Mean, Median, Mode and Range worksheet - Free Printable
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Step-by-step solution for: Mean, Median, Mode and Range worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Mean, Median, Mode and Range worksheet
Let’s solve each set of data one by one. We’ll find the mean, median, mode, and range for each.
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- Mean: Add all numbers → 2 + 5 + 5 + 6 + 9 = 27
Divide by count (5) → 27 ÷ 5 = 5.4
- Median: Order is already sorted: 2, 5, 5, 6, 9 → middle number is 5
- Mode: Most frequent number → 5 (appears twice)
- Range: Max - Min → 9 - 2 = 7
✔ Final for Set 1:
MEAN: 5.4
MODE: 5
MEDIAN: 5
RANGE: 7
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First, sort them: 19, 21, 28, 28, 32
- Mean: 19 + 21 + 28 + 28 + 32 = 128 → 128 ÷ 5 = 25.6
- Median: Middle of sorted list → 28
- Mode: 28 appears twice → 28
- Range: 32 - 19 = 13
✔ Final for Set 2:
MEAN: 25.6
MODE: 28
MEDIAN: 28
RANGE: 13
---
Sort them: 89, 93, 93, 95, 95, 95
- Mean: 89 + 93 + 93 + 95 + 95 + 95 = let’s add step by step:
89 + 93 = 182
182 + 93 = 275
275 + 95 = 370
370 + 95 = 465
465 + 95 = 560
Count = 6 → 560 ÷ 6 ≈ 93.333... → we can write as 93.3 or keep fraction? But since others are decimals, use decimal. Actually, 560 ÷ 6 = 93.333... → round to 93.3 if needed, but maybe exact value? Let's check: 560/6 = 280/3 ≈ 93.333 — but in school context, often rounded to tenths. However, let’s see if it divides evenly? No. So we’ll write 93.3 (rounded). Wait — actually, let me double-check addition:
Wait! I think I made a mistake.
Numbers: 95, 93, 95, 95, 89, 93
Add again:
Start with 89
+93 = 182
+93 = 275
+95 = 370
+95 = 465
+95 = 560 → yes, correct.
560 ÷ 6 = 93.333... → so 93.3 if rounding to tenths. But sometimes they want exact fraction? The problem doesn’t specify. Looking at other sets, some will be whole numbers, some not. Let’s keep it as 93.3 for now.
But wait — let me check if I miscounted the numbers. There are six numbers: yes.
Actually, let’s do this differently: group same numbers.
Three 95s: 95 × 3 = 285
Two 93s: 93 × 2 = 186
One 89: 89
Total: 285 + 186 = 471; 471 + 89 = 560 → same.
So mean = 560 / 6 = 93.333... → we'll write 93.3 (but note: in many classrooms, they might accept 93.3 or 93.33 — but since range is integer, perhaps leave as fraction? But instructions don't say. Let’s go with 93.3)
Wait — actually, looking ahead, Set 4 has large numbers, probably expects decimal. Let’s proceed.
- Median: Sorted: 89, 93, 93, 95, 95, 95 → even number of values → average of 3rd and 4th:
3rd = 93, 4th = 95 → (93 + 95)/2 = 188/2 = 94
- Mode: 95 appears three times → 95
- Range: 95 - 89 = 6
✔ Final for Set 3:
MEAN: 93.3 (or 93.33? Let’s recalculate division: 560 ÷ 6 = 93.333... → typically written as 93.3 if rounding to tenths. But to be precise, maybe write 93.33? However, in elementary/middle school, often one decimal place. Let’s stick with 93.3)
Actually, let me check: 6 × 93.3 = 559.8 → close to 560. 6 × 93.33 = 559.98 → still not exact. Better to write as fraction? But the worksheet likely expects decimal. Since 560 ÷ 6 = 93 1/3, which is 93.333..., so perhaps write 93.3 or 93.33? I think for consistency, let’s use 93.3 (tenths place).
But wait — let’s look at Set 4: 343, 270, 221, 270 — sum is 343+270=613; +221=834; +270=1104; divided by 4 = 276 → whole number. So maybe Set 3 should be exact? 560/6 = 280/3 ≈ 93.333 — so perhaps write 93.3 or 93.33? I think safest is to write 93.3 as per common practice.
Alternatively, maybe I miscalculated the sum? Let me add again:
List: 89, 93, 93, 95, 95, 95
Add pairs:
89 + 95 = 184
93 + 95 = 188
93 + 95 = 188
Now: 184 + 188 = 372; 372 + 188 = 560 → yes.
So mean = 560/6 = 93.333... → I’ll write 93.3 for now.
But to be accurate, let’s note that in some contexts, they might expect the fractional form, but since the worksheet has blanks without specification, and other answers are decimals or integers, I’ll use 93.3.
Actually, let’s move on and come back if needed.
- Median: as above, 94
- Mode: 95
- Range: 6
✔ Set 3: MEAN: 93.3, MODE: 95, MEDIAN: 94, RANGE: 6
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Sort: 221, 270, 270, 343
- Mean: 221 + 270 + 270 + 343 =
221 + 270 = 491
491 + 270 = 761
761 + 343 = 1104
Count = 4 → 1104 ÷ 4 = 276
- Median: Even number → average of 2nd and 3rd: both 270 → (270 + 270)/2 = 270
- Mode: 270 appears twice → 270
- Range: 343 - 221 = 122
✔ Set 4:
MEAN: 276
MODE: 270
MEDIAN: 270
RANGE: 122
---
Sort them: 7, 12, 16, 17, 17, 18, 19
Count = 7
- Mean: 7 + 12 = 19; +16 = 35; +17 = 52; +17 = 69; +18 = 87; +19 = 106
106 ÷ 7 ≈ ?
7 × 15 = 105 → so 106 ÷ 7 = 15.142857... → approximately 15.1 (to tenths)
Let me calculate exactly: 106 / 7 = 15.142857... → so 15.1 if rounding to tenths.
- Median: 7 numbers → 4th number in sorted list: positions: 1:7, 2:12, 3:16, 4:17, 5:17, 6:18, 7:19 → median = 17
- Mode: 17 appears twice → 17
- Range: 19 - 7 = 12
✔ Set 5:
MEAN: 15.1
MODE: 17
MEDIAN: 17
RANGE: 12
---
Sort: 202, 211, 215, 215, 275
- Mean: 202 + 211 = 413; +215 = 628; +215 = 843; +275 = 1118
Count = 5 → 1118 ÷ 5 = 223.6
- Median: 5 numbers → 3rd is 215
- Mode: 215 appears twice → 215
- Range: 275 - 202 = 73
✔ Set 6:
MEAN: 223.6
MODE: 215
MEDIAN: 215
RANGE: 73
---
Now, let’s compile all answers.
Note: For Set 3, mean is 560/6 = 93.333... — I used 93.3, but perhaps it’s better to write as 93.33? Or check if the problem expects exact value. Since 560 ÷ 6 = 93 1/3, and in decimal, it’s repeating. In many educational contexts, they might accept 93.3 or 93.33. To be safe, let’s use 93.3 as it’s consistent with Set 5 (15.1) and Set 6 (223.6), which are to one decimal place.
Set 5: 106/7 ≈ 15.142 → rounded to 15.1
Set 6: 1118/5 = 223.6 exactly
Set 1: 27/5 = 5.4 exactly
Set 2: 128/5 = 25.6 exactly
Set 3: 560/6 ≈ 93.333 → if we round to one decimal, it’s 93.3
Set 4: 276 exactly
So yes, using one decimal place where needed is fine.
Final Answers:
──────────────────────────────────────
Final Answer:
Set 1:
MEAN: 5.4
MODE: 5
MEDIAN: 5
RANGE: 7
Set 2:
MEAN: 25.6
MODE: 28
MEDIAN: 28
RANGE: 13
Set 3:
MEAN: 93.3
MODE: 95
MEDIAN: 94
RANGE: 6
Set 4:
MEAN: 276
MODE: 270
MEDIAN: 270
RANGE: 122
Set 5:
MEAN: 15.1
MODE: 17
MEDIAN: 17
RANGE: 12
Set 6:
MEAN: 223.6
MODE: 215
MEDIAN: 215
RANGE: 73
---
Set 1: 2, 5, 5, 6, 9
- Mean: Add all numbers → 2 + 5 + 5 + 6 + 9 = 27
Divide by count (5) → 27 ÷ 5 = 5.4
- Median: Order is already sorted: 2, 5, 5, 6, 9 → middle number is 5
- Mode: Most frequent number → 5 (appears twice)
- Range: Max - Min → 9 - 2 = 7
✔ Final for Set 1:
MEAN: 5.4
MODE: 5
MEDIAN: 5
RANGE: 7
---
Set 2: 21, 32, 28, 19, 28
First, sort them: 19, 21, 28, 28, 32
- Mean: 19 + 21 + 28 + 28 + 32 = 128 → 128 ÷ 5 = 25.6
- Median: Middle of sorted list → 28
- Mode: 28 appears twice → 28
- Range: 32 - 19 = 13
✔ Final for Set 2:
MEAN: 25.6
MODE: 28
MEDIAN: 28
RANGE: 13
---
Set 3: 95, 93, 95, 95, 89, 93
Sort them: 89, 93, 93, 95, 95, 95
- Mean: 89 + 93 + 93 + 95 + 95 + 95 = let’s add step by step:
89 + 93 = 182
182 + 93 = 275
275 + 95 = 370
370 + 95 = 465
465 + 95 = 560
Count = 6 → 560 ÷ 6 ≈ 93.333... → we can write as 93.3 or keep fraction? But since others are decimals, use decimal. Actually, 560 ÷ 6 = 93.333... → round to 93.3 if needed, but maybe exact value? Let's check: 560/6 = 280/3 ≈ 93.333 — but in school context, often rounded to tenths. However, let’s see if it divides evenly? No. So we’ll write 93.3 (rounded). Wait — actually, let me double-check addition:
Wait! I think I made a mistake.
Numbers: 95, 93, 95, 95, 89, 93
Add again:
Start with 89
+93 = 182
+93 = 275
+95 = 370
+95 = 465
+95 = 560 → yes, correct.
560 ÷ 6 = 93.333... → so 93.3 if rounding to tenths. But sometimes they want exact fraction? The problem doesn’t specify. Looking at other sets, some will be whole numbers, some not. Let’s keep it as 93.3 for now.
But wait — let me check if I miscounted the numbers. There are six numbers: yes.
Actually, let’s do this differently: group same numbers.
Three 95s: 95 × 3 = 285
Two 93s: 93 × 2 = 186
One 89: 89
Total: 285 + 186 = 471; 471 + 89 = 560 → same.
So mean = 560 / 6 = 93.333... → we'll write 93.3 (but note: in many classrooms, they might accept 93.3 or 93.33 — but since range is integer, perhaps leave as fraction? But instructions don't say. Let’s go with 93.3)
Wait — actually, looking ahead, Set 4 has large numbers, probably expects decimal. Let’s proceed.
- Median: Sorted: 89, 93, 93, 95, 95, 95 → even number of values → average of 3rd and 4th:
3rd = 93, 4th = 95 → (93 + 95)/2 = 188/2 = 94
- Mode: 95 appears three times → 95
- Range: 95 - 89 = 6
✔ Final for Set 3:
MEAN: 93.3 (or 93.33? Let’s recalculate division: 560 ÷ 6 = 93.333... → typically written as 93.3 if rounding to tenths. But to be precise, maybe write 93.33? However, in elementary/middle school, often one decimal place. Let’s stick with 93.3)
Actually, let me check: 6 × 93.3 = 559.8 → close to 560. 6 × 93.33 = 559.98 → still not exact. Better to write as fraction? But the worksheet likely expects decimal. Since 560 ÷ 6 = 93 1/3, which is 93.333..., so perhaps write 93.3 or 93.33? I think for consistency, let’s use 93.3 (tenths place).
But wait — let’s look at Set 4: 343, 270, 221, 270 — sum is 343+270=613; +221=834; +270=1104; divided by 4 = 276 → whole number. So maybe Set 3 should be exact? 560/6 = 280/3 ≈ 93.333 — so perhaps write 93.3 or 93.33? I think safest is to write 93.3 as per common practice.
Alternatively, maybe I miscalculated the sum? Let me add again:
List: 89, 93, 93, 95, 95, 95
Add pairs:
89 + 95 = 184
93 + 95 = 188
93 + 95 = 188
Now: 184 + 188 = 372; 372 + 188 = 560 → yes.
So mean = 560/6 = 93.333... → I’ll write 93.3 for now.
But to be accurate, let’s note that in some contexts, they might expect the fractional form, but since the worksheet has blanks without specification, and other answers are decimals or integers, I’ll use 93.3.
Actually, let’s move on and come back if needed.
- Median: as above, 94
- Mode: 95
- Range: 6
✔ Set 3: MEAN: 93.3, MODE: 95, MEDIAN: 94, RANGE: 6
---
Set 4: 343, 270, 221, 270
Sort: 221, 270, 270, 343
- Mean: 221 + 270 + 270 + 343 =
221 + 270 = 491
491 + 270 = 761
761 + 343 = 1104
Count = 4 → 1104 ÷ 4 = 276
- Median: Even number → average of 2nd and 3rd: both 270 → (270 + 270)/2 = 270
- Mode: 270 appears twice → 270
- Range: 343 - 221 = 122
✔ Set 4:
MEAN: 276
MODE: 270
MEDIAN: 270
RANGE: 122
---
Set 5: 7, 12, 17, 16, 18, 19, 17
Sort them: 7, 12, 16, 17, 17, 18, 19
Count = 7
- Mean: 7 + 12 = 19; +16 = 35; +17 = 52; +17 = 69; +18 = 87; +19 = 106
106 ÷ 7 ≈ ?
7 × 15 = 105 → so 106 ÷ 7 = 15.142857... → approximately 15.1 (to tenths)
Let me calculate exactly: 106 / 7 = 15.142857... → so 15.1 if rounding to tenths.
- Median: 7 numbers → 4th number in sorted list: positions: 1:7, 2:12, 3:16, 4:17, 5:17, 6:18, 7:19 → median = 17
- Mode: 17 appears twice → 17
- Range: 19 - 7 = 12
✔ Set 5:
MEAN: 15.1
MODE: 17
MEDIAN: 17
RANGE: 12
---
Set 6: 202, 211, 215, 275, 215
Sort: 202, 211, 215, 215, 275
- Mean: 202 + 211 = 413; +215 = 628; +215 = 843; +275 = 1118
Count = 5 → 1118 ÷ 5 = 223.6
- Median: 5 numbers → 3rd is 215
- Mode: 215 appears twice → 215
- Range: 275 - 202 = 73
✔ Set 6:
MEAN: 223.6
MODE: 215
MEDIAN: 215
RANGE: 73
---
Now, let’s compile all answers.
Note: For Set 3, mean is 560/6 = 93.333... — I used 93.3, but perhaps it’s better to write as 93.33? Or check if the problem expects exact value. Since 560 ÷ 6 = 93 1/3, and in decimal, it’s repeating. In many educational contexts, they might accept 93.3 or 93.33. To be safe, let’s use 93.3 as it’s consistent with Set 5 (15.1) and Set 6 (223.6), which are to one decimal place.
Set 5: 106/7 ≈ 15.142 → rounded to 15.1
Set 6: 1118/5 = 223.6 exactly
Set 1: 27/5 = 5.4 exactly
Set 2: 128/5 = 25.6 exactly
Set 3: 560/6 ≈ 93.333 → if we round to one decimal, it’s 93.3
Set 4: 276 exactly
So yes, using one decimal place where needed is fine.
Final Answers:
──────────────────────────────────────
Final Answer:
Set 1:
MEAN: 5.4
MODE: 5
MEDIAN: 5
RANGE: 7
Set 2:
MEAN: 25.6
MODE: 28
MEDIAN: 28
RANGE: 13
Set 3:
MEAN: 93.3
MODE: 95
MEDIAN: 94
RANGE: 6
Set 4:
MEAN: 276
MODE: 270
MEDIAN: 270
RANGE: 122
Set 5:
MEAN: 15.1
MODE: 17
MEDIAN: 17
RANGE: 12
Set 6:
MEAN: 223.6
MODE: 215
MEDIAN: 215
RANGE: 73
Parent Tip: Review the logic above to help your child master the concept of median and mode worksheet grade 4.
