Question

the data set represents the number of minutes dan spent on his homework each night.
30, 35, 35, 45, 46, 46, 52, 55, 57
which box plot correctly represents the data?
four box plot options with number lines from 30 to 58, each with different box and whisker positions

Explanation:

Step1: Find minimum value

Minimum = 30

Step2: Find maximum value

Maximum = 57

Step3: Calculate median (2nd quartile)

Data set: 30, 35, 35, 45, 46, 46, 52, 55, 57
Median = 5th value = 46

Step4: Calculate 1st quartile (Q1)

Lower half: 30, 35, 35, 45
Q1 = median of lower half = $\frac{35+35}{2}=35$

Step5: Calculate 3rd quartile (Q3)

Upper half: 46, 52, 55, 57
Q3 = median of upper half = $\frac{52+55}{2}=53.5$

Answer:

The correct box plot is the one with:

• Left whisker at 30, right whisker at 57
• Left box edge (Q1) at 35, right box edge (Q3) at 53.5
• Median line at 46

(This corresponds to the first option in the image)