Statistics Worksheets - Free Printable

Let’s go step by step to solve this problem. We’re working with two sets of numbers: Set A and Set B.

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Set A (sorted):
4, 10, 12, 13, 14, 18, 20 → 7 numbers

Set B (sorted):
2, 7, 7, 9, 10, 15, 20, 23 → 8 numbers

We need to find:

1. Mean (Average)
2. Median
3. Range
4. Quartiles (Q1, Q2, Q3)
5. Interquartile Range (IQR)
6. Mean Absolute Deviation (MAD)

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1. Mean (Average)

Set A:
Add all numbers:
4 + 10 + 12 + 13 + 14 + 18 + 20 = let’s add step by step:
4+10=14; 14+12=26; 26+13=39; 39+14=53; 53+18=71; 71+20=91
Divide by 7: 91 ÷ 7 = 13

✔ Set A mean = 13

Set B:
Add all numbers:
2 + 7 + 7 + 9 + 10 + 15 + 20 + 23
Step by step:
2+7=9; 9+7=16; 16+9=25; 25+10=35; 35+15=50; 50+20=70; 70+23=93
Divide by 8: 93 ÷ 8 = 11.625, but the sheet says 11.6 — probably rounded to one decimal place.

Wait — let me check: 93 ÷ 8 = 11.625 → if we round to one decimal, it’s 11.6? Actually, 11.625 rounds to 11.6 only if we truncate, but standard rounding would be 11.6 (since 2 < 5). Wait — no: 11.625 → look at hundredths digit is 2, so yes, rounds to 11.6? Actually, no — 11.625 to one decimal: look at second decimal (2), which is less than 5, so it stays 11.6. But actually, 11.625 is exactly halfway between 11.6 and 11.7? No — 11.625 is closer to 11.6? Let me calculate again.

Actually, 8 × 11.6 = 92.8 → 93 - 92.8 = 0.2 → so 11.6 is a bit low.
But in the original sheet, they wrote 11.6 — maybe they used 11.6 as an approximation. For accuracy, we’ll use 11.625, but since the sheet uses 11.6, we’ll follow that for consistency.

Wait — looking back at the image, under “Mean” for Set B, it says:
“93 ÷ 8 = 11.6” — that’s incorrect mathematically. 93 ÷ 8 = 11.625. But perhaps they meant to write 11.6 as a rounded value? Or maybe it’s a typo? In the MAD section, they use 11.6 consistently.

To match the worksheet, we’ll use 11.6 as given, even though it’s slightly inaccurate. Maybe they expect us to use 11.6 for calculations.

So:

✔ Set B mean = 11.6 (as per worksheet)

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2. Median

Set A: 7 numbers → middle is 4th number:
Positions: 1:4, 2:10, 3:12, 4:13, 5:14, 6:18, 7:20 → median = 13

✔ Set A median = 13

Set B: 8 numbers → average of 4th and 5th:
Sorted: 2, 7, 7, 9, 10, 15, 20, 23
4th = 9, 5th = 10 → (9 + 10) ÷ 2 = 19 ÷ 2 = 9.5

✔ Set B median = 9.5

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3. Range

Set A: largest - smallest = 20 - 4 = 16

✔ Set A range = 16

Set B: 23 - 2 = 21

✔ Set B range = 21

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4. Quartiles

Split into quarters.

Set A (7 numbers):
We can think of positions:
Lower half: first 3 numbers → 4, 10, 12 → Q1 = middle of these = 10
Upper half: last 3 numbers → 14, 18, 20 → Q3 = middle = 18
Q2 = median = 13

✔ Set A: Q1=10, Q2=13, Q3=18

Set B (8 numbers):
Split into two halves:
First half: 2, 7, 7, 9 → Q1 = average of 2nd and 3rd = (7 + 7)/2 = 7
Second half: 10, 15, 20, 23 → Q3 = average of 2nd and 3rd in this half = (15 + 20)/2 = 35/2 = 17.5
Q2 = median = 9.5

✔ Set B: Q1=7, Q2=9.5, Q3=17.5

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5. Interquartile Range (IQR)

IQR = Q3 - Q1

Set A: 18 - 10 = 8

✔ Set A IQR = 8

Set B: 17.5 - 7 = 10.5

✔ Set B IQR = 10.5

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6. Mean Absolute Deviation (MAD)

This is the average distance from each number to the mean.

Set A (mean = 13):

Numbers: 4, 10, 12, 13, 14, 18, 20

Distances from 13:
- |4 - 13| = 9
- |10 - 13| = 3
- |12 - 13| = 1
- |13 - 13| = 0
- |14 - 13| = 1
- |18 - 13| = 5
- |20 - 13| = 7

Sum of distances: 9 + 3 + 1 + 0 + 1 + 5 + 7 = let’s add:
9+3=12; 12+1=13; 13+0=13; 13+1=14; 14+5=19; 19+7=26

Average: 26 ÷ 7 ≈ 3.714... → worksheet says 3.7 → rounded to one decimal.

✔ Set A MAD = 3.7

Set B (mean = 11.6):

Numbers: 2, 7, 7, 9, 10, 15, 20, 23

Distances from 11.6:
- |2 - 11.6| = 9.6
- |7 - 11.6| = 4.6
- |7 - 11.6| = 4.6
- |9 - 11.6| = 2.6
- |10 - 11.6| = 1.6
- |15 - 11.6| = 3.4
- |20 - 11.6| = 8.4
- |23 - 11.6| = 11.4

Sum: 9.6 + 4.6 + 4.6 + 2.6 + 1.6 + 3.4 + 8.4 + 11.4

Let’s add step by step:

Start with 9.6 + 4.6 = 14.2
14.2 + 4.6 = 18.8
18.8 + 2.6 = 21.4
21.4 + 1.6 = 23.0
23.0 + 3.4 = 26.4
26.4 + 8.4 = 34.8
34.8 + 11.4 = 46.2

Average: 46.2 ÷ 8 = 5.775 → worksheet says 5.8 → rounded to one decimal.

✔ Set B MAD = 5.8

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All values match the worksheet except possibly the mean of Set B (should be 11.625, but they used 11.6). Since the worksheet uses 11.6 throughout, we accept that for consistency.

Final Answer:

Set A:
- Mean: 13
- Median: 13
- Range: 16
- Q1: 10, Q2: 13, Q3: 18
- IQR: 8
- MAD: 3.7

Set B:
- Mean: 11.6
- Median: 9.5
- Range: 21
- Q1: 7, Q2: 9.5, Q3: 17.5
- IQR: 10.5
- MAD: 5.8