Mean Median Mode Range Worksheets - Math Monks - Free Printable
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Step-by-step solution for: Mean Median Mode Range Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Mean Median Mode Range Worksheets - Math Monks
Let’s solve each problem step by step.
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Problem 1: 3, 0, 0, 2, 0, 3, 0, 2, 2, 2, 3, 3
First, list the numbers in order:
0, 0, 0, 0, 2, 2, 2, 2, 3, 3, 3, 3 → 12 numbers
- Mean: Add all numbers → 0+0+0+0+2+2+2+2+3+3+3+3 = 20
Divide by 12 → 20 ÷ 12 = 1.666... ≈ 1.67 (rounded to two decimals)
- Median: Middle of 12 numbers → average of 6th and 7th → both are 2 → 2
- Mode: Most frequent → 0 appears 4 times, 2 appears 4 times, 3 appears 4 times → 0, 2, 3 (bimodal or trimodal — but since all appear same, we say all three)
Wait — let’s recount:
Original: 3, 0, 0, 2, 0, 3, 0, 2, 2, 2, 3, 3
Count:
- 0: positions 2,3,5,7 → 4 times
- 2: positions 4,8,9,10 → 4 times
- 3: positions 1,6,11,12 → 4 times
Yes — all appear 4 times → so mode is 0, 2, 3
- Range: Max - Min = 3 - 0 = 3
✔ Problem 1: Mean=1.67, Median=2, Mode=0,2,3, Range=3
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Problem 2: 40, 61, 95, 79, 9, 50, 80, 63, 109, 42
Sort: 9, 40, 42, 50, 61, 63, 79, 80, 95, 109 → 10 numbers
- Mean: Sum = 9+40+42+50+61+63+79+80+95+109 = let’s add:
9+40=49; +42=91; +50=141; +61=202; +63=265; +79=344; +80=424; +95=519; +109=628
628 ÷ 10 = 62.8
- Median: Average of 5th and 6th → 61 and 63 → (61+63)/2 = 62
- Mode: All numbers appear once → no mode
- Range: 109 - 9 = 100
✔ Problem 2: Mean=62.8, Median=62, Mode=none, Range=100
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Problem 3: 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, 20
Sort: 20, 20, 30, 50, 60, 70, 70, 80, 80, 90, 90 → 11 numbers
- Mean: Sum = 20+20+30+50+60+70+70+80+80+90+90
= 20×2=40; 30; 50; 60; 70×2=140; 80×2=160; 90×2=180
Total: 40+30=70; +50=120; +60=180; +140=320; +160=480; +180=660
660 ÷ 11 = 60
- Median: 6th number → 70 → 70
- Mode: 20, 70, 80, 90 each appear twice → 20, 70, 80, 90
Wait — count again:
Original: 90,50,70,80,70,60,20,30,80,90,20
→ 20: 2 times
→ 30: 1
→ 50: 1
→ 60: 1
→ 70: 2
→ 80: 2
→ 90: 2
So modes: 20, 70, 80, 90
- Range: 90 - 20 = 70
✔ Problem 3: Mean=60, Median=70, Mode=20,70,80,90, Range=70
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Problem 4: 98, 100, 65, 78, 98, 35, 100, 45, 50
Sort: 35, 45, 50, 65, 78, 98, 98, 100, 100 → 9 numbers
- Mean: Sum = 35+45=80; +50=130; +65=195; +78=273; +98=371; +98=469; +100=569; +100=669
669 ÷ 9 = 74.333... ≈ 74.33
- Median: 5th number → 78 → 78
- Mode: 98 and 100 each appear twice → 98, 100
- Range: 100 - 35 = 65
✔ Problem 4: Mean=74.33, Median=78, Mode=98,100, Range=65
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Problem 5: 8, 2, 9, 4, 2, 7, 8, 0, 4, 1
Sort: 0, 1, 2, 2, 4, 4, 7, 8, 8, 9 → 10 numbers
- Mean: Sum = 0+1+2+2+4+4+7+8+8+9 =
0+1=1; +2=3; +2=5; +4=9; +4=13; +7=20; +8=28; +8=36; +9=45
45 ÷ 10 = 4.5
- Median: Average of 5th and 6th → 4 and 4 → 4
- Mode: 2, 4, 8 each appear twice → 2, 4, 8
- Range: 9 - 0 = 9
✔ Problem 5: Mean=4.5, Median=4, Mode=2,4,8, Range=9
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Problem 6: 32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20
That’s 30 numbers. Let’s sort them:
List:
6, 8, 10, 10, 11, 12, 12, 15, 16, 16, 17, 18, 18, 20, 21, 21, 23, 24, 24, 24, 29, 30, 31, 32, 32, 32, 35, 36, 39, 40
Check count: 30 numbers ✔️
- Mean: Sum all.
Let’s group:
6
8
10+10=20
11
12+12=24
15
16+16=32
17
18+18=36
20
21+21=42
23
24+24+24=72
29
30
31
32+32+32=96
35
36
39
40
Now add step by step:
Start with 6+8=14
+20=34
+11=45
+24=69
+15=84
+32=116
+17=133
+36=169
+20=189
+42=231
+23=254
+72=326
+29=355
+30=385
+31=416
+96=512
+35=547
+36=583
+39=622
+40=662
Sum = 662
Mean = 662 ÷ 30 = 22.066... ≈ 22.07
- Median: 30 numbers → average of 15th and 16th
Sorted list (index 1 to 30):
1:6, 2:8, 3:10, 4:10, 5:11, 6:12, 7:12, 8:15, 9:16, 10:16,
11:17, 12:18, 13:18, 14:20, 15:21, 16:21, 17:23, 18:24, 19:24, 20:24,
21:29, 22:30, 23:31, 24:32, 25:32, 26:32, 27:35, 28:36, 29:39, 30:40
15th = 21, 16th = 21 → median = (21+21)/2 = 21
- Mode: Which appears most?
Look at counts:
24 appears 3 times
32 appears 3 times
Others: 10,12,16,18,21 appear 2 times → so modes: 24, 32
- Range: 40 - 6 = 34
✔ Problem 6: Mean=22.07, Median=21, Mode=24,32, Range=34
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Final Answers:
1. Mean: 1.67, Median: 2, Mode: 0, 2, 3, Range: 3
2. Mean: 62.8, Median: 62, Mode: none, Range: 100
3. Mean: 60, Median: 70, Mode: 20, 70, 80, 90, Range: 70
4. Mean: 74.33, Median: 78, Mode: 98, 100, Range: 65
5. Mean: 4.5, Median: 4, Mode: 2, 4, 8, Range: 9
6. Mean: 22.07, Median: 21, Mode: 24, 32, Range: 34
Final Answer:
1. Mean: 1.67, Median: 2, Mode: 0, 2, 3, Range: 3
2. Mean: 62.8, Median: 62, Mode: none, Range: 100
3. Mean: 60, Median: 70, Mode: 20, 70, 80, 90, Range: 70
4. Mean: 74.33, Median: 78, Mode: 98, 100, Range: 65
5. Mean: 4.5, Median: 4, Mode: 2, 4, 8, Range: 9
6. Mean: 22.07, Median: 21, Mode: 24, 32, Range: 34
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Problem 1: 3, 0, 0, 2, 0, 3, 0, 2, 2, 2, 3, 3
First, list the numbers in order:
0, 0, 0, 0, 2, 2, 2, 2, 3, 3, 3, 3 → 12 numbers
- Mean: Add all numbers → 0+0+0+0+2+2+2+2+3+3+3+3 = 20
Divide by 12 → 20 ÷ 12 = 1.666... ≈ 1.67 (rounded to two decimals)
- Median: Middle of 12 numbers → average of 6th and 7th → both are 2 → 2
- Mode: Most frequent → 0 appears 4 times, 2 appears 4 times, 3 appears 4 times → 0, 2, 3 (bimodal or trimodal — but since all appear same, we say all three)
Wait — let’s recount:
Original: 3, 0, 0, 2, 0, 3, 0, 2, 2, 2, 3, 3
Count:
- 0: positions 2,3,5,7 → 4 times
- 2: positions 4,8,9,10 → 4 times
- 3: positions 1,6,11,12 → 4 times
Yes — all appear 4 times → so mode is 0, 2, 3
- Range: Max - Min = 3 - 0 = 3
✔ Problem 1: Mean=1.67, Median=2, Mode=0,2,3, Range=3
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Problem 2: 40, 61, 95, 79, 9, 50, 80, 63, 109, 42
Sort: 9, 40, 42, 50, 61, 63, 79, 80, 95, 109 → 10 numbers
- Mean: Sum = 9+40+42+50+61+63+79+80+95+109 = let’s add:
9+40=49; +42=91; +50=141; +61=202; +63=265; +79=344; +80=424; +95=519; +109=628
628 ÷ 10 = 62.8
- Median: Average of 5th and 6th → 61 and 63 → (61+63)/2 = 62
- Mode: All numbers appear once → no mode
- Range: 109 - 9 = 100
✔ Problem 2: Mean=62.8, Median=62, Mode=none, Range=100
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Problem 3: 90, 50, 70, 80, 70, 60, 20, 30, 80, 90, 20
Sort: 20, 20, 30, 50, 60, 70, 70, 80, 80, 90, 90 → 11 numbers
- Mean: Sum = 20+20+30+50+60+70+70+80+80+90+90
= 20×2=40; 30; 50; 60; 70×2=140; 80×2=160; 90×2=180
Total: 40+30=70; +50=120; +60=180; +140=320; +160=480; +180=660
660 ÷ 11 = 60
- Median: 6th number → 70 → 70
- Mode: 20, 70, 80, 90 each appear twice → 20, 70, 80, 90
Wait — count again:
Original: 90,50,70,80,70,60,20,30,80,90,20
→ 20: 2 times
→ 30: 1
→ 50: 1
→ 60: 1
→ 70: 2
→ 80: 2
→ 90: 2
So modes: 20, 70, 80, 90
- Range: 90 - 20 = 70
✔ Problem 3: Mean=60, Median=70, Mode=20,70,80,90, Range=70
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Problem 4: 98, 100, 65, 78, 98, 35, 100, 45, 50
Sort: 35, 45, 50, 65, 78, 98, 98, 100, 100 → 9 numbers
- Mean: Sum = 35+45=80; +50=130; +65=195; +78=273; +98=371; +98=469; +100=569; +100=669
669 ÷ 9 = 74.333... ≈ 74.33
- Median: 5th number → 78 → 78
- Mode: 98 and 100 each appear twice → 98, 100
- Range: 100 - 35 = 65
✔ Problem 4: Mean=74.33, Median=78, Mode=98,100, Range=65
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Problem 5: 8, 2, 9, 4, 2, 7, 8, 0, 4, 1
Sort: 0, 1, 2, 2, 4, 4, 7, 8, 8, 9 → 10 numbers
- Mean: Sum = 0+1+2+2+4+4+7+8+8+9 =
0+1=1; +2=3; +2=5; +4=9; +4=13; +7=20; +8=28; +8=36; +9=45
45 ÷ 10 = 4.5
- Median: Average of 5th and 6th → 4 and 4 → 4
- Mode: 2, 4, 8 each appear twice → 2, 4, 8
- Range: 9 - 0 = 9
✔ Problem 5: Mean=4.5, Median=4, Mode=2,4,8, Range=9
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Problem 6: 32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20
That’s 30 numbers. Let’s sort them:
List:
6, 8, 10, 10, 11, 12, 12, 15, 16, 16, 17, 18, 18, 20, 21, 21, 23, 24, 24, 24, 29, 30, 31, 32, 32, 32, 35, 36, 39, 40
Check count: 30 numbers ✔️
- Mean: Sum all.
Let’s group:
6
8
10+10=20
11
12+12=24
15
16+16=32
17
18+18=36
20
21+21=42
23
24+24+24=72
29
30
31
32+32+32=96
35
36
39
40
Now add step by step:
Start with 6+8=14
+20=34
+11=45
+24=69
+15=84
+32=116
+17=133
+36=169
+20=189
+42=231
+23=254
+72=326
+29=355
+30=385
+31=416
+96=512
+35=547
+36=583
+39=622
+40=662
Sum = 662
Mean = 662 ÷ 30 = 22.066... ≈ 22.07
- Median: 30 numbers → average of 15th and 16th
Sorted list (index 1 to 30):
1:6, 2:8, 3:10, 4:10, 5:11, 6:12, 7:12, 8:15, 9:16, 10:16,
11:17, 12:18, 13:18, 14:20, 15:21, 16:21, 17:23, 18:24, 19:24, 20:24,
21:29, 22:30, 23:31, 24:32, 25:32, 26:32, 27:35, 28:36, 29:39, 30:40
15th = 21, 16th = 21 → median = (21+21)/2 = 21
- Mode: Which appears most?
Look at counts:
24 appears 3 times
32 appears 3 times
Others: 10,12,16,18,21 appear 2 times → so modes: 24, 32
- Range: 40 - 6 = 34
✔ Problem 6: Mean=22.07, Median=21, Mode=24,32, Range=34
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Final Answers:
1. Mean: 1.67, Median: 2, Mode: 0, 2, 3, Range: 3
2. Mean: 62.8, Median: 62, Mode: none, Range: 100
3. Mean: 60, Median: 70, Mode: 20, 70, 80, 90, Range: 70
4. Mean: 74.33, Median: 78, Mode: 98, 100, Range: 65
5. Mean: 4.5, Median: 4, Mode: 2, 4, 8, Range: 9
6. Mean: 22.07, Median: 21, Mode: 24, 32, Range: 34
Final Answer:
1. Mean: 1.67, Median: 2, Mode: 0, 2, 3, Range: 3
2. Mean: 62.8, Median: 62, Mode: none, Range: 100
3. Mean: 60, Median: 70, Mode: 20, 70, 80, 90, Range: 70
4. Mean: 74.33, Median: 78, Mode: 98, 100, Range: 65
5. Mean: 4.5, Median: 4, Mode: 2, 4, 8, Range: 9
6. Mean: 22.07, Median: 21, Mode: 24, 32, Range: 34
Parent Tip: Review the logic above to help your child master the concept of finding mean median mode worksheet.
