Mean, Median, Mode and Range Worksheets - Free Printable
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Step-by-step solution for: Mean, Median, Mode and Range Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Mean, Median, Mode and Range Worksheets
Let’s solve each problem step by step.
We are given 6 sets of numbers. For each set, we need to find:
- Mean → Add all numbers and divide by how many there are.
- Median → Put the numbers in order and pick the middle one (or average of two middle if even count).
- Mode → The number that appears most often.
- Range → Largest number minus smallest number.
---
Problem 1:
Numbers: 13, 6, 24, 18, 5, 13, 9, 48, 8, 11, 50, 28, 15, 13, 7
Step 1: Sort them → 5, 6, 7, 8, 9, 11, 13, 13, 13, 15, 18, 24, 28, 48, 50
Count = 15 numbers
→ Mean: Sum = 5+6+7+8+9+11+13+13+13+15+18+24+28+48+50 = let’s add:
Group:
(5+6+7+8+9) = 35
(11+13+13+13+15) = 65
(18+24+28+48+50) = 168
Total = 35 + 65 + 168 = 268
Mean = 268 ÷ 15 ≈ 17.87 (round to nearest hundredth? Usually keep as decimal or fraction — but since others may be whole, check context. We’ll use 2 decimals unless specified.)
Actually, let me recalculate sum carefully:
List again:
5, 6, 7, 8, 9, 11, 13, 13, 13, 15, 18, 24, 28, 48, 50
Add step by step:
Start with 0
+5=5
+6=11
+7=18
+8=26
+9=35
+11=46
+13=59
+13=72
+13=85
+15=100
+18=118
+24=142
+28=170
+48=218
+50=268 ✔
So Mean = 268 / 15 = 17.866... → Round to 2 decimal places: 17.87
→ Median: Middle of 15 numbers → 8th number → sorted list: position 8 is 13
→ Mode: 13 appears 3 times → more than any other → 13
→ Range: 50 - 5 = 45
---
Problem 2:
Numbers: 34, 16, 41, 29, 38, 81, 62, 74, 82, 32, 22, 58
Sort: 16, 22, 29, 32, 34, 38, 41, 58, 62, 74, 81, 82
Count = 12 (even)
→ Mean: Sum = 16+22+29+32+34+38+41+58+62+74+81+82
Calculate:
16+22=38
+29=67
+32=99
+34=133
+38=171
+41=212
+58=270
+62=332
+74=406
+81=487
+82=569
Sum = 569
Mean = 569 ÷ 12 ≈ 47.416... → 47.42
→ Median: Average of 6th and 7th → 6th=38, 7th=41 → (38+41)/2 = 79/2 = 39.5
→ Mode: All appear once → no mode → write “no mode” or leave blank? In school worksheets, sometimes they expect “none”. But let’s see — actually, recheck: all unique → no mode
→ Range: 82 - 16 = 66
---
Problem 3:
Numbers: 52, 18, 43, 23, 48, 29, 33, 52, 32, 33, 51, 62, 42
Sort: 18, 23, 29, 32, 33, 33, 42, 43, 48, 51, 52, 52, 62
Count = 13
→ Mean: Sum = 18+23+29+32+33+33+42+43+48+51+52+52+62
Add:
18+23=41
+29=70
+32=102
+33=135
+33=168
+42=210
+43=253
+48=301
+51=352
+52=404
+52=456
+62=518
Sum = 518
Mean = 518 ÷ 13 ≈ 39.846 → 39.85
→ Median: 7th number → sorted: positions 1 to 13 → 7th is 42
→ Mode: 33 appears twice, 52 appears twice → both occur twice → so bimodal: 33 and 52
But some worksheets might accept only one — but technically, multiple modes are allowed. Let’s note both.
→ Range: 62 - 18 = 44
---
Problem 4:
Numbers: 86, 44, 73, 87, 88, 60, 95, 89
Sort: 44, 60, 73, 84? Wait — wait, original: 86, 44, 73, 87, 88, 60, 95, 89
Sorted: 44, 60, 73, 86, 87, 88, 89, 95
Wait — did I miss a number? Original has 8 numbers.
List: 44, 60, 73, 86, 87, 88, 89, 95 → yes, 8 numbers.
→ Mean: Sum = 44+60+73+86+87+88+89+95
Add:
44+60=104
+73=177
+86=263
+87=350
+88=438
+89=527
+95=622
Sum = 622
Mean = 622 ÷ 8 = 77.75
→ Median: Even count → average of 4th and 5th → 4th=86, 5th=87 → (86+87)/2 = 173/2 = 86.5
→ Mode: All appear once → no mode
→ Range: 95 - 44 = 51
---
Problem 5:
Numbers: 25, 65, 40, 63, 26, 30, 44, 32, 15, 73, 18, 67
Sort: 15, 18, 25, 26, 30, 32, 40, 44, 63, 65, 67, 73
Count = 12
→ Mean: Sum = 15+18+25+26+30+32+40+44+63+65+67+73
Add:
15+18=33
+25=58
+26=84
+30=114
+32=146
+40=186
+44=230
+63=293
+65=358
+67=425
+73=498
Sum = 498
Mean = 498 ÷ 12 = 41.5
→ Median: Average of 6th and 7th → 6th=32, 7th=40 → (32+40)/2 = 72/2 = 36
→ Mode: All unique → no mode
→ Range: 73 - 15 = 58
---
Problem 6:
Numbers: 61, 21, 89, 46, 37, 77, 58, 65, 46, 30
Sort: 21, 30, 37, 46, 46, 58, 61, 65, 77, 89
Count = 10
→ Mean: Sum = 21+30+37+46+46+58+61+65+77+89
Add:
21+30=51
+37=88
+46=134
+46=180
+58=238
+61=299
+65=364
+77=441
+89=530
Sum = 530
Mean = 530 ÷ 10 = 53
→ Median: Average of 5th and 6th → 5th=46, 6th=58 → (46+58)/2 = 104/2 = 52
→ Mode: 46 appears twice → others once → 46
→ Range: 89 - 21 = 68
---
Now compile all answers:
1.
Mean: 17.87
Median: 13
Mode: 13
Range: 45
2.
Mean: 47.42
Median: 39.5
Mode: no mode
Range: 66
3.
Mean: 39.85
Median: 42
Mode: 33 and 52
Range: 44
4.
Mean: 77.75
Median: 86.5
Mode: no mode
Range: 51
5.
Mean: 41.5
Median: 36
Mode: no mode
Range: 58
6.
Mean: 53
Median: 52
Mode: 46
Range: 68
Note: For modes with multiple values, we list both. If worksheet expects single, it might be an issue — but mathematically correct.
Also, for mean, we rounded to two decimal places where needed. Some teachers prefer exact fractions — but decimals are standard here.
Final Answer:
1. Mean: 17.87, Median: 13, Mode: 13, Range: 45
2. Mean: 47.42, Median: 39.5, Mode: no mode, Range: 66
3. Mean: 39.85, Median: 42, Mode: 33 and 52, Range: 44
4. Mean: 77.75, Median: 86.5, Mode: no mode, Range: 51
5. Mean: 41.5, Median: 36, Mode: no mode, Range: 58
6. Mean: 53, Median: 52, Mode: 46, Range: 68
We are given 6 sets of numbers. For each set, we need to find:
- Mean → Add all numbers and divide by how many there are.
- Median → Put the numbers in order and pick the middle one (or average of two middle if even count).
- Mode → The number that appears most often.
- Range → Largest number minus smallest number.
---
Problem 1:
Numbers: 13, 6, 24, 18, 5, 13, 9, 48, 8, 11, 50, 28, 15, 13, 7
Step 1: Sort them → 5, 6, 7, 8, 9, 11, 13, 13, 13, 15, 18, 24, 28, 48, 50
Count = 15 numbers
→ Mean: Sum = 5+6+7+8+9+11+13+13+13+15+18+24+28+48+50 = let’s add:
Group:
(5+6+7+8+9) = 35
(11+13+13+13+15) = 65
(18+24+28+48+50) = 168
Total = 35 + 65 + 168 = 268
Mean = 268 ÷ 15 ≈ 17.87 (round to nearest hundredth? Usually keep as decimal or fraction — but since others may be whole, check context. We’ll use 2 decimals unless specified.)
Actually, let me recalculate sum carefully:
List again:
5, 6, 7, 8, 9, 11, 13, 13, 13, 15, 18, 24, 28, 48, 50
Add step by step:
Start with 0
+5=5
+6=11
+7=18
+8=26
+9=35
+11=46
+13=59
+13=72
+13=85
+15=100
+18=118
+24=142
+28=170
+48=218
+50=268 ✔
So Mean = 268 / 15 = 17.866... → Round to 2 decimal places: 17.87
→ Median: Middle of 15 numbers → 8th number → sorted list: position 8 is 13
→ Mode: 13 appears 3 times → more than any other → 13
→ Range: 50 - 5 = 45
---
Problem 2:
Numbers: 34, 16, 41, 29, 38, 81, 62, 74, 82, 32, 22, 58
Sort: 16, 22, 29, 32, 34, 38, 41, 58, 62, 74, 81, 82
Count = 12 (even)
→ Mean: Sum = 16+22+29+32+34+38+41+58+62+74+81+82
Calculate:
16+22=38
+29=67
+32=99
+34=133
+38=171
+41=212
+58=270
+62=332
+74=406
+81=487
+82=569
Sum = 569
Mean = 569 ÷ 12 ≈ 47.416... → 47.42
→ Median: Average of 6th and 7th → 6th=38, 7th=41 → (38+41)/2 = 79/2 = 39.5
→ Mode: All appear once → no mode → write “no mode” or leave blank? In school worksheets, sometimes they expect “none”. But let’s see — actually, recheck: all unique → no mode
→ Range: 82 - 16 = 66
---
Problem 3:
Numbers: 52, 18, 43, 23, 48, 29, 33, 52, 32, 33, 51, 62, 42
Sort: 18, 23, 29, 32, 33, 33, 42, 43, 48, 51, 52, 52, 62
Count = 13
→ Mean: Sum = 18+23+29+32+33+33+42+43+48+51+52+52+62
Add:
18+23=41
+29=70
+32=102
+33=135
+33=168
+42=210
+43=253
+48=301
+51=352
+52=404
+52=456
+62=518
Sum = 518
Mean = 518 ÷ 13 ≈ 39.846 → 39.85
→ Median: 7th number → sorted: positions 1 to 13 → 7th is 42
→ Mode: 33 appears twice, 52 appears twice → both occur twice → so bimodal: 33 and 52
But some worksheets might accept only one — but technically, multiple modes are allowed. Let’s note both.
→ Range: 62 - 18 = 44
---
Problem 4:
Numbers: 86, 44, 73, 87, 88, 60, 95, 89
Sort: 44, 60, 73, 84? Wait — wait, original: 86, 44, 73, 87, 88, 60, 95, 89
Sorted: 44, 60, 73, 86, 87, 88, 89, 95
Wait — did I miss a number? Original has 8 numbers.
List: 44, 60, 73, 86, 87, 88, 89, 95 → yes, 8 numbers.
→ Mean: Sum = 44+60+73+86+87+88+89+95
Add:
44+60=104
+73=177
+86=263
+87=350
+88=438
+89=527
+95=622
Sum = 622
Mean = 622 ÷ 8 = 77.75
→ Median: Even count → average of 4th and 5th → 4th=86, 5th=87 → (86+87)/2 = 173/2 = 86.5
→ Mode: All appear once → no mode
→ Range: 95 - 44 = 51
---
Problem 5:
Numbers: 25, 65, 40, 63, 26, 30, 44, 32, 15, 73, 18, 67
Sort: 15, 18, 25, 26, 30, 32, 40, 44, 63, 65, 67, 73
Count = 12
→ Mean: Sum = 15+18+25+26+30+32+40+44+63+65+67+73
Add:
15+18=33
+25=58
+26=84
+30=114
+32=146
+40=186
+44=230
+63=293
+65=358
+67=425
+73=498
Sum = 498
Mean = 498 ÷ 12 = 41.5
→ Median: Average of 6th and 7th → 6th=32, 7th=40 → (32+40)/2 = 72/2 = 36
→ Mode: All unique → no mode
→ Range: 73 - 15 = 58
---
Problem 6:
Numbers: 61, 21, 89, 46, 37, 77, 58, 65, 46, 30
Sort: 21, 30, 37, 46, 46, 58, 61, 65, 77, 89
Count = 10
→ Mean: Sum = 21+30+37+46+46+58+61+65+77+89
Add:
21+30=51
+37=88
+46=134
+46=180
+58=238
+61=299
+65=364
+77=441
+89=530
Sum = 530
Mean = 530 ÷ 10 = 53
→ Median: Average of 5th and 6th → 5th=46, 6th=58 → (46+58)/2 = 104/2 = 52
→ Mode: 46 appears twice → others once → 46
→ Range: 89 - 21 = 68
---
Now compile all answers:
1.
Mean: 17.87
Median: 13
Mode: 13
Range: 45
2.
Mean: 47.42
Median: 39.5
Mode: no mode
Range: 66
3.
Mean: 39.85
Median: 42
Mode: 33 and 52
Range: 44
4.
Mean: 77.75
Median: 86.5
Mode: no mode
Range: 51
5.
Mean: 41.5
Median: 36
Mode: no mode
Range: 58
6.
Mean: 53
Median: 52
Mode: 46
Range: 68
Note: For modes with multiple values, we list both. If worksheet expects single, it might be an issue — but mathematically correct.
Also, for mean, we rounded to two decimal places where needed. Some teachers prefer exact fractions — but decimals are standard here.
Final Answer:
1. Mean: 17.87, Median: 13, Mode: 13, Range: 45
2. Mean: 47.42, Median: 39.5, Mode: no mode, Range: 66
3. Mean: 39.85, Median: 42, Mode: 33 and 52, Range: 44
4. Mean: 77.75, Median: 86.5, Mode: no mode, Range: 51
5. Mean: 41.5, Median: 36, Mode: no mode, Range: 58
6. Mean: 53, Median: 52, Mode: 46, Range: 68
Parent Tip: Review the logic above to help your child master the concept of mean median mode range worksheet 5th grade.
