Mean Median Mode Range Worksheets - Free Printable

Let’s solve each problem step by step.

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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 from smallest to largest:
{45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65}

→ Ordered list has 14 numbers.

Step 2: Mean = sum of all numbers ÷ count
Sum = 45+48+49+51+52+53+55+57+57+57+60+60+61+65
Let’s add:
45+48=93; +49=142; +51=193; +52=245; +53=298; +55=353; +57=410; +57=467; +57=524; +60=584; +60=644; +61=705; +65=770
Mean = 770 ÷ 14 = 55

Step 3: Median — since there are 14 numbers (even), take average of 7th and 8th numbers.
7th = 55, 8th = 57 → (55 + 57) ÷ 2 = 56

Step 4: Mode — most frequent number. 57 appears 3 times → 57

Step 5: Range = max - min = 65 - 45 = 20

✔ Problem 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}

Step 1: Order:
{110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129}

Count = 13 numbers.

Step 2: Mean = sum ÷ 13
Sum: 110+110=220; +112=332; +113=445; +113=558; +115=673; +115=788; +115=903; +121=1024; +121=1145; +123=1268; +124=1392; +129=1521
Mean = 1521 ÷ 13 = 117

Step 3: Median — 7th number in ordered list of 13 → 115

Step 4: Mode — 115 appears 3 times → 115

Step 5: Range = 129 - 110 = 19

✔ Problem 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}

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

Count = 16 numbers.

Step 2: Mean = sum ÷ 16
Sum: Let’s group positives and negatives.

Negatives: -8 + (-6) + (-5) + (-4) + (-2) + (-2) = -27
Positives: 1+4+4+5+7+7+7+12+13+15 = let’s add:
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

Step 3: Median — average of 8th and 9th numbers → 8th=4, 9th=4 → (4+4)/2 = 4

Step 4: Mode — 7 appears 3 times → 7

Step 5: Range = 15 - (-8) = 15 + 8 = 23

✔ Problem 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}

Step 1: Order:
{72, 76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91}

Count = 15 numbers.

Step 2: Mean = sum ÷ 15
Sum: 72+76=148; +77=225; +77=302; +77=379; +77=456; +79=535; +81=616; +81=697; +81=778; +83=861; +83=944; +85=1029; +87=1116; +91=1207
Mean = 1207 ÷ 15 ≈ 80.466... → Round to nearest tenth? But worksheet doesn’t specify. Since others are whole numbers, maybe keep as decimal or check if exact.

Wait — 1207 ÷ 15 = 80.466… → Actually, let me recheck sum:

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

Add carefully:

Start over:

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.

1207 ÷ 15 = 80.466... → We’ll write as 80.47 if rounding to hundredths, but perhaps the worksheet expects integer? Wait — no, decimals are fine. But looking at other problems, they’re integers. Maybe I made a mistake?

Wait — count again: 15 numbers. Sum 1207. 1207 / 15 = 80.466...

But let’s see if it’s supposed to be exact. Perhaps we leave it as fraction? No, for school level, decimal is fine. But maybe I miscounted the data?

Original data: {83, 77, 81, 79, 85, 77, 76, 72, 87, 81, 83, 77, 91, 81, 77} → that’s 15 numbers. Yes.

So Mean = 1207 ÷ 15 = 80.466... → Let’s round to one decimal: 80.5? Or keep as is? The worksheet blanks don’t specify. In previous problems, answers were integers. Maybe I should double-check addition.

Alternative way: Use calculator-style grouping.

Group same values:

72 ×1 = 72
76 ×1 = 76
77 ×4 = 308
79 ×1 = 79
81 ×3 = 243
83 ×2 = 166
85 ×1 = 85
87 ×1 = 87
91 ×1 = 91

Now sum:
72+76=148
148+308=456
456+79=535
535+243=778
778+166=944
944+85=1029
1029+87=1116
1116+91=1207 → Same.

So Mean = 1207/15 = 80.466... → For consistency with worksheet style (all other means are integers), perhaps this is meant to be rounded? Or maybe I have an error.

Wait — look back at original data: Is “91” correct? Yes. All seem right.

Perhaps accept decimal. But let’s proceed.

Actually, in many worksheets, they expect exact decimals or fractions. But here, since others are integers, maybe I missed something.

Wait — problem 5 and 6 have decimals, so it’s okay.

We’ll go with 80.47 if rounding to two decimals, but perhaps better to use exact value or one decimal.

Looking at problem 5 and 6, they have decimals in data, so mean can be decimal.

For now, I’ll compute exactly: 1207 ÷ 15 = 80.466... → Let’s write as 80.47 (rounded to nearest hundredth).

But actually, let’s see what the median and mode give us first.

Step 3: Median — 8th number in 15-number list → position 8: from ordered list:
Positions: 1:72, 2:76, 3:77, 4:77, 5:77, 6:77, 7:79, 8:81 → 81

Step 4: Mode — 77 appears 4 times, which is more than any other → 77

Step 5: Range = 91 - 72 = 19

Back to mean: 1207 ÷ 15 = 80.466... → I think we should report as 80.47 or perhaps the worksheet allows fraction? But unlikely. Maybe I miscalculated sum.

Another way: Add in pairs.

(72+91)=163
(76+87)=163
(77+85)=162
(77+83)=160
(77+83)=160
(77+81)=158
(79+81)=160
And one left: 81? Wait, 15 numbers — 7 pairs and one middle.

Better not. Accept 1207/15 = 80.466...

In educational context, often rounded to one decimal. So 80.5

But let’s check online or standard practice. Since problem 5 and 6 have tenths, we can do tenths.

I'll use 80.5 for mean.

Actually, 1207 ÷ 15 = 80.466... which rounds to 80.5 if to one decimal.

Yes.

✔ Problem 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}

Step 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}

Count = 13 numbers.

Step 2: Mean = sum ÷ 13
Sum: 0.2+0.2+0.2=0.6; +0.3=0.9; +0.4=1.3; +0.6=1.9; +0.7=2.6; +0.7=3.3; +0.9=4.2; +1.1=5.3; +1.1=6.4; +1.2=7.6; +1.5=9.1
Mean = 9.1 ÷ 13 = 0.7

Step 3: Median — 7th number → 0.7 → 0.7

Step 4: Mode — 0.2 appears 3 times → 0.2

Step 5: Range = 1.5 - 0.2 = 1.3

✔ Problem 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}

Step 1: 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}

Count = 12 numbers.

Step 2: Mean = sum ÷ 12
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

Step 3: Median — average of 6th and 7th numbers → 6th=5.4, 7th=5.6 → (5.4 + 5.6)/2 = 5.5

Step 4: Mode — 6.2 appears 3 times → 6.2

Step 5: Range = 6.4 - 4.5 = 1.9

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

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Final Answers:

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

Note: For problem 4, mean is approximately 80.47, but rounded to one decimal as 80.5 for consistency with worksheet's likely expectation.

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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