Math worksheet for finding mean, median, mode, and range of numerical data sets.

Let’s solve each problem step by step. We’ll find the mean, median, mode, and range for each data set.

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Definitions (quick reminder):

- Mean: Add all numbers, divide by how many there are.
- Median: Put numbers in order; middle number (or average of two middle if even count).
- Mode: Number that appears most often. If none repeat, say “none”.
- Range: Largest minus smallest.

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## Problem 1:
Data: 5, 3, 2, 4, 6, 2, 5

Step 1: Sort → 2, 2, 3, 4, 5, 5, 6
Count = 7 numbers

→ Mean: (2+2+3+4+5+5+6) = 27 → 27 ÷ 7 ≈ 3.857 (we’ll round to 2 decimals unless told otherwise → 3.86)
→ Median: Middle is 4th number → 4
→ Mode: 2 and 5 both appear twice → bimodal: 2 and 5 (but sometimes they want just one — check instructions. Since it says “mode(s)”, we list both)
→ Range: 6 - 2 = 4

Wait — let me double-check sum:
2+2=4; +3=7; +4=11; +5=16; +5=21; +6=27 → yes. 27/7 = 3.857... → 3.86

But maybe keep as fraction? No, decimal is fine.

Actually, let’s be precise: 27 ÷ 7 = 3.857142... → round to 3.86

Mode: 2 and 5 → write both.

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## Problem 2:
Data: 24, 12, 10, 15, 12, 19, 21

Sort: 10, 12, 12, 15, 19, 21, 24
Count = 7

→ Mean: 10+12+12+15+19+21+24 = let’s add:
10+12=22; +12=34; +15=49; +19=68; +21=89; +24=113 → 113 ÷ 7 ≈ 16.14

→ Median: 4th number → 15

→ Mode: 12 appears twice → 12

→ Range: 24 - 10 = 14

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## Problem 3:
Data: 14, 9, 20, 17, 13

Sort: 9, 13, 14, 17, 20
Count = 5

→ Mean: 9+13=22; +14=36; +17=53; +20=73 → 73 ÷ 5 = 14.6

→ Median: middle (3rd) → 14

→ Mode: no repeats → none

→ Range: 20 - 9 = 11

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## Problem 4:
Data: 21, 15, 16, 23, 18

Sort: 15, 16, 18, 21, 23
Count = 5

→ Mean: 15+16=31; +18=49; +21=70; +23=93 → 93 ÷ 5 = 18.6

→ Median: 3rd → 18

→ Mode: none → none

→ Range: 23 - 15 = 8

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## Problem 5:
Data: 20, 17, 10, 31, 25, 18, 12

Sort: 10, 12, 17, 18, 20, 25, 31
Count = 7

→ Mean: 10+12=22; +17=39; +18=57; +20=77; +25=102; +31=133 → 133 ÷ 7 = 19

→ Median: 4th → 18

→ Mode: none → none

→ Range: 31 - 10 = 21

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## Problem 6:
Data: 48, 40, 53, 43, 52, 46

Sort: 40, 43, 46, 48, 52, 53
Count = 6 (even)

→ Mean: 40+43=83; +46=129; +48=177; +52=229; +53=282 → 282 ÷ 6 = 47

→ Median: average of 3rd and 4th → (46 + 48)/2 = 47

→ Mode: none → none

→ Range: 53 - 40 = 13

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## Problem 7:
Data: 9, 15, 28, 10, 8

Sort: 8, 9, 10, 15, 28
Count = 5

→ Mean: 8+9=17; +10=27; +15=42; +28=70 → 70 ÷ 5 = 14

→ Median: 3rd → 10

→ Mode: none → none

→ Range: 28 - 8 = 20

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## Problem 8:
Data: 32, 33, 22, 85, 58

Sort: 22, 32, 33, 58, 85
Count = 5

→ Mean: 22+32=54; +33=87; +58=145; +85=230 → 230 ÷ 5 = 46

→ Median: 3rd → 33

→ Mode: none → none

→ Range: 85 - 22 = 63

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## Problem 9:
Data: 24, 35, 18, 20, 17, 30

Sort: 17, 18, 20, 24, 30, 35
Count = 6 (even)

→ Mean: 17+18=35; +20=55; +24=79; +30=109; +35=144 → 144 ÷ 6 = 24

→ Median: average of 3rd and 4th → (20 + 24)/2 = 22

→ Mode: none → none

→ Range: 35 - 17 = 18

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## Problem 10:
Data: 116, 130, 120, 125, 143, 129

Sort: 116, 120, 125, 129, 130, 143
Count = 6 (even)

→ Mean: 116+120=236; +125=361; +129=490; +130=620; +143=763 → 763 ÷ 6 ≈ 127.17

Check: 6 × 127 = 762 → so 763 ÷ 6 = 127.166... → 127.17

→ Median: average of 3rd and 4th → (125 + 129)/2 = 127

→ Mode: none → none

→ Range: 143 - 116 = 27

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Now, let’s compile final answers clearly.

Note: For mode, if multiple modes exist, list them. If none, write "none".

Also, for mean, I rounded to 2 decimal places where needed. Some problems had whole numbers.

Let me verify Problem 1 again — mode: 2 and 5 both appear twice. So bimodal. The worksheet says “mode(s)” — plural allowed. So we list both.

Similarly, others have single or none.

Final Answers:

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Final Answer:
1) mean: 3.86, median: 4, mode: 2 and 5, range: 4
2) mean: 16.14, median: 15, mode: 12, range: 14
3) mean: 14.6, median: 14, mode: none, range: 11
4) mean: 18.6, median: 18, mode: none, range: 8
5) mean: 19, median: 18, mode: none, range: 21
6) mean: 47, median: 47, mode: none, range: 13
7) mean: 14, median: 10, mode: none, range: 20
8) mean: 46, median: 33, mode: none, range: 63
9) mean: 24, median: 22, mode: none, range: 18
10) mean: 127.17, median: 127, mode: none, range: 27