and - leaf plot is 67.

Now, check each box - plot:

• Option A: The minimum value is not 22, so it is incorrect.
• Option B: The minimum value is not 22, so it is incorrect.
• Option C: The median value is not 41, so it is incorrect.
• Option D: The minimum value is 22, $Q_1\approx35$, $Q_2 = 41$, $Q_3\approx49$, and the maximum value is 67, which is correct.
• Option E: The median value is not 41, so it is incorrect.

Answer:

D.