5 Worksheets for Calculating Mean Averages - Free Printable
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Step-by-step solution for: 5 Worksheets for Calculating Mean Averages
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Show Answer Key & Explanations
Step-by-step solution for: 5 Worksheets for Calculating Mean Averages
Let’s solve each problem step by step. To find the mean, we:
1. Add up all the numbers in the set.
2. Count how many numbers there are.
3. Divide the total sum by the count.
We’ll do this for each of the 10 problems.
---
Problem 1: 8, 3, 52, 48, 7, 78
Sum = 8 + 3 + 52 + 48 + 7 + 78
= (8+3)=11; (11+52)=63; (63+48)=111; (111+7)=118; (118+78)=196
Count = 6
Mean = 196 ÷ 6 = 32.666... → Let’s write as fraction or round? Since it’s a worksheet, probably decimal is fine. But let’s check if divisible evenly — 196 ÷ 6 = 32.666… Actually, 6 × 32 = 192, remainder 4 → so 32 and 4/6 = 32 and 2/3 ≈ 32.67
Wait — maybe I made an error? Let me recalculate sum:
8 + 3 = 11
11 + 52 = 63
63 + 48 = 111
111 + 7 = 118
118 + 78 = 196 → correct.
But 196 ÷ 6 = 32.666... Hmm. Maybe they expect exact fraction? Or perhaps I should double-check the numbers.
Actually, looking again — maybe I misread? The numbers are: 8, 3, 52, 48, 7, 78 — yes.
Alternatively, perhaps the worksheet expects rounding to whole number? But no instruction says that. Let’s keep it as decimal with two places unless it divides evenly.
Wait — let’s try Problem 2 first to see pattern.
---
Problem 2: 6, 26, 92, 13, 3, 48
Sum = 6 + 26 = 32; 32 + 92 = 124; 124 + 13 = 137; 137 + 3 = 140; 140 + 48 = 188
Count = 6
Mean = 188 ÷ 6 = 31.333...
Hmm, not nice numbers. Maybe I should just calculate accurately and report decimals rounded to two places? Or maybe leave as fractions? But since it’s “calculate the mean”, and these are likely designed to be clean, perhaps I made addition errors.
Let me recheck Problem 1:
8 + 3 = 11
52 + 48 = 100 → that’s easy! So 11 + 100 = 111
Then 7 + 78 = 85
So 111 + 85 = 196 → same as before.
196 ÷ 6 = 32.666... → 32.67 if rounded.
But let’s look at Problem 3: 55, 22, 33, 59, 2, 4
Sum: 55+22=77; 77+33=110; 110+59=169; 169+2=171; 171+4=175
Count=6 → 175÷6≈29.17
This seems messy. Wait — maybe some sets have different counts?
Look at Problem 4: 7, 85, 9, 1, 67, 8 → that’s 6 numbers.
Problem 5: 36, 2, 81, 83, 79, 2 → 6 numbers.
Problem 6: 62, 97, 16, 28, 3, 2 → 6 numbers.
Problem 7: 7, 53, 9, 39, 9, 36 → 6 numbers.
Problem 8: 8, 29, 64, 3, 7, 5 → 6 numbers.
Problem 9: 1, 6, 87, 26, 8, 1 → 6 numbers.
Problem 10: 18, 98, 9, 88, 59, 98 → 6 numbers.
All have 6 numbers? Then why are sums not divisible by 6? Maybe they are, and I’m miscalculating.
Let me try Problem 10: 18, 98, 9, 88, 59, 98
Add: 18+98=116; 116+9=125; 125+88=213; 213+59=272; 272+98=370
370 ÷ 6 = 61.666... Still not integer.
Perhaps the worksheet allows decimal answers. Or maybe I need to use calculator-style precision.
Another thought: maybe "how many numbers" includes something else? No, it's clear: add all numbers, divide by how many there are.
Perhaps for consistency, I'll compute each exactly and report to two decimal places, as is common in such worksheets.
Let me make a table:
---
Problem 1: 8, 3, 52, 48, 7, 78
Sum = 8+3+52+48+7+78
Group: (8+3)=11, (52+48)=100, (7+78)=85 → 11+100=111, 111+85=196
Count = 6
Mean = 196 / 6 = 32.666... ≈ 32.67
But let's see if 196 ÷ 6 can be simplified: 196 ÷ 2 = 98, 6÷2=3 → 98/3 = 32 2/3. But probably decimal is expected.
I recall that in some curricula, they might expect fractional form, but given the context, decimal is safer.
Wait — let's check Problem 4: 7, 85, 9, 1, 67, 8
Sum: 7+85=92; 92+9=101; 101+1=102; 102+67=169; 169+8=177
177 ÷ 6 = 29.5 → oh! That's nice.
Similarly, Problem 5: 36, 2, 81, 83, 79, 2
36+2=38; 38+81=119; 119+83=202; 202+79=281; 281+2=283
283 ÷ 6 = 47.166... Not nice.
Problem 6: 62, 97, 16, 28, 3, 2
62+97=159; 159+16=175; 175+28=203; 203+3=206; 206+2=208
208 ÷ 6 = 34.666...
Problem 7: 7, 53, 9, 39, 9, 36
7+53=60; 60+9=69; 69+39=108; 108+9=117; 117+36=153
153 ÷ 6 = 25.5 → nice!
Problem 8: 8, 29, 64, 3, 7, 5
8+29=37; 37+64=101; 101+3=104; 104+7=111; 111+5=116
116 ÷ 6 = 19.333...
Problem 9: 1, 6, 87, 26, 8, 1
1+6=7; 7+87=94; 94+26=120; 120+8=128; 128+1=129
129 ÷ 6 = 21.5 → nice!
Problem 10: 18, 98, 9, 88, 59, 98
As before, 370 ÷ 6 = 61.666...
And Problem 2: 6,26,92,13,3,48 = 188 ÷ 6 = 31.333...
Problem 3: 55,22,33,59,2,4 = 175 ÷ 6 = 29.166...
So only Problems 4,7,9 give .5, others are repeating decimals.
Perhaps the worksheet expects us to leave as mixed numbers or round. But since it's "calculate the mean", and no specification, I think reporting to two decimal places is standard.
To be precise, let's calculate each exactly and then decide.
I can write them as fractions, but for student level, decimal is better.
Another idea: maybe I should verify if any set has different number of elements? Let's count again.
Problem 1: six numbers — yes.
All seem to have six. Except — wait, Problem 4 is listed as "4. 7, 85, 9, 1, 67, 8" — that's six.
In the image description, it's written as:
1. 8,3,52,48,7,78
2. 6,26,92,13,3,48
3. 55,22,33,59,2,4
4. 7,85,9,1,67,8
5. 36,2,81,83,79,2
6. 62,97,16,28,3,2
7. 7,53,9,39,9,36
8. 8,29,64,3,7,5
9. 1,6,87,26,8,1
10. 18,98,9,88,59,98
All six numbers per set.
Perhaps the answer key expects rounded values. I'll proceed with calculating each sum and dividing by 6, and report to two decimal places where necessary.
Let me list them systematically:
1. Sum = 8+3+52+48+7+78 = let's add in pairs:
(8+78)=86, (3+7)=10, (52+48)=100 → 86+10=96, 96+100=196 → 196/6 = 32.666... → 32.67
2. 6+26+92+13+3+48
(6+48)=54, (26+3)=29, (92+13)=105 → 54+29=83, 83+105=188 → 188/6 = 31.333... → 31.33
3. 55+22+33+59+2+4
(55+22)=77, (33+59)=92, (2+4)=6 → 77+92=169, 169+6=175 → 175/6 = 29.166... → 29.17
4. 7+85+9+1+67+8
(7+8)=15, (85+1)=86, (9+67)=76 → 15+86=101, 101+76=177 → 177/6 = 29.5 → 29.50
5. 36+2+81+83+79+2
(36+2)=38, (81+83)=164, (79+2)=81 → 38+164=202, 202+81=283 → 283/6 = 47.166... → 47.17
6. 62+97+16+28+3+2
(62+28)=90, (97+3)=100, (16+2)=18 → 90+100=190, 190+18=208 → 208/6 = 34.666... → 34.67
7. 7+53+9+39+9+36
(7+53)=60, (9+39)=48, (9+36)=45 → 60+48=108, 108+45=153 → 153/6 = 25.5 → 25.50
8. 8+29+64+3+7+5
(8+5)=13, (29+7)=36, (64+3)=67 → 13+36=49, 49+67=116 → 116/6 = 19.333... → 19.33
9. 1+6+87+26+8+1
(1+1)=2, (6+8)=14, (87+26)=113 → 2+14=16, 16+113=129 → 129/6 = 21.5 → 21.50
10. 18+98+9+88+59+98
(18+98)=116, (9+88)=97, (59+98)=157 → 116+97=213, 213+157=370 → 370/6 = 61.666... → 61.67
Now, to confirm, let's see if any can be exact fractions, but for the purpose of this worksheet, decimal answers to two places are appropriate.
Some teachers might prefer mixed numbers, but since the instruction is "calculate the mean", and no specification, decimal is fine.
I think this is accurate.
Final Answer:
1. 32.67
2. 31.33
3. 29.17
4. 29.50
5. 47.17
6. 34.67
7. 25.50
8. 19.33
9. 21.50
10. 61.67
But let me double-check one more time for accuracy.
For example, Problem 5: 36,2,81,83,79,2
36+2=38
38+81=119
119+83=202
202+79=281
281+2=283 → yes
283 ÷ 6 = 47.1666... → rounds to 47.17
Problem 6: 62,97,16,28,3,2
62+97=159
159+16=175
175+28=203
203+3=206
206+2=208 → 208÷6=34.666...→34.67
Problem 10: 18+98=116, 116+9=125, 125+88=213, 213+59=272, 272+98=370 → 370÷6=61.666...→61.67
All good.
So the final answers are as above.
1. Add up all the numbers in the set.
2. Count how many numbers there are.
3. Divide the total sum by the count.
We’ll do this for each of the 10 problems.
---
Problem 1: 8, 3, 52, 48, 7, 78
Sum = 8 + 3 + 52 + 48 + 7 + 78
= (8+3)=11; (11+52)=63; (63+48)=111; (111+7)=118; (118+78)=196
Count = 6
Mean = 196 ÷ 6 = 32.666... → Let’s write as fraction or round? Since it’s a worksheet, probably decimal is fine. But let’s check if divisible evenly — 196 ÷ 6 = 32.666… Actually, 6 × 32 = 192, remainder 4 → so 32 and 4/6 = 32 and 2/3 ≈ 32.67
Wait — maybe I made an error? Let me recalculate sum:
8 + 3 = 11
11 + 52 = 63
63 + 48 = 111
111 + 7 = 118
118 + 78 = 196 → correct.
But 196 ÷ 6 = 32.666... Hmm. Maybe they expect exact fraction? Or perhaps I should double-check the numbers.
Actually, looking again — maybe I misread? The numbers are: 8, 3, 52, 48, 7, 78 — yes.
Alternatively, perhaps the worksheet expects rounding to whole number? But no instruction says that. Let’s keep it as decimal with two places unless it divides evenly.
Wait — let’s try Problem 2 first to see pattern.
---
Problem 2: 6, 26, 92, 13, 3, 48
Sum = 6 + 26 = 32; 32 + 92 = 124; 124 + 13 = 137; 137 + 3 = 140; 140 + 48 = 188
Count = 6
Mean = 188 ÷ 6 = 31.333...
Hmm, not nice numbers. Maybe I should just calculate accurately and report decimals rounded to two places? Or maybe leave as fractions? But since it’s “calculate the mean”, and these are likely designed to be clean, perhaps I made addition errors.
Let me recheck Problem 1:
8 + 3 = 11
52 + 48 = 100 → that’s easy! So 11 + 100 = 111
Then 7 + 78 = 85
So 111 + 85 = 196 → same as before.
196 ÷ 6 = 32.666... → 32.67 if rounded.
But let’s look at Problem 3: 55, 22, 33, 59, 2, 4
Sum: 55+22=77; 77+33=110; 110+59=169; 169+2=171; 171+4=175
Count=6 → 175÷6≈29.17
This seems messy. Wait — maybe some sets have different counts?
Look at Problem 4: 7, 85, 9, 1, 67, 8 → that’s 6 numbers.
Problem 5: 36, 2, 81, 83, 79, 2 → 6 numbers.
Problem 6: 62, 97, 16, 28, 3, 2 → 6 numbers.
Problem 7: 7, 53, 9, 39, 9, 36 → 6 numbers.
Problem 8: 8, 29, 64, 3, 7, 5 → 6 numbers.
Problem 9: 1, 6, 87, 26, 8, 1 → 6 numbers.
Problem 10: 18, 98, 9, 88, 59, 98 → 6 numbers.
All have 6 numbers? Then why are sums not divisible by 6? Maybe they are, and I’m miscalculating.
Let me try Problem 10: 18, 98, 9, 88, 59, 98
Add: 18+98=116; 116+9=125; 125+88=213; 213+59=272; 272+98=370
370 ÷ 6 = 61.666... Still not integer.
Perhaps the worksheet allows decimal answers. Or maybe I need to use calculator-style precision.
Another thought: maybe "how many numbers" includes something else? No, it's clear: add all numbers, divide by how many there are.
Perhaps for consistency, I'll compute each exactly and report to two decimal places, as is common in such worksheets.
Let me make a table:
---
Problem 1: 8, 3, 52, 48, 7, 78
Sum = 8+3+52+48+7+78
Group: (8+3)=11, (52+48)=100, (7+78)=85 → 11+100=111, 111+85=196
Count = 6
Mean = 196 / 6 = 32.666... ≈ 32.67
But let's see if 196 ÷ 6 can be simplified: 196 ÷ 2 = 98, 6÷2=3 → 98/3 = 32 2/3. But probably decimal is expected.
I recall that in some curricula, they might expect fractional form, but given the context, decimal is safer.
Wait — let's check Problem 4: 7, 85, 9, 1, 67, 8
Sum: 7+85=92; 92+9=101; 101+1=102; 102+67=169; 169+8=177
177 ÷ 6 = 29.5 → oh! That's nice.
Similarly, Problem 5: 36, 2, 81, 83, 79, 2
36+2=38; 38+81=119; 119+83=202; 202+79=281; 281+2=283
283 ÷ 6 = 47.166... Not nice.
Problem 6: 62, 97, 16, 28, 3, 2
62+97=159; 159+16=175; 175+28=203; 203+3=206; 206+2=208
208 ÷ 6 = 34.666...
Problem 7: 7, 53, 9, 39, 9, 36
7+53=60; 60+9=69; 69+39=108; 108+9=117; 117+36=153
153 ÷ 6 = 25.5 → nice!
Problem 8: 8, 29, 64, 3, 7, 5
8+29=37; 37+64=101; 101+3=104; 104+7=111; 111+5=116
116 ÷ 6 = 19.333...
Problem 9: 1, 6, 87, 26, 8, 1
1+6=7; 7+87=94; 94+26=120; 120+8=128; 128+1=129
129 ÷ 6 = 21.5 → nice!
Problem 10: 18, 98, 9, 88, 59, 98
As before, 370 ÷ 6 = 61.666...
And Problem 2: 6,26,92,13,3,48 = 188 ÷ 6 = 31.333...
Problem 3: 55,22,33,59,2,4 = 175 ÷ 6 = 29.166...
So only Problems 4,7,9 give .5, others are repeating decimals.
Perhaps the worksheet expects us to leave as mixed numbers or round. But since it's "calculate the mean", and no specification, I think reporting to two decimal places is standard.
To be precise, let's calculate each exactly and then decide.
I can write them as fractions, but for student level, decimal is better.
Another idea: maybe I should verify if any set has different number of elements? Let's count again.
Problem 1: six numbers — yes.
All seem to have six. Except — wait, Problem 4 is listed as "4. 7, 85, 9, 1, 67, 8" — that's six.
In the image description, it's written as:
1. 8,3,52,48,7,78
2. 6,26,92,13,3,48
3. 55,22,33,59,2,4
4. 7,85,9,1,67,8
5. 36,2,81,83,79,2
6. 62,97,16,28,3,2
7. 7,53,9,39,9,36
8. 8,29,64,3,7,5
9. 1,6,87,26,8,1
10. 18,98,9,88,59,98
All six numbers per set.
Perhaps the answer key expects rounded values. I'll proceed with calculating each sum and dividing by 6, and report to two decimal places where necessary.
Let me list them systematically:
1. Sum = 8+3+52+48+7+78 = let's add in pairs:
(8+78)=86, (3+7)=10, (52+48)=100 → 86+10=96, 96+100=196 → 196/6 = 32.666... → 32.67
2. 6+26+92+13+3+48
(6+48)=54, (26+3)=29, (92+13)=105 → 54+29=83, 83+105=188 → 188/6 = 31.333... → 31.33
3. 55+22+33+59+2+4
(55+22)=77, (33+59)=92, (2+4)=6 → 77+92=169, 169+6=175 → 175/6 = 29.166... → 29.17
4. 7+85+9+1+67+8
(7+8)=15, (85+1)=86, (9+67)=76 → 15+86=101, 101+76=177 → 177/6 = 29.5 → 29.50
5. 36+2+81+83+79+2
(36+2)=38, (81+83)=164, (79+2)=81 → 38+164=202, 202+81=283 → 283/6 = 47.166... → 47.17
6. 62+97+16+28+3+2
(62+28)=90, (97+3)=100, (16+2)=18 → 90+100=190, 190+18=208 → 208/6 = 34.666... → 34.67
7. 7+53+9+39+9+36
(7+53)=60, (9+39)=48, (9+36)=45 → 60+48=108, 108+45=153 → 153/6 = 25.5 → 25.50
8. 8+29+64+3+7+5
(8+5)=13, (29+7)=36, (64+3)=67 → 13+36=49, 49+67=116 → 116/6 = 19.333... → 19.33
9. 1+6+87+26+8+1
(1+1)=2, (6+8)=14, (87+26)=113 → 2+14=16, 16+113=129 → 129/6 = 21.5 → 21.50
10. 18+98+9+88+59+98
(18+98)=116, (9+88)=97, (59+98)=157 → 116+97=213, 213+157=370 → 370/6 = 61.666... → 61.67
Now, to confirm, let's see if any can be exact fractions, but for the purpose of this worksheet, decimal answers to two places are appropriate.
Some teachers might prefer mixed numbers, but since the instruction is "calculate the mean", and no specification, decimal is fine.
I think this is accurate.
Final Answer:
1. 32.67
2. 31.33
3. 29.17
4. 29.50
5. 47.17
6. 34.67
7. 25.50
8. 19.33
9. 21.50
10. 61.67
But let me double-check one more time for accuracy.
For example, Problem 5: 36,2,81,83,79,2
36+2=38
38+81=119
119+83=202
202+79=281
281+2=283 → yes
283 ÷ 6 = 47.1666... → rounds to 47.17
Problem 6: 62,97,16,28,3,2
62+97=159
159+16=175
175+28=203
203+3=206
206+2=208 → 208÷6=34.666...→34.67
Problem 10: 18+98=116, 116+9=125, 125+88=213, 213+59=272, 272+98=370 → 370÷6=61.666...→61.67
All good.
So the final answers are as above.
Parent Tip: Review the logic above to help your child master the concept of average worksheet.
