Question

Choose the correct box and whiskers plot of the following data:
$2,3,8,6,4,15,18,12,22,26$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given, the sample of the data is:
$2,3,8,6,4,15,18,12,22,26$

Step 1: Order the data from smallest to largest.
$2,3,4,6,8,12,15,18,22,26$

Step 2: Find the median.
Here, we have 10 numbers (even), so we will find the middle pair of numbers, and then take the average of them.
$2,3,4,6,\text{8,12},15,18,22,26$

Median of the given numbers = average of 8 and 12
$=\frac{8+12}{2}$
$=\frac{20}{2}$
$=10$


Step 3: Find the quartiles.

The lower quartile is the median of the data points to the left of the median.
$2,3,\text{4},6,8$
Here, we have 5 numbers (odd), so the middle number is the median of the given numbers.
$\text{Lower quartile}\left(Q_1\right)=4$


The upper quartile is the median of the data points to the right of the median.
$12,15,\text{18},22,26$
$\text{Upper quartile}\left(Q_3\right)=18$

Step 4: Find the minimum and maximum.
The minimum is the smallest data point, which is 2.
The maximum is the highest data point, which is 26.

Step 5: Draw a box from $Q_1\left(4\right)$ to $Q_3\left(18\right)$ with a vertical line through the median$\left(10\right)$.

Step 6: Draw a whisker from the minimum$\left(2\right)$ to $Q_1\left(4\right)$ and from $Q_3\left(18\right)$ to the maximum$\left(26\right)$.

Hence, option (d.) is the correct choice.