Box Plot Worksheets - Free Printable

Let’s solve each part step by step, carefully reading the box plots and using what we know about them.

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Problem 1: Rainfall Box Plot

The box plot shows annual rainfall in inches across U.S. states.

From the number line:
- Left whisker ends at 16 (minimum)
- Left edge of box is at 24 → Q1 (first quartile)
- Line inside box is at 30 → median
- Right edge of box is at 41 → Q3 (third quartile)
- Right whisker ends at 59 (maximum)

Now answer each question:

a) Median = middle value → 30 inches

b) Highest rainfall = maximum → 59 inches

c) Skewness: The right whisker (from 41 to 59) is longer than the left whisker (from 16 to 24). Also, the median is closer to Q1 than Q3. That means data is stretched out on the right → skewed to the right

d) Range = max - min = 59 - 16 = 43 inches

e) About 25% of states have rainfall less than Q1 → 24 inches

f) About 25% of states have rainfall more than Q3 → 41 inches

g) Interquartile range (IQR) = Q3 - Q1 = 41 - 24 = 17 inches

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Problem 2: Basketball Points Box Plot

Box plot for points scored by players.

From the number line:
- Left whisker ends at 41 (minimum)
- Left edge of box is at 54 → Q1
- Line inside box is at 63 → median
- Right edge of box is at 71 → Q3
- Right whisker ends at 87 (maximum)

Answer each:

a) Median = 63 points

b) Highest scoring player = maximum = 87 points

c) Range = max - min = 87 - 41 = 46 points

d) “Most of the players scored more than 65 points” — Let’s think:
Median is 63, so half scored below 63, half above.
Q3 is 71, so 25% scored between 63 and 71, and 25% above 71.
So total above 65? We don’t know exactly where 65 falls — it’s between median (63) and Q3 (71). But since 65 > 63, fewer than 50% scored above 65. So “most” (meaning >50%) did NOT score more than 65 → false

e) Skewness: Left whisker (41 to 54) is longer than right whisker (71 to 87)? Wait — actually, left side from min to Q1 is 54-41=13, right side from Q3 to max is 87-71=16. Also, median (63) is closer to Q1 (54) than to Q3 (71)? 63-54=9, 71-63=8 → almost symmetric, but slightly closer to Q3? Actually, let’s look again:
Left tail: 41 to 54 → length 13
Right tail: 71 to 87 → length 16 → longer on right
Also, box: from 54 to 71, median at 63 → 63-54=9, 71-63=8 → very close.
But overall, right whisker is longer → slight skew right? Or maybe symmetric?
Wait — standard rule: if median is near center of box and whiskers are similar, it’s symmetric. Here, median is almost centered in box (9 vs 8), and whiskers are 13 vs 16 — not too different. But technically, since right whisker is longer and median is slightly left of center, it might be slightly skewed right. However, many would call this approximately symmetric. But looking at options, we must pick one. Since the right side is a bit longer, and median is not perfectly centered, I’ll go with skewed to the right — but wait, let me double-check.

Actually, another way: if the distance from Q1 to median is less than median to Q3, it’s skewed right. Here: 63-54=9, 71-63=8 → 9>8, so actually median is closer to Q3 → that suggests skewed to the left? No — wait, confusion.

Standard:
If median is closer to Q1 → skewed right
If median is closer to Q3 → skewed left

Here: median (63) - Q1 (54) = 9
Q3 (71) - median (63) = 8
So median is closer to Q3 → that means the bulk of data is on the right, so tail is on the left → skewed to the left

Yes! Because the left side has a longer tail (min to Q1 is 13 units, while Q3 to max is 16 — wait no, 16 is bigger). Hmm.

Let me calculate distances:

Left whisker: 54 - 41 = 13
Right whisker: 87 - 71 = 16 → right whisker longer → suggests right skew

But within box:
Q1 to median: 9
Median to Q3: 8 → so median is closer to Q3 → which suggests left skew? Contradiction?

Actually, the box itself being asymmetric can override whiskers. But typically, we look at both.

In many curricula, they teach: if the median is not in the middle of the box, and the longer whisker is on the same side as the longer part of the box, then it's skewed that way.

Here, the box is almost symmetric (9 vs 8), and right whisker is longer (16 vs 13), so overall, slightly skewed to the right.

But let’s see the exact values. Perhaps it’s intended to be symmetric? Looking at the plot visually (even though we’re going by numbers), the median line is almost in the middle, and whiskers are somewhat balanced. But 16 vs 13 is noticeable.

To resolve: In most school contexts, if the median is very close to center and whiskers are similar, they say symmetric. But here, let’s check the difference.

Perhaps I made a mistake in reading the plot.

Looking back at the image description: for problem 2, the box plot has:

Min: 41
Q1: 54
Med: 63
Q3: 71
Max: 87

Now, IQR = 71-54=17
Distance from Q1 to med: 9
Med to Q3: 8 → so med is closer to Q3 → this indicates that the lower half is more spread out, so data is piled up on the right, meaning tail on left → skewed to the left

Yes, that’s correct. When the median is closer to Q3, it means the first half (below median) is more spread out, so left-skewed.

Example: if you have data like 1,2,3,4,100 — median is 3, Q1=1.5, Q3=50 — median closer to Q1? No, 3-1.5=1.5, 50-3=47 — so median closer to Q1, and it’s right-skewed.

General rule:
- If median < (Q1+Q3)/2 → skewed right
- If median > (Q1+Q3)/2 → skewed left

Here, (Q1+Q3)/2 = (54+71)/2 = 125/2 = 62.5
Median = 63 > 62.5 → so slightly skewed left.

Yes! So skewed to the left

f) IQR = Q3 - Q1 = 71 - 54 = 17 points

g) “About 75% of players scored more than 71 points” — 71 is Q3, which means 25% scored above 71, 75% scored below or equal to 71. So only 25% scored more than 71, not 75%. So statement is false

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Final Answers:

Problem 1:
a) 30
b) 59
c) skewed to the right
d) 43
e) 24
f) 41
g) 17

Problem 2:
a) 63
b) 87
c) 46
d) false
e) skewed to the left
f) 17
g) false