Question

the following are the ages of 16 physics teachers in a school district. 26, 29, 30, 33, 34, 37, 38, 39, 50, 51, 52, 53, 53, 55, 56, 57. notice that the ages are ordered from least to greatest. make a box-and-whisker plot for the data.

Explanation:

Step1: Find the minimum and maximum

The minimum value (smallest age) is 26, and the maximum value (largest age) is 57.

Step2: Find the median (Q2)

Since there are 16 data points (even number), the median is the average of the 8th and 9th values. The 8th value is 39, and the 9th value is 50. So the median $Q2 = \frac{39 + 50}{2} = 44.5$.

Step3: Find the lower quartile (Q1)

The lower half of the data is the first 8 values: 26, 29, 30, 33, 34, 37, 38, 39. The median of this lower half (Q1) is the average of the 4th and 5th values. The 4th value is 33, and the 5th value is 34. So $Q1 = \frac{33 + 34}{2} = 33.5$.

Step4: Find the upper quartile (Q3)

The upper half of the data is the last 8 values: 50, 51, 52, 53, 53, 55, 56, 57. The median of this upper half (Q3) is the average of the 4th and 5th values. The 4th value is 53, and the 5th value is 53. So $Q3 = \frac{53 + 53}{2} = 53$.

Step5: Draw the box - and - whisker plot

• The left whisker extends from the minimum (26) to Q1 (33.5).
• The box extends from Q1 (33.5) to Q3 (53), with a line inside the box at the median (44.5).
• The right whisker extends from Q3 (53) to the maximum (57).

Answer:

To draw the box - and - whisker plot:

• Mark the minimum value (26) on the number line.
• Mark Q1 (33.5) on the number line.
• Draw a box from Q1 (33.5) to Q3 (53), and draw a vertical line inside the box at the median (44.5).
• Mark Q3 (53) on the number line.
• Mark the maximum value (57) on the number line.
• Connect the minimum to Q1 with a whisker, and Q3 to the maximum with a whisker.