Math worksheet for calculating mean, mode, median, and range from given data sets.

Explanation:
We are given 8 sets of numbers. For each set, we need to find four things:

- 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. If there’s an even number of values, average the two middle ones.
- Mode: The number that appears most often. If no number repeats, there is *no mode* (or sometimes written as “none”).
- Range: Subtract the smallest number from the largest number.

Let’s solve each one carefully.

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Problem 1:
Numbers: 82, 23, 59, 94, 70, 26, 32, 83, 87, 94, 32
Count = 11 numbers

Step 1: Sort them:
23, 26, 32, 32, 59, 70, 82, 83, 87, 94, 94

Mean:
Add them:
23 + 26 = 49
49 + 32 = 81
81 + 32 = 113
113 + 59 = 172
172 + 70 = 242
242 + 82 = 324
324 + 83 = 407
407 + 87 = 494
494 + 94 = 588
588 + 94 = 682
Total = 682
Mean = 682 ÷ 11 = 62

Median: 11 numbers → middle is the 6th number (since (11+1)/2 = 6)
Sorted list:
1:23, 2:26, 3:32, 4:32, 5:59, 6:70, 7:82, …
→ Median = 70

Mode: Which numbers repeat?
32 appears twice, 94 appears twice → both appear 2 times → bimodal: 32 and 94
But usually in basic math, if two values tie for most frequency, we say both are modes. So mode = 32 and 94
(If only one answer allowed, some teachers accept “32 and 94”, or write “32, 94”.)

Range: Largest = 94, smallest = 23 → 94 − 23 = 71

✔ So for #1: Mean = 62, Median = 70, Mode = 32 and 94, Range = 71

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Problem 2:
83, 93, 77, 33, 62, 28, 23
Count = 7

Sort: 23, 28, 33, 62, 77, 83, 93

Mean:
23 + 28 = 51
51 + 33 = 84
84 + 62 = 146
146 + 77 = 223
223 + 83 = 306
306 + 93 = 399
Total = 399
Mean = 399 ÷ 7 = 57

Median: 7 numbers → 4th number = 62

Mode: All numbers appear once → no mode (or “none”)

Range: 93 − 23 = 70

✔ #2: Mean = 57, Median = 62, Mode = none, Range = 70

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Problem 3:
31, 92, 25, 69, 80, 31, 29
Count = 7

Sort: 25, 29, 31, 31, 69, 80, 92

Mean:
25 + 29 = 54
54 + 31 = 85
85 + 31 = 116
116 + 69 = 185
185 + 80 = 265
265 + 92 = 357
Total = 357
Mean = 357 ÷ 7 = 51

Median: 4th number = 31

Mode: 31 appears twice, others once → 31

Range: 92 − 25 = 67

✔ #3: Mean = 51, Median = 31, Mode = 31, Range = 67

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Problem 6:
67, 70, 49, 95, 40, 97, 62, 54, 42
Count = 9

Sort: 40, 42, 49, 54, 62, 67, 70, 95, 97

Mean:
40 + 42 = 82
82 + 49 = 131
131 + 54 = 185
185 + 62 = 247
247 + 67 = 314
314 + 70 = 384
384 + 95 = 479
479 + 97 = 576
Total = 576
Mean = 576 ÷ 9 = 64

Median: 9 numbers → 5th = 62

Mode: All unique → none

Range: 97 − 40 = 57

✔ #6: Mean = 64, Median = 62, Mode = none, Range = 57

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Problem 7:
86, 13, 60, 55, 61, 97, 30, 98, 79, 52, 18
Count = 11

Sort: 13, 18, 30, 52, 55, 60, 61, 79, 86, 97, 98

Mean:
13 + 18 = 31
31 + 30 = 61
61 + 52 = 113
113 + 55 = 168
168 + 60 = 228
228 + 61 = 289
289 + 79 = 368
368 + 86 = 454
454 + 97 = 551
551 + 98 = 649
Total = 649
Mean = 649 ÷ 11 = 59 (since 11 × 59 = 649 — yes!)

Median: 6th number = 60

Mode: All unique → none

Range: 98 − 13 = 85

✔ #7: Mean = 59, Median = 60, Mode = none, Range = 85

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Problem 8:
24, 22, 32, 59, 99, 59, 76, 83, 21, 95, 57
Count = 11

Sort: 21, 22, 24, 32, 57, 59, 59, 76, 83, 95, 99

Mean:
21 + 22 = 43
43 + 24 = 67
67 + 32 = 99
99 + 57 = 156
156 + 59 = 215
215 + 59 = 274
274 + 76 = 350
350 + 83 = 433
433 + 95 = 528
528 + 99 = 627
Total = 627
Mean = 627 ÷ 11 = 57 (11 × 57 = 627 — correct)

Median: 6th number = 59

Mode: 59 appears twice, others once → 59

Range: 99 − 21 = 78

✔ #8: Mean = 57, Median = 59, Mode = 59, Range = 78

Now double-check all calculations quickly:

#1: sum 682 /11 = 62 ✔
#2: 399/7 = 57 ✔
#3: 357/7 = 51 ✔
#6: 576/9 = 64 ✔
#7: 649/11 = 59 ✔
#8: 627/11 = 57 ✔

Medians and ranges also match sorted lists.

Final Answer:
1) Mean 62, Median 70, Mode 32 and 94, Range 71
2) Mean 57, Median 62, Mode none, Range 70
3) Mean 51, Median 31, Mode 31, Range 67
6) Mean 64, Median 62, Mode none, Range 57
7) Mean 59, Median 60, Mode none, Range 85
8) Mean 57, Median 59, Mode 59, Range 78