Median Worksheets - Free Printable

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

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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 “no mode”.
- Range: Biggest number minus smallest number.

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## Problem 1:
Data: 15, 23, 18, 20, 23

→ Already sorted? Let’s sort to be safe:
15, 18, 20, 23, 23

- Mean: (15 + 18 + 20 + 23 + 23) = 99 → 99 ÷ 5 = 19.8
- Median: Middle of 5 numbers → 3rd number = 20
- Mode: 23 appears twice → 23
- Range: 23 - 15 = 8

✔ Matches given answers — good!

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## Problem 2:
Data: 2, 7, 4, 2, 3, 6, 11

Sort them:
2, 2, 3, 4, 6, 7, 11

- Mean: 2+2+3+4+6+7+11 = 35 → 35 ÷ 7 = 5
- Median: 7 numbers → 4th number = 4
- Mode: 2 appears twice → 2
- Range: 11 - 2 = 9

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## Problem 3:
Data: 70, 65, 81, 82, 83

Sort:
65, 70, 81, 82, 83

- Mean: 65+70+81+82+83 = 381 → 381 ÷ 5 = 76.2
- Median: 5 numbers → 3rd = 81
- Mode: All appear once → no mode
- Range: 83 - 65 = 18

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## Problem 4:
Data: 11, 4, 7, 8, 2, 6, 4

Sort:
2, 4, 4, 6, 7, 8, 11

- Mean: 2+4+4+6+7+8+11 = 42 → 42 ÷ 7 = 6
- Median: 7 numbers → 4th = 6
- Mode: 4 appears twice → 4
- Range: 11 - 2 = 9

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## Problem 5:
Data: 22, 10, 18, 23, 37, 51, 82

Sort:
10, 18, 22, 23, 37, 51, 82

- Mean: 10+18+22+23+37+51+82 = 243 → 243 ÷ 7 ≈ 34.71 (we’ll keep as fraction or decimal? Let’s use exact: 243/7 = 34.714... but maybe round to one decimal? The sheet doesn’t specify. Since others are whole or .2, let’s do 34.7)

Wait — let me recalculate sum:

10 + 18 = 28
28 + 22 = 50
50 + 23 = 73
73 + 37 = 110
110 + 51 = 161
161 + 82 = 243 → yes.

243 ÷ 7 = 34.714... → probably write as 34.7 (one decimal place like problem 3)

But let’s check if it divides evenly? No. So we’ll go with 34.7

Actually — wait! Maybe they expect exact fraction? But looking at other problems, #3 had 76.2 which is exact. Here 243/7 is not nice. Let me double-check addition again:

10
18 → 28
22 → 50
23 → 73
37 → 110
51 → 161
82 → 243 ✔

So mean = 243 ÷ 7 = 34.714... → perhaps leave as 34.7 (rounded to tenths)

But let’s see what the pattern is. In problem 3, 381÷5=76.2 exactly. Here it’s not. Maybe we should write as mixed number? Unlikely for this level. I think 34.7 is acceptable.

Alternatively, maybe I made a mistake? Let me try adding differently:

Group: (10+82)=92, (18+51)=69, (22+37)=59, plus 23 → 92+69=161, +59=220, +23=243 ✔

Okay, so mean = 243/7 ≈ 34.7

But let’s hold off and compute others first.

- Median: 7 numbers → 4th = 23
- Mode: All unique → no mode
- Range: 82 - 10 = 72

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## Problem 6:
Data: 6, 2, 13, 7, 1, 11, 10, 6, 2

Count: 9 numbers

Sort:
1, 2, 2, 6, 6, 7, 10, 11, 13

- Mean: 1+2+2+6+6+7+10+11+13 = let’s add:

1+2=3; +2=5; +6=11; +6=17; +7=24; +10=34; +11=45; +13=58 → total 58

58 ÷ 9 ≈ 6.444... → again, not nice. Round to one decimal? 6.4

Wait — let me verify sum:

List: 1,2,2,6,6,7,10,11,13

Add pairs:
(1+13)=14
(2+11)=13
(2+10)=12
(6+7)=13
and left with 6 → wait no, that’s 9 numbers.

Better:
Start over:

1 + 2 = 3
3 + 2 = 5
5 + 6 = 11
11 + 6 = 17
17 + 7 = 24
24 + 10 = 34
34 + 11 = 45
45 + 13 = 58 ✔

58 ÷ 9 = 6.444... → 6.4 (to one decimal)

- Median: 9 numbers → 5th number = 6
- Mode: 2 and 6 both appear twice → bimodal: 2 and 6? But usually in these sheets, if multiple modes, list both? Or sometimes they say “modes” plural. But looking at format, probably list both.

Wait — the sheet says “Mode” singular. Hmm. In some curricula, if more than one, you list all. Let’s assume we list both: 2, 6

But let’s check frequency:

1: once
2: twice
6: twice
7: once
10: once
11: once
13: once

Yes, two modes.

In answer space, probably write “2 and 6” or “2, 6”

I’ll write 2, 6

- Range: 13 - 1 = 12

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## Problem 7:
Data: 105, 104, 96, 109, 104, 107, 98

Sort:
96, 98, 104, 104, 105, 107, 109

- Mean: 96+98+104+104+105+107+109

Calculate:

96+98 = 194
194+104 = 298
298+104 = 402
402+105 = 507
507+107 = 614
614+109 = 723

723 ÷ 7 = ?

7 × 103 = 721 → remainder 2 → so 103.285... → round to 103.3? Or 103.29? But previous decimals were to one place.

Wait — 723 ÷ 7:

7 × 100 = 700 → 723 - 700 = 23 → 23 ÷ 7 ≈ 3.2857 → so 103.2857 → 103.3 (to one decimal)

But let’s see if it’s exact? No.

Alternatively, maybe I miscalculated sum?

Double-check:

96
98 → 194
104 → 298
104 → 402
105 → 507
107 → 614
109 → 723 ✔

Yes.

So mean = 723/7 ≈ 103.3

- Median: 7 numbers → 4th = 104
- Mode: 104 appears twice → 104
- Range: 109 - 96 = 13

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## Problem 8:
Data: 14, 68, 38, 85, 95, 57, 65

Sort:
14, 38, 57, 65, 68, 85, 95

- Mean: 14+38+57+65+68+85+95

Add:

14+38 = 52
52+57 = 109
109+65 = 174
174+68 = 242
242+85 = 327
327+95 = 422

422 ÷ 7 = ?

7 × 60 = 420 → remainder 2 → so 60.285... → 60.3 (to one decimal)

Check sum again:

14
38 → 52
57 → 109
65 → 174
68 → 242
85 → 327
95 → 422 ✔

Yes.

- Median: 7 numbers → 4th = 65
- Mode: All unique → no mode
- Range: 95 - 14 = 81

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Now, compiling all answers neatly.

Note: For means that are repeating decimals, I rounded to one decimal place consistently, matching problem 3 (76.2).

Also, for modes with multiple values, I listed both separated by comma.

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Final Answer:

Problem 2:
Mean: 5
Median: 4
Mode: 2
Range: 9

Problem 3:
Mean: 76.2
Median: 81
Mode: no mode
Range: 18

Problem 4:
Mean: 6
Median: 6
Mode: 4
Range: 9

Problem 5:
Mean: 34.7
Median: 23
Mode: no mode
Range: 72

Problem 6:
Mean: 6.4
Median: 6
Mode: 2, 6
Range: 12

Problem 7:
Mean: 103.3
Median: 104
Mode: 104
Range: 13

Problem 8:
Mean: 60.3
Median: 65
Mode: no mode
Range: 81