Explanation:
Let’s solve each part step by step using the box plots.
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Problem 1: Annual rainfall (inches)
The box plot has:
- Left whisker ends at
15 → minimum = 15
- Left edge of box (Q1) at
25
- Middle line in box (median, Q2) at
30
- Right edge of box (Q3) at
40
- Right whisker ends at
60 → maximum = 60
Now answer each subpart:
a) Median = middle line of box =
30 inches.
b) Highest rainfall = max =
60 inches.
c) Skewness: The right whisker (from 40 to 60) is longer than the left whisker (15 to 25), and the median is closer to Q1 than Q3 → this means the data is
skewed to the right.
d) Range = max − min = 60 − 15 =
45 inches.
e) 25% of data is below Q1 =
25 inches.
f) 25% of data is above Q3 =
40 inches.
g) IQR = Q3 − Q1 = 40 − 25 =
15 inches.
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Problem 2: Points scored in basketball tournament
Box plot shows:
- Left whisker ends at
40 → min = 40
- Left edge of box (Q1) at
55
- Median (Q2) at
65
- Right edge of box (Q3) at
71
- Right whisker ends at
88 → max = 88
(We assume the rightmost point is at 88 — the tick marks go 85, 90, and the dot is just before 90, aligned with ~88.)
Now answer:
a) Median =
65 points.
b) Highest score = max =
88 points.
c) Range = 88 − 40 =
48 points.
d) “Most of the players scored more than 65 points” — median is 65, so exactly 50% scored more than 65. “Most” means >50%, so this is
false.
e) Skewness: Right whisker (71 to 88 = 17 units) is longer than left whisker (40 to 55 = 15 units), and median (65) is closer to Q1 (55) than to Q3 (71) → skewed to the
right.
f) IQR = Q3 − Q1 = 71 − 55 =
16 points.
g) About 75% scored more than 71? No — Q3 = 71 means 25% scored *more* than 71, so 75% scored *less than or equal to* 71. So statement is
false.
Double-checking all values against standard box plot interpretation — yes, consistent.
Final Answer:
1a) 30
1b) 60
1c) skewed to the right
1d) 45
1e) 25
1f) 40
1g) 15
2a) 65
2b) 88
2c) 48
2d) false
2e) skewed to the right
2f) 16
2g) false
Parent Tip: Review the logic above to help your child master the concept of box plot worksheets.
