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

Step 1: Order the numbers (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), take average of 7th and 8th numbers.
Ordered list:
1:45, 2:48, 3:49, 4:51, 5:52, 6:53, 7:55, 8:57, ...
So median = (55 + 57) ÷ 2 = 56

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

Range: Max - Min = 65 - 45 = 20

✔ Problem 1 Answers:
Mean: 55, Median: 56, Mode: 57, Range: 20

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Problem 2: {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 → 115

Mode: 115 appears 3 times → 115

Range: 129 - 110 = 19

✔ Problem 2 Answers:
Mean: 117, Median: 115, Mode: 115, Range: 19

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Problem 3: {-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:
Start with negatives: -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
Add positives: 1+4=5; +4=9; +5=14; +7=21; +7=28; +7=35; +12=47; +13=60; +15=75
Total sum = -27 + 75 = 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, ...
So (4 + 4) ÷ 2 = 4

Mode: 7 appears 3 times → 7

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

✔ Problem 3 Answers:
Mean: 3, Median: 4, Mode: 7, Range: 23

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Problem 4: {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:
Group:
72+76=148
77×4 = 308 → total so far: 148+308=456
79 → 456+79=535
81×3=243 → 535+243=778
83×2=166 → 778+166=944
85+87+91 = 263 → 944+263=1207

Mean = 1207 ÷ 15 ≈ 80.466... → but let’s check if exact fraction or decimal?
Actually, 1207 ÷ 15 = 80.466... but maybe we made a mistake?

Wait — recount the numbers: original has 15 numbers? Let’s count:
{83,77,81,79,85,77,76,72,87,81,83,77,91,81,77} → yes, 15.

But 77 appears how many times? Positions: 2nd, 6th, 12th, 15th → 4 times? Wait no:
List:
1:83, 2:77, 3:81, 4:79, 5:85, 6:77, 7:76, 8:72, 9:87, 10:81, 11:83, 12:77, 13:91, 14:81, 15:77 → that’s 77 at positions 2,6,12,15 → 4 times? But earlier I said 4 sevens? In ordered list I wrote four 77s — correct.

But sum: let me recalculate carefully:

72
76 → 72+76=148
77 → 148+77=225
77 → 225+77=302
77 → 302+77=379
77 → 379+77=456
79 → 456+79=535
81 → 535+81=616
81 → 616+81=697
81 → 697+81=778
83 → 778+83=861
83 → 861+83=944
85 → 944+85=1029
87 → 1029+87=1116
91 → 1116+91=1207 → same as before.

1207 ÷ 15 = 80.466... → but perhaps it's meant to be rounded? Or did I miscount?

Wait — actually, 15 × 80 = 1200, so 1207 - 1200 = 7 → so 80 and 7/15 → which is approximately 80.47, but since this is a math worksheet, maybe they expect exact fraction or decimal? But looking at other problems, likely decimal is fine. However, let’s double-check if sum is right.

Alternative way: use calculator-style addition:

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 → correct.

So mean = 1207 / 15 = 80.466... → but perhaps write as fraction? Or maybe I should leave as decimal rounded to two places? But in context, maybe it's acceptable as 80.47? However, looking back at problem 1, we got whole numbers. Maybe I made an error in counting frequency?

Wait — mode: 77 appears 4 times? Let’s see: in original set: 77 appears at index 2,6,12,15 → yes 4 times. 81 appears at 3,10,14 → 3 times. So mode is 77.

Median: 15 numbers → 8th number in ordered list:
Ordered:
1:72, 2:76, 3:77, 4:77, 5:77, 6:77, 7:79, 8:81, 9:81, 10:81, 11:83, 12:83, 13:85, 14:87, 15:91
So 8th is 81 → median = 81

Range: 91 - 72 = 19

Mean: 1207 ÷ 15 = 80.466... → but perhaps the problem expects us to report as decimal? Or maybe I miscalculated sum?

Wait — let me add again using another method:

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

Add in pairs from outside:

72 + 91 = 163
76 + 87 = 163
77 + 85 = 162
77 + 83 = 160
77 + 83 = 160
77 + 81 = 158
79 + 81 = 160
And left with one 81? Wait no — 15 numbers, so 7 pairs and one middle.

Better: since 15 numbers, pair first and last:

Pair 1: 72+91=163
Pair 2: 76+87=163
Pair 3: 77+85=162
Pair 4: 77+83=160
Pair 5: 77+83=160
Pair 6: 77+81=158
Pair 7: 79+81=160
Left with middle: 81

Now sum pairs: 163+163=326; +162=488; +160=648; +160=808; +158=966; +160=1126; then +81=1207 → same.

So mean is indeed 1207/15 = 80.466... → but perhaps in the context of the worksheet, they might have intended different numbers? Or maybe it's okay to write as 80.47? But let's check online or think — actually, in many such worksheets, they design problems to have nice answers. Did I misread the set?

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

Count of 77: let's list indices: position 2,6,12,15 → that's four 77s. Position 3,10,14 → three 81s. Etc.

Perhaps the mean is supposed to be 80.47, but let's keep it as fraction or decimal. For now, I'll calculate exactly: 1207 ÷ 15 = 80.4666... → so 80.47 if rounded to two decimals, but since other problems had integers, maybe I made a mistake.

Wait — what if I add the numbers as given without ordering? Same thing.

Another idea: perhaps "order" means something else? No.

Maybe the set has 16 numbers? Let's count the commas: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77} — that's 15 items.

I think it's correct. So mean = 1207/15 = 80.466... → but for the sake of this, I'll write it as 80.47 or perhaps the problem allows fraction. But looking at the format, probably decimal is fine. However, let's proceed and see other problems.

Actually, upon second thought, in problem 5 and 6 there are decimals, so here it might be expected to be decimal. But 1207/15 is not nice. Perhaps I can leave it as mixed number? But I think for consistency, I'll calculate it as 80.47, but let's do exact value.

Wait — 15 * 80 = 1200, remainder 7, so 80 and 7/15, which is approximately 80.4667. But in educational contexts, sometimes they expect the exact fraction or decimal. Since the instruction doesn't specify, I'll use decimal rounded to two places: 80.47

But let's verify with actual calculation: 1207 ÷ 15 = 80.4666... so to two decimals, 80.47.

However, I recall that in some systems, they might want the exact value. But for now, I'll go with 80.47.

But wait — let's check if the sum is wrong. Let me add the numbers in the order given:

83 + 77 = 160
160 + 81 = 241
241 + 79 = 320
320 + 85 = 405
405 + 77 = 482
482 + 76 = 558
558 + 72 = 630
630 + 87 = 717
717 + 81 = 798
798 + 83 = 881
881 + 77 = 958
958 + 91 = 1049
1049 + 81 = 1130
1130 + 77 = 1207 → same.

So it's correct. Mean = 1207/15 = 80.466... → I'll write it as 80.47 for practical purposes, but perhaps the worksheet expects the fraction. However, since other answers are integers, maybe I should re-express.

Another thought: perhaps "mean" is to be reported as integer if possible, but it's not. I think it's fine.

For now, I'll note it as 80.47, but let's move on and come back.

Actually, upon checking online or standard practice, in such worksheets, if the mean is not integer, they still report it as decimal. So I'll use 80.47.

But to be precise, let's calculate: 1207 ÷ 15 = 80.4666... so if we round to nearest hundredth, it's 80.47.

Okay.

Median: 8th number is 81 → 81

Mode: 77 appears 4 times → 77

Range: 91 - 72 = 19

✔ Problem 4 Answers:
Mean: 80.47, Median: 81, Mode: 77, Range: 19

But I feel uneasy about the mean. Let me see if there's a typo in my reading. The set is: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77} — yes.

Perhaps the "order" row is for students to fill, and mean is calculated correctly. I'll proceed.

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Problem 5: {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 them:
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 add: 0.6 + 1.3 = 1.9; +1.4 = 3.3; +0.9 = 4.2; +2.2 = 6.4; +2.7 = 9.1

Sum = 9.1

Mean = 9.1 ÷ 13 = 0.7

Median: 13 numbers → 7th number:
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

✔ Problem 5 Answers:
Mean: 0.7, Median: 0.7, Mode: 0.2, Range: 1.3

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Problem 6: {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
9.2 + 4.9 = 14.1
14.1 + 5.1 = 19.2
19.2 + 5.1 = 24.3
24.3 + 5.4 = 29.7
29.7 + 5.6 = 35.3
35.3 + 5.7 = 41.0
41.0 + 6.2 = 47.2
47.2 + 6.2 = 53.4
53.4 + 6.2 = 59.6
59.6 + 6.4 = 66.0

Sum = 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, ...
So (5.4 + 5.6) ÷ 2 = 11.0 ÷ 2 = 5.5

Mode: 6.2 appears 3 times → 6.2

Range: 6.4 - 4.5 = 1.9

✔ Problem 6 Answers:
Mean: 5.5, Median: 5.5, Mode: 6.2, Range: 1.9

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Now back to Problem 4. I think I have to accept that the mean is 1207/15 = 80.466... but perhaps in the context, they might have a different expectation. Let me calculate 1207 ÷ 15 exactly: 15 * 80 = 1200, remainder 7, so 80 + 7/15 = 80 7/15 or 80.466...

Since the other problems have nice numbers, and this one doesn't, but it's possible. Perhaps I can write it as a fraction, but the worksheet likely expects decimal. I'll use 80.47 as approximation.

But to be accurate, let's see if the sum is correct by adding the numbers in a different way.

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

Add the 77s: 77*4 = 308
81*3 = 243
83*2 = 166
Then others: 72,76,79,85,87,91

Sum of others: 72+76=148; 148+79=227; 227+85=312; 312+87=399; 399+91=490

Now total: 308 (77s) + 243 (81s) = 551; +166 (83s) = 717; +490 = 1207 → same.

So mean is 1207/15 = 80.4666...

In many educational settings, they might round to one decimal place. 80.5? But 80.466 is closer to 80.5 than 80.4? 80.466 - 80.4 = 0.066, 80.5 - 80.466 = 0.034, so closer to 80.5. But typically, we round based on next digit: 80.466, the third decimal is 6>5, so round up second decimal from 6 to 7? No:

80.466 to two decimal places: look at third decimal is 6≥5, so round up the second decimal: 6 becomes 7, so 80.47.

Yes.

So I'll keep it as 80.47.

But let's confirm with the initial request: "solve accurately". So perhaps report as fraction? But the worksheet has blanks for numbers, likely decimal.

I think it's fine.

Final decision for Problem 4 mean: 80.47

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Now compile all answers.

Final Answer:

Problem 1:
Mean: 55, Median: 56, Mode: 57, Range: 20

Problem 2:
Mean: 117, Median: 115, Mode: 115, Range: 19

Problem 3:
Mean: 3, Median: 4, Mode: 7, Range: 23

Problem 4:
Mean: 80.47, Median: 81, Mode: 77, Range: 19

Problem 5:
Mean: 0.7, Median: 0.7, Mode: 0.2, Range: 1.3

Problem 6:
Mean: 5.5, Median: 5.5, Mode: 6.2, Range: 1.9

Note: For Problem 4, the mean is approximately 80.47 when rounded to two decimal places. If exact fraction is required, it is 1207/15, but given the context, decimal is appropriate.