Worksheet with answers for creating box plots from data sets on books read and basketball points scored.

Let’s go step by step to verify and solve both problems correctly.

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Problem 1: Books Read by Students

Data given (unordered):
13, 12, 9, 11, 10, 12, 8, 15, 9, 10, 7, 5

Step 1: Order the data from smallest to largest.

Ordered:
5, 7, 8, 9, 9, 10, 10, 11, 12, 12, 13, 15 → ✔ Correct as shown.

There are 12 numbers.

Step 2: Find Minimum and Maximum.

Min = 5
Max = 15 → ✔ Correct.

Step 3: Find Median.

Since there are 12 numbers (even), median is average of 6th and 7th values.

6th value = 10
7th value = 10
Median = (10 + 10) / 2 = 10 → ✔ Correct.

Step 4: Find 1st Quartile (Q1).

Q1 is the median of the first half of the data.

First half (first 6 numbers): 5, 7, 8, 9, 9, 10

Median of these 6: average of 3rd and 4th → (8 + 9)/2 = 8.5 → ✔ Correct.

Step 5: Find 3rd Quartile (Q3).

Q3 is the median of the second half of the data.

Second half (last 6 numbers): 10, 11, 12, 12, 13, 15

Median of these 6: average of 3rd and 4th in this half → which are 12 and 12 → (12+12)/2 = 12 → ✔ Correct.

Step 6: Range = Max - Min = 15 - 5 = 10 → ✔ Correct.

Step 7: Interquartile Range (IQR) = Q3 - Q1 = 12 - 8.5 = 3.5 → ✔ Correct.

Box plot should have:
- Left whisker at 5
- Box starts at 8.5
- Line inside box at 10
- Box ends at 12
- Right whisker at 15

→ All matches the provided answer.

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Problem 2: Points Scored by Basketball Players

Data given (unordered):
23, 18, 20, 27, 22, 15, 29, 21, 22

Wait — let’s count: that’s 9 numbers? But in the “Ordered” row, they show 10 numbers:

Ordered: 15, 18, 20, 21, 22, 22, 23, 27, 29 → That’s only 9 numbers listed here? Wait no — looking again:

In the table under “Points scored”, it lists:

23, 18, 20, 27, 22, 15, 29, 21, 22 → that’s 9 numbers.

But in the “Ordered” row below, it shows:

15, 18, 20, 21, 22, 22, 23, 27, 29 → still 9 numbers.

BUT — wait! In the summary table, they list:

Minimum: 15
1st quartile: 19 ← Hmm, that doesn’t match if we have 9 numbers.

Let me recount the original data carefully.

Original unordered list:
23, 18, 20, 27, 22, 15, 29, 21, 22 → that’s 9 numbers.

But in the “Ordered” row in the image, it says:

Ordered: 15, 18, 20, 21, 22, 22, 23, 27, 29 → still 9.

However, in the summary table, they say:

Minimum: 15
1st quartile: 19
Median: 22
3rd quartile: 25
Maximum: 29
Range: 14
IQR: 6

This suggests they think there are 10 numbers? Because with 9 numbers, median is the 5th, Q1 is median of first 4, Q3 is median of last 4.

Let’s check what happens if we assume there are 10 numbers.

Wait — look back at the original problem statement:

“Points scored | 23 | 18 | 20 | 27 | 22 | 15 | 29 | 21 | 22”

That’s 9 entries.

But in the “Ordered” row, they wrote:

“Ordered | 15 | 18 | 20 | 21 | 22 | 22 | 23 | 27 | 29” → still 9.

Yet their calculated Q1 is 19 and Q3 is 25 — which implies they used a different method or miscounted.

Wait — perhaps I missed one number? Let me read the image again.

Actually, looking closely at the user-uploaded image description (though I’m not describing it), the “Points scored” row has 10 columns? Let me simulate:

The table for Problem 2:

Points scored: 23, 18, 20, 27, 22, 15, 29, 21, 22 → that’s 9.

But then “Ordered”: 15, 18, 20, 21, 22, 22, 23, 27, 29 → 9.

But in the summary, they have:

Min: 15
Q1: 19
Med: 22
Q3: 25
Max: 29
Range: 14
IQR: 6

How did they get Q1=19 and Q3=25?

If there were 10 numbers, ordered:

Suppose the data was actually: 15, 18, 20, 21, 22, 22, 23, 27, 29, ??? — missing one?

Wait — perhaps the original data had 10 numbers? Let me re-express.

Looking at the “Ordered” row in the image: it says:

Ordered: 15, 18, 20, 21, 22, 22, 23, 27, 29 — but that’s 9.

Unless... maybe it's 10 numbers and I miscounted.

Wait — in the user’s text representation, it says:

"Points scored | 23 | 18 | 20 | 27 | 22 | 15 | 29 | 21 | 22"

That’s 9 values.

But in the “Ordered” row, it says:

"Ordered | 15 | 18 | 20 | 21 | 22 | 22 | 23 | 27 | 29" — also 9.

However, in the summary table, they calculate:

Q1 = 19 — which would be the average of 2nd and 3rd in the first half if n=10.

Assume n=10.

Then ordered data must be 10 numbers.

Perhaps the original data included another number? Or maybe it's a typo.

Wait — let’s look at the box plot drawn: it goes from 15 to 29, box from ~19 to ~25, median at 22.

And they say Q1=19, Q3=25.

How do you get Q1=19 and Q3=25?

If we have 10 numbers, ordered:

Position: 1 2 3 4 5 6 7 8 9 10

Values: 15,18,20,21,22,22,23,27,29,? — need a 10th.

What if the 10th number is 22? Then ordered: 15,18,20,21,22,22,22,23,27,29

Then:

Min=15, Max=29

Median = avg of 5th and 6th = (22+22)/2 = 22 → matches.

Q1 = median of first 5: positions 1-5: 15,18,20,21,22 → median is 20 → not 19.

Not matching.

What if the 10th number is 19? Ordered: 15,18,19,20,21,22,22,23,27,29

Then:

Min=15, Max=29

Median = (21+22)/2 = 21.5 — not 22.

No.

What if the data is: 15,18,20,21,22,22,23,25,27,29 — but 25 isn't in original.

Alternatively, perhaps they used a different method for quartiles.

Some methods use:

For Q1: position = (n+1)*0.25

For n=9: (9+1)*0.25 = 2.5 → average of 2nd and 3rd: (18+20)/2 = 19 → ah!

Similarly, Q3: (9+1)*0.75 = 7.5 → average of 7th and 8th: (23+27)/2 = 25

Yes! So they are using the (n+1) method for quartiles.

Let’s verify:

Data ordered: 15, 18, 20, 21, 22, 22, 23, 27, 29 → 9 numbers.

Using (n+1) method:

Q1 position = (9+1)*0.25 = 2.5 → between 2nd and 3rd: 18 and 20 → (18+20)/2 = 19 → ✔

Median position = (9+1)*0.5 = 5 → 5th value = 22 → ✔

Q3 position = (9+1)*0.75 = 7.5 → between 7th and 8th: 23 and 27 → (23+27)/2 = 25 → ✔

Min=15, Max=29

Range=29-15=14 → ✔

IQR=25-19=6 → ✔

Perfect.

So even though the data has 9 numbers, they used the (n+1) interpolation method for quartiles, which is valid.

Now, box plot:

Left whisker: 15

Box starts at Q1=19

Line at median=22

Box ends at Q3=25

Right whisker at 29

Matches the drawing.

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All calculations are correct as per the methods used.

Final Answer: The answers provided in the worksheet are correct for both problems. For Problem 1: Min=5, Q1=8.5, Med=10, Q3=12, Max=15, Range=10, IQR=3.5. For Problem 2: Min=15, Q1=19, Med=22, Q3=25, Max=29, Range=14, IQR=6.