Mean Median Mode Range 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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Problem 1:

Data: {61, 57, 49, 60, 45, 51, 57, 60, 53, 57, 55, 48, 65, 52}

Step 1: Order the data (smallest to largest)
45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65

There are 14 numbers.

Mean: Add all numbers → divide by 14
Sum = 45+48+49+51+52+53+55+57+57+57+60+60+61+65
Let’s add in groups:
(45+65)=110, (48+61)=109, (49+60)=109, (51+60)=111, (52+57)=109, (53+57)=110, (55+57)=112
Wait — better to just add sequentially:

45 + 48 = 93
93 + 49 = 142
142 + 51 = 193
193 + 52 = 245
245 + 53 = 298
298 + 55 = 353
353 + 57 = 410
410 + 57 = 467
467 + 57 = 524
524 + 60 = 584
584 + 60 = 644
644 + 61 = 705
705 + 65 = 770

Mean = 770 ÷ 14 = 55

Median: Since there are 14 numbers (even), median is average of 7th and 8th numbers.
Ordered list:
1:45, 2:48, 3:49, 4:51, 5:52, 6:53, 7:55, 8:57, 9:57, 10:57, 11:60, 12:60, 13:61, 14:65
7th = 55, 8th = 57 → Median = (55 + 57) ÷ 2 = 56

Mode: Most frequent number → 57 appears 3 times → 57

Range: Max - Min = 65 - 45 = 20

✔ Final for #1: Mean=55, Median=56, Mode=57, Range=20

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Problem 2:

Data: {129, 113, 110, 123, 112, 115, 110, 124, 121, 113, 115, 121, 115}

Order them:
110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129 → 13 numbers

Sum: Let’s add:

110+110=220
220+112=332
332+113=445
445+113=558
558+115=673
673+115=788
788+115=903
903+121=1024
1024+121=1145
1145+123=1268
1268+124=1392
1392+129=1521

Mean = 1521 ÷ 13 = 117

Median: 13 numbers → middle is 7th number → 115

Mode: 115 appears 3 times → most frequent → 115

Range: 129 - 110 = 19

✔ Final for #2: Mean=117, Median=115, Mode=115, Range=19

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Problem 3:

Data: {-4, 7, 4, -8, 13, 4, -2, -5, 7, -6, 5, 15, -2, 1, 12, 7}

Order them:
-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15 → 16 numbers

Sum: Let’s group positives and negatives.

Negatives: -8, -6, -5, -4, -2, -2 → sum = -8-6=-14; -14-5=-19; -19-4=-23; -23-2=-25; -25-2=-27

Positives: 1,4,4,5,7,7,7,12,13,15 →
1+4=5; +4=9; +5=14; +7=21; +7=28; +7=35; +12=47; +13=60; +15=75

Total sum = 75 + (-27) = 48

Mean = 48 ÷ 16 = 3

Median: 16 numbers → average of 8th and 9th
Ordered:
1:-8, 2:-6, 3:-5, 4:-4, 5:-2, 6:-2, 7:1, 8:4, 9:4, 10:5, 11:7, 12:7, 13:7, 14:12, 15:13, 16:15
8th=4, 9th=4 → Median = (4+4)/2 = 4

Mode: 7 appears 3 times → 7

Range: 15 - (-8) = 15 + 8 = 23

✔ Final for #3: Mean=3, Median=4, Mode=7, Range=23

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Problem 4:

Data: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77}

Order:
72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91 → 15 numbers

Sum:
72+76=148
148+77=225
225+77=302
302+77=379
379+77=456
456+79=535
535+81=616
616+81=697
697+81=778
778+83=861
861+83=944
944+85=1029
1029+87=1116
1116+91=1207

Mean = 1207 ÷ 15 ≈ 80.466... → let’s keep as fraction or decimal? Usually round to nearest tenth if needed. But since it's exact division? 1207 ÷ 15 = 80.466... → we can write as 80.5 if rounding, but let’s check: 15 × 80 = 1200, remainder 7 → so 80 and 7/15 → approximately 80.5

But maybe they want exact? In school worksheets, often rounded to one decimal. Let’s do 80.5

Actually, let me recalculate sum to be sure:

List: 72,76,77,77,77,77,79,81,81,81,83,83,85,87,91

Add again:

Start with 72+76=148
Then four 77s: 77×4=308 → 148+308=456
Then 79 → 456+79=535
Three 81s: 81×3=243 → 535+243=778
Two 83s: 83×2=166 → 778+166=944
Then 85,87,91: 85+87=172; 172+91=263 → 944+263=1207 → correct.

1207 ÷ 15 = 80.466... → typically rounded to 80.5

Median: 15 numbers → 8th number → ordered list position 8:
1:72, 2:76, 3:77, 4:77, 5:77, 6:77, 7:79, 8:81 → 81

Mode: 77 appears 4 times → 77

Range: 91 - 72 = 19

✔ Final for #4: Mean≈80.5, Median=81, Mode=77, Range=19

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Problem 5:

Data: {0.7, 0.2, 0.9, 1.2, 1.5, 0.4, 0.6, 0.2, 1.1, 0.3, 0.7, 0.2, 1.1}

Order:
0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5 → 13 numbers

Sum:
0.2×3 = 0.6
0.3 + 0.4 + 0.6 = 1.3
0.7×2 = 1.4
0.9
1.1×2 = 2.2
1.2 + 1.5 = 2.7

Now total: 0.6 + 1.3 = 1.9; +1.4=3.3; +0.9=4.2; +2.2=6.4; +2.7=9.1

Mean = 9.1 ÷ 13 = 0.7

Median: 13 numbers → 7th number → ordered:
1:0.2, 2:0.2, 3:0.2, 4:0.3, 5:0.4, 6:0.6, 7:0.7 → 0.7

Mode: 0.2 appears 3 times → 0.2

Range: 1.5 - 0.2 = 1.3

✔ Final for #5: Mean=0.7, Median=0.7, Mode=0.2, Range=1.3

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Problem 6:

Data: {6.2, 5.6, 4.9, 5.1, 6.2, 5.7, 5.1, 4.7, 5.4, 6.2, 4.5, 6.4}

Order:
4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4 → 12 numbers

Sum:
4.5 + 4.7 = 9.2
+4.9 = 14.1
+5.1 = 19.2
+5.1 = 24.3
+5.4 = 29.7
+5.6 = 35.3
+5.7 = 41.0
+6.2 = 47.2
+6.2 = 53.4
+6.2 = 59.6
+6.4 = 66.0

Mean = 66.0 ÷ 12 = 5.5

Median: 12 numbers → average of 6th and 7th
Ordered:
1:4.5, 2:4.7, 3:4.9, 4:5.1, 5:5.1, 6:5.4, 7:5.6, 8:5.7, 9:6.2, 10:6.2, 11:6.2, 12:6.4
6th=5.4, 7th=5.6 → Median = (5.4 + 5.6)/2 = 5.5

Mode: 6.2 appears 3 times → 6.2

Range: 6.4 - 4.5 = 1.9

✔ Final for #6: Mean=5.5, Median=5.5, Mode=6.2, Range=1.9

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Final Answer:

1) Mean = 55, Median = 56, Mode = 57, Range = 20
2) Mean = 117, Median = 115, Mode = 115, Range = 19
3) Mean = 3, Median = 4, Mode = 7, Range = 23
4) Mean = 80.5, Median = 81, Mode = 77, Range = 19
5) Mean = 0.7, Median = 0.7, Mode = 0.2, Range = 1.3
6) Mean = 5.5, Median = 5.5, Mode = 6.2, Range = 1.9