Practice worksheet for calculating mean, median, and mode with ten data sets.
Worksheet titled "Mean, Median and Mode I" with ten sets of numbers and a table for answers.
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Step-by-step solution for: Mean, median and mode worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Mean, median and mode worksheet
Let’s solve each problem one by one. For each set of numbers, we need to find:
- Mean: Add all the numbers and divide by how many there are.
- Median: Put the numbers in order from smallest to largest, then pick the middle number (or average the two middle ones if there’s an even count).
- Mode: The number that appears most often. If no number repeats, there is no mode. If multiple numbers tie for most frequent, list them all.
We’ll go row by row.
---
1) 75, 80, 86, 88, 72, 80
Step 1: Sort → 72, 75, 80, 80, 86, 88
Count = 6
Mean: (72 + 75 + 80 + 80 + 86 + 88) = let’s add:
72+75=147; 147+80=227; 227+80=307; 307+86=393; 393+88=481
→ 481 ÷ 6 = 80.166... ≈ 80.17 (but since original numbers are whole, maybe keep as fraction or round? Let’s check instructions — probably expect decimal or exact. We’ll use 80.17 but actually 481/6 = 80 1/6. But for school, often rounded to 1 decimal. Wait — let me recalculate sum:
72+75=147
147+80=227
227+80=307
307+86=393
393+88=481 → yes. 481 ÷ 6 = 80.166… → 80.2 if rounding to 1 decimal? Or leave as 80.17? Actually, let’s do exact: 481 ÷ 6 = 80.166... → I’ll write 80.2 for simplicity unless specified otherwise. But wait — maybe they want exact? Let’s see other problems. Actually, better to compute precisely and report as needed. Since it's a worksheet, likely expects decimal to 1 or 2 places. I’ll use 1 decimal place for mean unless it’s whole.
But let’s be precise: 481 ÷ 6 = 80.166... → 80.2 (rounded to 1 decimal)
Median: sorted: 72, 75, 80, 80, 86, 88 → middle two are 80 and 80 → median = (80+80)/2 = 80
Mode: 80 appears twice, others once → 80
So: Mean=80.2, Median=80, Mode=80
Wait — let me double-check sum: 72+75=147, +80=227, +80=307, +86=393, +88=481 → yes. 481/6=80.166... → if we keep as fraction, 80 1/6, but probably decimal is fine. I’ll use 80.2 for now.
Actually, let’s check if any problem has integer mean — maybe we should calculate exactly. But for consistency, I’ll use 1 decimal place for mean unless it’s whole.
Alternatively, perhaps the worksheet expects exact values. Let me try to be accurate.
I think for this level, they might accept 80.2, but let’s note: 481 ÷ 6 = 80.166... so if we write 80.17, that’s 2 decimals. Hmm. Looking at the data, all integers, so mean can be decimal. I’ll use 1 decimal place for mean in final answer unless it’s whole.
But to be safe, let’s calculate all means with 2 decimals and see.
Actually, let’s proceed and adjust if needed.
For now:
1) Mean: 481 ÷ 6 = 80.166... → 80.17 (if 2 decimals) or 80.2 (1 decimal). I think 1 decimal is sufficient. Let me check standard practice — in many worksheets, they use 1 decimal. I’ll go with 1 decimal.
So Mean = 80.2
But let’s confirm with another method: 72+88=160, 75+86=161, 80+80=160 → total 160+161+160=481 → same. 481/6=80.166... → 80.2 when rounded to 1 decimal.
Yes.
Median: 80
Mode: 80
---
2) 98, 85, 84, 83, 96, 93, 84
Sort: 83, 84, 84, 85, 93, 96, 98 → count=7
Sum: 83+84=167; +84=251; +85=336; +93=429; +96=525; +98=623
Mean: 623 ÷ 7 = 89 → exactly! Because 7*89=623? 7*80=560, 7*9=63, 560+63=623 → yes! So Mean=89
Median: middle of 7 numbers is 4th → 85
Mode: 84 appears twice, others once → 84
So: Mean=89, Median=85, Mode=84
---
3) 45, 51, 50, 43, 42, 43, 43, 52
Sort: 42, 43, 43, 43, 45, 50, 51, 52 → count=8
Sum: 42+43=85; +43=128; +43=171; +45=216; +50=266; +51=317; +52=369
Mean: 369 ÷ 8 = 46.125 → 46.1 (1 decimal) or 46.13? Let’s use 1 decimal: 46.1
But 369 ÷ 8 = 46.125 → rounds to 46.1 if 1 decimal? No: 46.125 to 1 decimal is 46.1? Wait, 46.125 — the second decimal is 2, which is less than 5, so 46.1? But 46.125 is closer to 46.1 than 46.2? Actually, rounding rules: look at the digit after the place you’re rounding to. For 1 decimal, look at hundredths place. Here, 46.125 — tenths is 1, hundredths is 2, so round down → 46.1
But sometimes they expect more precision. Let’s keep as 46.1 for now.
Median: 8 numbers, so average of 4th and 5th: 4th is 43, 5th is 45 → (43+45)/2 = 88/2 = 44
Mode: 43 appears three times → 43
So: Mean=46.1, Median=44, Mode=43
---
4) 49, 49, 34, 32, 41
Sort: 32, 34, 41, 49, 49 → count=5
Sum: 32+34=66; +41=107; +49=156; +49=205
Mean: 205 ÷ 5 = 41
Median: middle is 3rd → 41
Mode: 49 appears twice, others once → 49
So: Mean=41, Median=41, Mode=49
---
5) 77, 79, 67, 78, 69, 65, 65, 83
Sort: 65, 65, 67, 69, 77, 78, 79, 83 → count=8
Sum: 65+65=130; +67=197; +69=266; +77=343; +78=421; +79=500; +83=583
Mean: 583 ÷ 8 = 72.875 → 72.9 (1 decimal)
Median: average of 4th and 5th: 69 and 77 → (69+77)/2 = 146/2 = 73
Mode: 65 appears twice → 65
So: Mean=72.9, Median=73, Mode=65
---
6) 100, 78, 97, 97, 96, 90, 93
Sort: 78, 90, 93, 96, 97, 97, 100 → count=7
Sum: 78+90=168; +93=261; +96=357; +97=454; +97=551; +100=651
Mean: 651 ÷ 7 = 93 → because 7*93=651? 7*90=630, 7*3=21, 630+21=651 → yes! 93
Median: 4th number → 96
Mode: 97 appears twice → 97
So: Mean=93, Median=96, Mode=97
---
7) 52, 63, 55, 72, 70, 63
Sort: 52, 55, 63, 63, 70, 72 → count=6
Sum: 52+55=107; +63=170; +63=233; +70=303; +72=375
Mean: 375 ÷ 6 = 62.5 → 62.5
Median: average of 3rd and 4th: both 63 → (63+63)/2 = 63
Mode: 63 appears twice → 63
So: Mean=62.5, Median=63, Mode=63
---
8) 89, 72, 68, 76, 68, 85, 81
Sort: 68, 68, 72, 76, 81, 85, 89 → count=7
Sum: 68+68=136; +72=208; +76=284; +81=365; +85=450; +89=539
Mean: 539 ÷ 7 = 77 → because 7*77=539? 7*70=490, 7*7=49, 490+49=539 → yes! 77
Median: 4th number → 76
Mode: 68 appears twice → 68
So: Mean=77, Median=76, Mode=68
---
9) 52, 62, 69, 60, 67, 66, 59, 66
Sort: 52, 59, 60, 62, 66, 66, 67, 69 → count=8
Sum: 52+59=111; +60=171; +62=233; +66=299; +66=365; +67=432; +69=501
Mean: 501 ÷ 8 = 62.625 → 62.6 (1 decimal)
Median: average of 4th and 5th: 62 and 66 → (62+66)/2 = 128/2 = 64
Mode: 66 appears twice → 66
So: Mean=62.6, Median=64, Mode=66
---
10) 40, 40, 35, 26, 30, 21, 27, 36, 24
Sort: 21, 24, 26, 27, 30, 35, 36, 40, 40 → count=9
Sum: 21+24=45; +26=71; +27=98; +30=128; +35=163; +36=199; +40=239; +40=279
Mean: 279 ÷ 9 = 31 → because 9*31=279? 9*30=270, 9*1=9, 270+9=279 → yes! 31
Median: 5th number → 30
Mode: 40 appears twice, others once → 40
So: Mean=31, Median=30, Mode=40
---
Now, let’s compile all answers. I used 1 decimal place for mean where not whole number. But let me verify if any should be adjusted.
For problem 1: mean was 80.166... → I said 80.2, but 80.166 rounded to 1 decimal is 80.2? Yes, because 6>5, so 80.2.
Problem 3: 46.125 → to 1 decimal: look at hundredths digit 2<5, so 46.1
Problem 5: 72.875 → hundredths is 7>5, so round up tenths: 72.9
Problem 9: 62.625 → hundredths is 2<5, so 62.6
All good.
Now, for the table:
Row 1: Mean=80.2, Median=80, Mode=80
But wait — in problem 1, mode is 80, which is correct.
In the answer table, they have columns for Mean, Median, Mode.
Also, for rows where there is no mode? In all these, there is a mode. Problem 4 has mode 49, etc. All have at least one mode.
Now, let’s write the final answers per row.
I think for consistency, since some means are whole numbers, we can write them without decimal, and others with one decimal.
So:
1) Mean: 80.2, Median: 80, Mode: 80
2) Mean: 89, Median: 85, Mode: 84
3) Mean: 46.1, Median: 44, Mode: 43
4) Mean: 41, Median: 41, Mode: 49
5) Mean: 72.9, Median: 73, Mode: 65
6) Mean: 93, Median: 96, Mode: 97
7) Mean: 62.5, Median: 63, Mode: 63
8) Mean: 77, Median: 76, Mode: 68
9) Mean: 62.6, Median: 64, Mode: 66
10) Mean: 31, Median: 30, Mode: 40
Now, to present in the table format as requested.
Final Answer:
| | Mean | Median | Mode |
|---|-------|--------|------|
| 1 | 80.2 | 80 | 80 |
| 2 | 89 | 85 | 84 |
| 3 | 46.1 | 44 | 43 |
| 4 | 41 | 41 | 49 |
| 5 | 72.9 | 73 | 65 |
| 6 | 93 | 96 | 97 |
| 7 | 62.5 | 63 | 63 |
| 8 | 77 | 76 | 68 |
| 9 | 62.6 | 64 | 66 |
|10 | 31 | 30 | 40 |
I think this is correct. Let me quickly spot-check one more.
Problem 7: numbers 52,63,55,72,70,63 → sorted 52,55,63,63,70,72 → sum 52+55=107, +63=170, +63=233, +70=303, +72=375 → 375/6=62.5 → yes. Median (63+63)/2=63, mode 63 → correct.
Problem 10: sum 279/9=31, median 30 (5th in sorted), mode 40 → correct.
All seem good.
Final Answer:
| | Mean | Median | Mode |
|---|-------|--------|------|
| 1 | 80.2 | 80 | 80 |
| 2 | 89 | 85 | 84 |
| 3 | 46.1 | 44 | 43 |
| 4 | 41 | 41 | 49 |
| 5 | 72.9 | 73 | 65 |
| 6 | 93 | 96 | 97 |
| 7 | 62.5 | 63 | 63 |
| 8 | 77 | 76 | 68 |
| 9 | 62.6 | 64 | 66 |
|10 | 31 | 30 | 40 |
- Mean: Add all the numbers and divide by how many there are.
- Median: Put the numbers in order from smallest to largest, then pick the middle number (or average the two middle ones if there’s an even count).
- Mode: The number that appears most often. If no number repeats, there is no mode. If multiple numbers tie for most frequent, list them all.
We’ll go row by row.
---
1) 75, 80, 86, 88, 72, 80
Step 1: Sort → 72, 75, 80, 80, 86, 88
Count = 6
Mean: (72 + 75 + 80 + 80 + 86 + 88) = let’s add:
72+75=147; 147+80=227; 227+80=307; 307+86=393; 393+88=481
→ 481 ÷ 6 = 80.166... ≈ 80.17 (but since original numbers are whole, maybe keep as fraction or round? Let’s check instructions — probably expect decimal or exact. We’ll use 80.17 but actually 481/6 = 80 1/6. But for school, often rounded to 1 decimal. Wait — let me recalculate sum:
72+75=147
147+80=227
227+80=307
307+86=393
393+88=481 → yes. 481 ÷ 6 = 80.166… → 80.2 if rounding to 1 decimal? Or leave as 80.17? Actually, let’s do exact: 481 ÷ 6 = 80.166... → I’ll write 80.2 for simplicity unless specified otherwise. But wait — maybe they want exact? Let’s see other problems. Actually, better to compute precisely and report as needed. Since it's a worksheet, likely expects decimal to 1 or 2 places. I’ll use 1 decimal place for mean unless it’s whole.
But let’s be precise: 481 ÷ 6 = 80.166... → 80.2 (rounded to 1 decimal)
Median: sorted: 72, 75, 80, 80, 86, 88 → middle two are 80 and 80 → median = (80+80)/2 = 80
Mode: 80 appears twice, others once → 80
So: Mean=80.2, Median=80, Mode=80
Wait — let me double-check sum: 72+75=147, +80=227, +80=307, +86=393, +88=481 → yes. 481/6=80.166... → if we keep as fraction, 80 1/6, but probably decimal is fine. I’ll use 80.2 for now.
Actually, let’s check if any problem has integer mean — maybe we should calculate exactly. But for consistency, I’ll use 1 decimal place for mean unless it’s whole.
Alternatively, perhaps the worksheet expects exact values. Let me try to be accurate.
I think for this level, they might accept 80.2, but let’s note: 481 ÷ 6 = 80.166... so if we write 80.17, that’s 2 decimals. Hmm. Looking at the data, all integers, so mean can be decimal. I’ll use 1 decimal place for mean in final answer unless it’s whole.
But to be safe, let’s calculate all means with 2 decimals and see.
Actually, let’s proceed and adjust if needed.
For now:
1) Mean: 481 ÷ 6 = 80.166... → 80.17 (if 2 decimals) or 80.2 (1 decimal). I think 1 decimal is sufficient. Let me check standard practice — in many worksheets, they use 1 decimal. I’ll go with 1 decimal.
So Mean = 80.2
But let’s confirm with another method: 72+88=160, 75+86=161, 80+80=160 → total 160+161+160=481 → same. 481/6=80.166... → 80.2 when rounded to 1 decimal.
Yes.
Median: 80
Mode: 80
---
2) 98, 85, 84, 83, 96, 93, 84
Sort: 83, 84, 84, 85, 93, 96, 98 → count=7
Sum: 83+84=167; +84=251; +85=336; +93=429; +96=525; +98=623
Mean: 623 ÷ 7 = 89 → exactly! Because 7*89=623? 7*80=560, 7*9=63, 560+63=623 → yes! So Mean=89
Median: middle of 7 numbers is 4th → 85
Mode: 84 appears twice, others once → 84
So: Mean=89, Median=85, Mode=84
---
3) 45, 51, 50, 43, 42, 43, 43, 52
Sort: 42, 43, 43, 43, 45, 50, 51, 52 → count=8
Sum: 42+43=85; +43=128; +43=171; +45=216; +50=266; +51=317; +52=369
Mean: 369 ÷ 8 = 46.125 → 46.1 (1 decimal) or 46.13? Let’s use 1 decimal: 46.1
But 369 ÷ 8 = 46.125 → rounds to 46.1 if 1 decimal? No: 46.125 to 1 decimal is 46.1? Wait, 46.125 — the second decimal is 2, which is less than 5, so 46.1? But 46.125 is closer to 46.1 than 46.2? Actually, rounding rules: look at the digit after the place you’re rounding to. For 1 decimal, look at hundredths place. Here, 46.125 — tenths is 1, hundredths is 2, so round down → 46.1
But sometimes they expect more precision. Let’s keep as 46.1 for now.
Median: 8 numbers, so average of 4th and 5th: 4th is 43, 5th is 45 → (43+45)/2 = 88/2 = 44
Mode: 43 appears three times → 43
So: Mean=46.1, Median=44, Mode=43
---
4) 49, 49, 34, 32, 41
Sort: 32, 34, 41, 49, 49 → count=5
Sum: 32+34=66; +41=107; +49=156; +49=205
Mean: 205 ÷ 5 = 41
Median: middle is 3rd → 41
Mode: 49 appears twice, others once → 49
So: Mean=41, Median=41, Mode=49
---
5) 77, 79, 67, 78, 69, 65, 65, 83
Sort: 65, 65, 67, 69, 77, 78, 79, 83 → count=8
Sum: 65+65=130; +67=197; +69=266; +77=343; +78=421; +79=500; +83=583
Mean: 583 ÷ 8 = 72.875 → 72.9 (1 decimal)
Median: average of 4th and 5th: 69 and 77 → (69+77)/2 = 146/2 = 73
Mode: 65 appears twice → 65
So: Mean=72.9, Median=73, Mode=65
---
6) 100, 78, 97, 97, 96, 90, 93
Sort: 78, 90, 93, 96, 97, 97, 100 → count=7
Sum: 78+90=168; +93=261; +96=357; +97=454; +97=551; +100=651
Mean: 651 ÷ 7 = 93 → because 7*93=651? 7*90=630, 7*3=21, 630+21=651 → yes! 93
Median: 4th number → 96
Mode: 97 appears twice → 97
So: Mean=93, Median=96, Mode=97
---
7) 52, 63, 55, 72, 70, 63
Sort: 52, 55, 63, 63, 70, 72 → count=6
Sum: 52+55=107; +63=170; +63=233; +70=303; +72=375
Mean: 375 ÷ 6 = 62.5 → 62.5
Median: average of 3rd and 4th: both 63 → (63+63)/2 = 63
Mode: 63 appears twice → 63
So: Mean=62.5, Median=63, Mode=63
---
8) 89, 72, 68, 76, 68, 85, 81
Sort: 68, 68, 72, 76, 81, 85, 89 → count=7
Sum: 68+68=136; +72=208; +76=284; +81=365; +85=450; +89=539
Mean: 539 ÷ 7 = 77 → because 7*77=539? 7*70=490, 7*7=49, 490+49=539 → yes! 77
Median: 4th number → 76
Mode: 68 appears twice → 68
So: Mean=77, Median=76, Mode=68
---
9) 52, 62, 69, 60, 67, 66, 59, 66
Sort: 52, 59, 60, 62, 66, 66, 67, 69 → count=8
Sum: 52+59=111; +60=171; +62=233; +66=299; +66=365; +67=432; +69=501
Mean: 501 ÷ 8 = 62.625 → 62.6 (1 decimal)
Median: average of 4th and 5th: 62 and 66 → (62+66)/2 = 128/2 = 64
Mode: 66 appears twice → 66
So: Mean=62.6, Median=64, Mode=66
---
10) 40, 40, 35, 26, 30, 21, 27, 36, 24
Sort: 21, 24, 26, 27, 30, 35, 36, 40, 40 → count=9
Sum: 21+24=45; +26=71; +27=98; +30=128; +35=163; +36=199; +40=239; +40=279
Mean: 279 ÷ 9 = 31 → because 9*31=279? 9*30=270, 9*1=9, 270+9=279 → yes! 31
Median: 5th number → 30
Mode: 40 appears twice, others once → 40
So: Mean=31, Median=30, Mode=40
---
Now, let’s compile all answers. I used 1 decimal place for mean where not whole number. But let me verify if any should be adjusted.
For problem 1: mean was 80.166... → I said 80.2, but 80.166 rounded to 1 decimal is 80.2? Yes, because 6>5, so 80.2.
Problem 3: 46.125 → to 1 decimal: look at hundredths digit 2<5, so 46.1
Problem 5: 72.875 → hundredths is 7>5, so round up tenths: 72.9
Problem 9: 62.625 → hundredths is 2<5, so 62.6
All good.
Now, for the table:
Row 1: Mean=80.2, Median=80, Mode=80
But wait — in problem 1, mode is 80, which is correct.
In the answer table, they have columns for Mean, Median, Mode.
Also, for rows where there is no mode? In all these, there is a mode. Problem 4 has mode 49, etc. All have at least one mode.
Now, let’s write the final answers per row.
I think for consistency, since some means are whole numbers, we can write them without decimal, and others with one decimal.
So:
1) Mean: 80.2, Median: 80, Mode: 80
2) Mean: 89, Median: 85, Mode: 84
3) Mean: 46.1, Median: 44, Mode: 43
4) Mean: 41, Median: 41, Mode: 49
5) Mean: 72.9, Median: 73, Mode: 65
6) Mean: 93, Median: 96, Mode: 97
7) Mean: 62.5, Median: 63, Mode: 63
8) Mean: 77, Median: 76, Mode: 68
9) Mean: 62.6, Median: 64, Mode: 66
10) Mean: 31, Median: 30, Mode: 40
Now, to present in the table format as requested.
Final Answer:
| | Mean | Median | Mode |
|---|-------|--------|------|
| 1 | 80.2 | 80 | 80 |
| 2 | 89 | 85 | 84 |
| 3 | 46.1 | 44 | 43 |
| 4 | 41 | 41 | 49 |
| 5 | 72.9 | 73 | 65 |
| 6 | 93 | 96 | 97 |
| 7 | 62.5 | 63 | 63 |
| 8 | 77 | 76 | 68 |
| 9 | 62.6 | 64 | 66 |
|10 | 31 | 30 | 40 |
I think this is correct. Let me quickly spot-check one more.
Problem 7: numbers 52,63,55,72,70,63 → sorted 52,55,63,63,70,72 → sum 52+55=107, +63=170, +63=233, +70=303, +72=375 → 375/6=62.5 → yes. Median (63+63)/2=63, mode 63 → correct.
Problem 10: sum 279/9=31, median 30 (5th in sorted), mode 40 → correct.
All seem good.
Final Answer:
| | Mean | Median | Mode |
|---|-------|--------|------|
| 1 | 80.2 | 80 | 80 |
| 2 | 89 | 85 | 84 |
| 3 | 46.1 | 44 | 43 |
| 4 | 41 | 41 | 49 |
| 5 | 72.9 | 73 | 65 |
| 6 | 93 | 96 | 97 |
| 7 | 62.5 | 63 | 63 |
| 8 | 77 | 76 | 68 |
| 9 | 62.6 | 64 | 66 |
|10 | 31 | 30 | 40 |
Parent Tip: Review the logic above to help your child master the concept of median worksheet.
