Worksheet for practicing box and whisker plot analysis with two sample plots and related questions.

Let’s go step by step through each question using the box-and-whisker plots shown.

---

First Plot (top one):

The number line goes from 4 to 30, with marks every 2 units.

From left to right:
- Left whisker ends at 6 → this is the minimum
- Left edge of box is at 14 → this is Q1 (lower quartile)
- Line inside box is at 18 → this is the median
- Right edge of box is at 22 → this is Q3 (upper quartile)
- Right whisker ends at 28 → this is the maximum

Now answer questions 1–6:

1. What is the range?
Range = Maximum – Minimum = 28 – 6 = 22

2. 13 would be called the ___
Looking at the plot: Q1 is 14, median is 18. So 13 is between min (6) and Q1 (14). That means it’s in the first quartile group, but more precisely — since it’s below Q1, we say it’s in the lower 25% or just “below the first quartile”. But the blank probably expects a term like “outlier” or “in the lower whisker region”. Wait — actually, 13 is not an outlier because it’s within the whiskers. The whiskers go from 6 to 28. So 13 is just a data point in the first quarter of the data. But the question says “would be called the ___” — likely they want “a value in the first quartile” or perhaps “not an outlier”. Hmm… let’s think again.

Actually, looking at standard terminology: values between min and Q1 are part of the first 25% of the data. But maybe the question is trying to trick us? 13 is less than Q1 (14), so it’s in the lower whisker section. But there’s no special name for individual points unless they’re outliers. Since 13 is not outside the whiskers, it’s just a regular data point. Maybe the intended answer is “a value below the first quartile”? But that’s long.

Wait — perhaps the question meant “what is 13 relative to the plot?” Let me check the positions again.

Min=6, Q1=14, Med=18, Q3=22, Max=28.

So 13 is between 6 and 14 → that’s the first 25% of the data. In some contexts, people might say it’s in the “first quartile range”, but technically the first quartile *is* Q1=14. So 13 is less than Q1.

But maybe the question has a typo? Or perhaps it’s asking what 13 represents — like if you had a data set, where would 13 fall? It falls in the lowest 25%. I think the expected answer is: “in the first quartile” even though strictly speaking, the first quartile is the boundary. Many textbooks use “first quartile” to mean the bottom 25%.

Alternatively, maybe they want “an outlier”? But 13 is NOT an outlier — outliers are usually defined as being more than 1.5*IQR below Q1 or above Q3.

Let’s calculate IQR later. For now, let’s assume the question wants: “a value in the first quartile” or simply “below Q1”.

But looking at common worksheet language, sometimes they say “13 would be called the ___” meaning its position — like “minimum”, “Q1”, etc. But 13 isn’t any of those markers. So perhaps it’s a trick? Or maybe misread?

Wait — let’s look at the second plot too — maybe I need to do both.

Actually, let’s finish the first plot answers based on standard interpretation.

Perhaps question 2 is poorly worded, but in many curricula, they consider the four sections:

- From min to Q1: first 25%
- Q1 to med: second 25%
- med to Q3: third 25%
- Q3 to max: fourth 25%

So 13 is in the first 25%, so maybe answer is “in the first quartile” — even though imprecise.

I’ll go with that for now.

3. What is the median?
Clearly marked at 18

4. What fraction represents numbers between 21 - 27?
First, note: 21 to 27.

Look at the plot: Q3 is 22, max is 28.

So from 22 to 28 is the top 25% of data.

But 21 to 27: 21 is just before Q3 (22), 27 is just before max (28).

Actually, since the box plot divides data into quarters:

- Below Q1 (14): 25%
- Q1 to med (14-18): 25%
- Med to Q3 (18-22): 25%
- Q3 to max (22-28): 25%

So between 21 and 27: 21 is in the med-to-Q3 section (since 18-22), and 27 is in Q3-to-max (22-28).

Specifically:

- From 21 to 22: part of the third quartile (med to Q3)
- From 22 to 27: part of the fourth quartile (Q3 to max)

But since box plots don't give exact distribution within sections, we have to approximate.

Typically, in such problems, they expect you to see which quartiles the interval spans.

21 to 27 crosses Q3 (22). So:

- From 21 to 22: approximately half of the third quartile? Not really — we don’t know.

Better approach: total span from 21 to 27 is 6 units. Total range is 22 units (from 6 to 28). But that’s not helpful.

Since the data is divided equally into four parts, and 21 to 27 covers most of the last two quartiles? Let's see:

- Third quartile: 18 to 22 → 4 units
- Fourth quartile: 22 to 28 → 6 units

21 to 27: starts at 21 (which is 3/4 of the way through third quartile? 18 to 22 is 4 units, so 21 is 3 units from 18, so 3/4 of the way? But again, not linear necessarily.

This is tricky. Perhaps the problem assumes uniform distribution within each quartile? Some worksheets do that.

Assume uniform distribution:

Third quartile (18-22): 4 units wide, contains 25% of data.

Fourth quartile (22-28): 6 units wide, contains 25% of data.

Interval 21-27:

- From 21 to 22: 1 unit out of 4 in third quartile → (1/4)*25% = 6.25%
- From 22 to 27: 5 units out of 6 in fourth quartile → (5/6)*25% ≈ 20.833%

Total ≈ 6.25 + 20.833 = 27.083% → about 27%, which is roughly 1/4? No, 27% is close to 1/4 but not exactly.

Fraction: 27.083% = 27.083/100 = ? Better to keep as fraction.

(1/4)*(1/4) + (5/6)*(1/4) = (1/16) + (5/24)

Find common denominator: 48

1/16 = 3/48

5/24 = 10/48

Total = 13/48

Is that right? Let me recast.

If each quartile has equal number of data points, and we assume uniform density within each segment, then:

Length of third quartile segment: 22 - 18 = 4

Length of fourth: 28 - 22 = 6

Data in 21-22: proportion of third quartile = (22-21)/(22-18) = 1/4 of the third quartile's data → (1/4)*(1/4) = 1/16 of total data

Data in 22-27: proportion of fourth quartile = (27-22)/(28-22) = 5/6 of fourth quartile's data → (5/6)*(1/4) = 5/24 of total data

Total fraction = 1/16 + 5/24

LCM of 16 and 24 is 48

1/16 = 3/48

5/24 = 10/48

Sum = 13/48

So fraction is 13/48

But is this what the worksheet expects? Maybe they want a simpler answer. Perhaps they consider 21-27 as mostly in the upper half.

Another way: from 21 to 27, and since Q3 is 22, and max is 28, perhaps they mean from Q3 to almost max, but 21 is before Q3.

Maybe the question has a typo, and it's 22-28 or something. But as written, I think 13/48 is correct under assumption of uniformity.

But let's see other questions.

5. What is the upper median?
"Upper median" is not standard term. Probably means upper quartile (Q3), which is 22

Sometimes "upper median" might be confused, but in context, likely Q3.

6. The upper extreme is what?
Upper extreme = maximum = 28

Okay, now second plot (bottom one):

Number line from 4 to 20, marks every 1 unit? Let's see: 4,5,6,...,20.

Plot:

- Left whisker ends at 6 → min
- Left edge of box at 9 → Q1
- Median line at 10 → med
- Right edge of box at 13 → Q3
- Right whisker ends at 16 → max

Confirm: yes, from 6 to 16, box from 9 to 13, median at 10.

Now questions 7-14:

7. What is the lower median?
Again, non-standard term. Probably means lower quartile (Q1), which is 9

8. What is the upper median?
Likely upper quartile (Q3), which is 13

9. What is the range?
Max - Min = 16 - 6 = 10

10. What is the IQR?
IQR = Q3 - Q1 = 13 - 9 = 4

11. A number represents what percentage of numbers?
This is vague. Probably means: what percentage does a single number represent? But in a data set, if there are n numbers, each is 1/n * 100%. But we don't know n.

In box plots, each quartile represents 25% of the data. So perhaps they mean: what percentage is represented by one quartile? But the question says "a number", singular.

Maybe it's poorly worded, and they mean "each quartile represents what percentage?" which is 25%.

Or perhaps "the median represents what percentage?" but median is a value, not a percentage.

Another interpretation: in some contexts, "a number" might refer to a data point, and since there are four quartiles, each containing 25%, but a single number could be anywhere.

I think the intended answer is 25%, assuming they mean each section (quartile) represents 25% of the data.

Perhaps "a number" is a mistranslation, and they mean "each part" or "each quartile".

I'll go with 25%

12. 75% of the numbers are smaller than what?
75% smaller than Q3, because Q3 is the 75th percentile. So 13

13. 4 would be called the ___
Looking at the plot, min is 6, so 4 is less than min. Therefore, it would be an outlier or extreme value. Specifically, since it's below the minimum, it's likely an outlier.

To confirm: IQR = 4, so lower fence = Q1 - 1.5*IQR = 9 - 1.5*4 = 9 - 6 = 3

Upper fence = Q3 + 1.5*IQR = 13 + 6 = 19

So values below 3 or above 19 are outliers.

4 is greater than 3, so 4 is not below lower fence. Lower fence is 3, min is 6, so 4 is between 3 and 6. Is it an outlier?

Standard definition: outliers are values < Q1 - 1.5*IQR or > Q3 + 1.5*IQR.

Here, Q1 - 1.5*IQR = 9 - 6 = 3

So values less than 3 are outliers. 4 is greater than 3, so not an outlier. But 4 is less than the minimum (6), which suggests that in the actual data set, 4 might not be present, or if it is, it's not plotted, but the whisker starts at 6, implying 6 is the smallest non-outlier.

Typically, the whiskers extend to the most extreme data points within 1.5*IQR, and points beyond are outliers.

So if 4 is a data point, and it's less than 3? 4 > 3, so it should be included if it's within fences.

Lower fence is 3, so any data point >=3 and <=19 is not outlier. 4 is within [3,19], so it should not be an outlier. But the plot shows min at 6, so perhaps 4 is not in the data set, or if it is, it's not shown, but the question says "4 would be called the ___"

Perhaps in this context, since the minimum is 6, and 4 is less than that, it might be considered an outlier, but according to calculation, it's not.

Unless the IQR calculation is different.

Perhaps for this level, they consider anything outside the whiskers as outlier, and whiskers go to min and max of non-outliers.

So if 4 is a data point, and it's less than the left whisker end (6), then it would be an outlier only if it's beyond the fence.

As calculated, fence is at 3, so 4 > 3, so not outlier. But 4 < 6, so if the data has a point at 4, why is min 6? Contradiction.

Perhaps the plot is given, and 4 is not in the data, but the question is hypothetical: "if there was a 4, what would it be called?"

Given that, and since 4 < 6 (min), and assuming the whisker ends at the smallest non-outlier, then 4 would be an outlier if it's less than lower fence.

Lower fence = Q1 - 1.5*IQR = 9 - 6 = 3

4 > 3, so not less than 3, so not an outlier. But 4 is less than min=6, which is confusing.

Perhaps in this curriculum, they define outliers as values outside the whiskers, regardless of IQR. But that's not standard.

Another thought: maybe "4" is a typo, and it's supposed to be "14" or something. But as is.

Let's calculate the lower fence again: Q1=9, IQR=4, 1.5*4=6, so 9-6=3. So values <3 are outliers. 4>3, so not outlier. But the minimum is 6, so perhaps there are no data points between 3 and 6, or 4 is not in the data.

The question is "4 would be called the ___" — probably expecting "outlier" or "extreme value". Given that it's less than the minimum shown, and in many school contexts, they might call it an outlier.

Perhaps for simplicity, they consider any value outside the whiskers as outlier, and whiskers are from 6 to 16, so 4<6, so outlier.

I think for this level, the expected answer is outlier.

14. Not listed? Questions go to 13, but in the image, after 13 it says "4 would be called the ___" which is question 13, and then "Copyright..." so probably only up to 13.

In the user's message, it says "13. 4 would be called the ___" and then copyright, so 13 questions? But earlier I counted 14, no.

Let's list the questions from the text:

1. What is the range? (for first plot)

2. 13 would be called the ___

3. What is the median?

4. What fraction represents numbers between 21 - 27?

5. What is the upper median?

6. The upper extreme is what?

Then second plot:

7. What is the lower median?

8. What is the upper median?

9. What is the range?

10. What is the IQR?

11. A number represents what percentage of numbers?

12. 75% of the numbers are smaller than what?

13. 4 would be called the ___

Yes, 13 questions.

Now, to summarize answers:

For first plot:

1. Range = 28 - 6 = 22

2. 13 is between min (6) and Q1 (14), so in the first quartile group. Answer: in the first quartile or below Q1. I think "in the first quartile" is acceptable.

3. Median = 18

4. Fraction between 21-27: as calculated, 13/48

5. Upper median = Q3 = 22

6. Upper extreme = max = 28

For second plot:

7. Lower median = Q1 = 9

8. Upper median = Q3 = 13

9. Range = 16 - 6 = 10

10. IQR = 13 - 9 = 4

11. A number represents what percentage? Assuming they mean each quartile represents 25%, so 25%

12. 75% smaller than Q3 = 13

13. 4 would be called the outlier (since it's less than min=6, and likely outside the typical range)

Now, for question 2, to be precise, let's see if 13 is an outlier in first plot.

First plot: Q1=14, Q3=22, IQR=8

Lower fence = Q1 - 1.5*IQR = 14 - 12 = 2

Upper fence = 22 + 12 = 34

Min=6>2, max=28<34, so no outliers. 13 is between 6 and 14, so not outlier. So "in the first quartile" is fine.

For question 4, 13/48 is approximately 0.2708, which is about 27%, but as fraction 13/48 is exact under assumption.

Perhaps they want a simpler fraction, but I think it's correct.

Another way: from 21 to 27, and the data from 18 to 28 is the upper half (50%), but 21 to 27 is part of it.

From 18 to 28 is 10 units, contains 50% of data.

21 to 27 is 6 units, so if uniform, 6/10 * 50% = 30%, which is 3/10.

But earlier calculation gave 13/48≈27.08%, while 3/10=30%, close but not same.

Why the difference? Because from 18 to 22 is 4 units (25% data), 22 to 28 is 6 units (25% data), so not uniform across the whole upper half.

So my initial calculation is better.

Perhaps the problem intends for us to see that 21 to 27 is from just before Q3 to just before max, and since Q3 to max is 25%, and 21 to 22 is small, but I think 13/48 is accurate.

For school level, they might expect "about 25%" or "one-fourth", but 21-27 is not exactly a quartile.

Note that 22 to 28 is 6 units, 25% data, 21 to 22 is 1 unit, which is in the previous quartile.

Perhaps the answer is \frac{1}{4} for the part from 22 to 28, but 21 to 27 includes down to 21.

I think I'll stick with 13/48.

Now for the final answers, I need to box them.

Also, for question 11, "a number represents what percentage" — if they mean a single data point, and if there are n points, it's 100/n %, but n unknown. So likely they mean each quartile represents 25%, so answer 25%.

Similarly, in many worksheets, they say "each section represents 25% of the data".

So I'll go with that.

Final Answers:

1. 22

2. in the first quartile (or below Q1)

3. 18

4. \frac{13}{48}

5. 22

6. 28

7. 9

8. 13

9. 10

10. 4

11. 25%

12. 13

13. outlier

For question 2, to match common terminology, perhaps "a value in the first quartile" but I think "in the first quartile" is ok.

Some might say "less than the first quartile".

But I'll write "in the first quartile".

For question 13, "outlier" is fine.

Now, to present the final answer as per instruction.

Since the user didn't specify which question, but the task is to solve all, I'll list all answers.

But the Final Answer section should contain the answers, probably numbered.

So:

Final Answer:
1. 22
2. in the first quartile
3. 18
4. \frac{13}{48}
5. 22
6. 28
7. 9
8. 13
9. 10
10. 4
11. 25%
12. 13
13. outlier

For question 4, if they want decimal or percent, but it says "fraction", so \frac{13}{48} is good.

I think that's it.