Mean Median Mode Range Worksheets - Free Printable

Let's solve each problem step by step. For each set of data, we need to find:

- Mean: The average of the numbers.
$$
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
$$

- Median: The middle value when the data is ordered. If there's an even number of values, it's the average of the two middle numbers.

- Mode: The most frequently occurring value(s). If no number repeats, there is no mode.

- Range: The difference between the largest and smallest values.
$$
\text{Range} = \text{Max} - \text{Min}
$$

---

1) {61, 57, 49, 60, 45, 51, 57, 60, 53, 57, 55, 48, 65, 52}

Step 1: Order the data
$$
\{45, 48, 49, 51, 52, 53, 55, 57, 57, 57, 60, 60, 61, 65\}
$$

Step 2: Mean
Sum = 45 + 48 + 49 + 51 + 52 + 53 + 55 + 57 + 57 + 57 + 60 + 60 + 61 + 65
= Let's compute:
- 45+48=93; +49=142; +51=193; +52=245; +53=300; +55=355; +57=412; +57=469; +57=526; +60=586; +60=646; +61=707; +65=772
Sum = 772
Count = 14
Mean = 772 ÷ 14 ≈ 55.14

Step 3: Median
Ordered list has 14 values (even), so median = average of 7th and 8th values:
- 7th = 55, 8th = 57 → (55 + 57)/2 = 56

Step 4: Mode
Most frequent: 57 appears 3 times, 60 appears 2 times → 57

Step 5: Range
Max = 65, Min = 45 → Range = 65 - 45 = 20

✔ Answer 1:
- Mean: 55.14
- Median: 56
- Mode: 57
- Range: 20

---

2) {129, 113, 110, 123, 112, 115, 110, 124, 121, 113, 115, 121, 115}

Order:
$$
\{110, 110, 112, 113, 113, 115, 115, 115, 121, 121, 123, 124, 129\}
$$

Mean:
Sum = 110+110=220; +112=332; +113=445; +113=558; +115=673; +115=788; +115=903; +121=1024; +121=1145; +123=1268; +124=1392; +129=1521
Sum = 1521, Count = 13
Mean = 1521 ÷ 13 = 117

Median: 13 values → 7th value = 115

Mode: 115 appears 3 times → 115

Range: Max = 129, Min = 110 → 129 - 110 = 19

✔ Answer 2:
- Mean: 117
- Median: 115
- Mode: 115
- Range: 19

---

3) {-4, 7, 4, -8, 13, 4, -2, -5, 7, -6, 5, 15, -2, 1, 12, 7}

Order:
$$
\{-8, -6, -5, -4, -2, -2, 1, 4, 4, 5, 7, 7, 7, 12, 13, 15\}
$$

Mean:
Sum = (-8)+(-6)= -14; +(-5)= -19; +(-4)= -23; +(-2)= -25; +(-2)= -27; +1= -26; +4= -22; +4= -18; +5= -13; +7= -6; +7= 1; +7= 8; +12= 20; +13= 33; +15= 48
Sum = 48, Count = 16
Mean = 48 ÷ 16 = 3

Median: 16 values → average of 8th and 9th: 4 and 4 → (4+4)/2 = 4

Mode: 7 appears 3 times, others appear less → 7

Range: Max = 15, Min = -8 → 15 - (-8) = 23

✔ Answer 3:
- Mean: 3
- Median: 4
- Mode: 7
- Range: 23

---

4) {83, 77, 81, 79, 85, 77, 76, 87, 81, 83, 77, 91, 81, 77}

Order:
$$
\{76, 77, 77, 77, 77, 79, 81, 81, 81, 83, 83, 85, 87, 91\}
$$

Mean:
Sum = 76 + 77×4 = 76 + 308 = 384; +79=463; +81×3=463+243=706; +83×2=706+166=872; +85=957; +87=1044; +91=1135
Sum = 1135, Count = 14
Mean = 1135 ÷ 14 ≈ 81.07

Median: 14 values → average of 7th and 8th: 81 and 81 → (81+81)/2 = 81

Mode: 77 appears 4 times → 77

Range: Max = 91, Min = 76 → 91 - 76 = 15

✔ Answer 4:
- Mean: 81.07
- Median: 81
- Mode: 77
- Range: 15

---

5) {0.7, 0.2, 0.9, 1.2, 1.5, 0.4, 0.6, 0.2, 1.1, 0.3, 0.7, 0.2, 1.1}

Order:
$$
\{0.2, 0.2, 0.2, 0.3, 0.4, 0.6, 0.7, 0.7, 0.9, 1.1, 1.1, 1.2, 1.5\}
$$

Mean:
Sum = 0.2×3 = 0.6; +0.3=0.9; +0.4=1.3; +0.6=1.9; +0.7=2.6; +0.7=3.3; +0.9=4.2; +1.1=5.3; +1.1=6.4; +1.2=7.6; +1.5=9.1
Sum = 9.1, Count = 13
Mean = 9.1 ÷ 13 ≈ 0.7

Median: 13 values → 7th value = 0.7

Mode: 0.2 appears 3 times → 0.2

Range: Max = 1.5, Min = 0.2 → 1.5 - 0.2 = 1.3

✔ Answer 5:
- Mean: 0.7
- Median: 0.7
- Mode: 0.2
- Range: 1.3

---

6) {6.2, 5.6, 4.9, 5.1, 6.2, 5.7, 5.1, 4.7, 5.4, 6.2, 4.5, 6.4}

Order:
$$
\{4.5, 4.7, 4.9, 5.1, 5.1, 5.4, 5.6, 5.7, 6.2, 6.2, 6.2, 6.4\}
$$

Mean:
Sum = 4.5 + 4.7 = 9.2; +4.9 = 14.1; +5.1 = 19.2; +5.1 = 24.3; +5.4 = 29.7; +5.6 = 35.3; +5.7 = 41.0; +6.2 = 47.2; +6.2 = 53.4; +6.2 = 59.6; +6.4 = 66.0
Sum = 66.0, Count = 12
Mean = 66.0 ÷ 12 = 5.5

Median: 12 values → average of 6th and 7th: 5.4 and 5.6 → (5.4 + 5.6)/2 = 5.5

Mode: 6.2 appears 3 times → 6.2

Range: Max = 6.4, Min = 4.5 → 6.4 - 4.5 = 1.9

✔ Answer 6:
- Mean: 5.5
- Median: 5.5
- Mode: 6.2
- Range: 1.9

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✔ Final Answers Summary:

| # | Mean | Median | Mode | Range |
|---|----------|--------|--------|-------|
| 1 | 55.14 | 56 | 57 | 20 |
| 2 | 117 | 115 | 115 | 19 |
| 3 | 3 | 4 | 7 | 23 |
| 4 | 81.07 | 81 | 77 | 15 |
| 5 | 0.7 | 0.7 | 0.2 | 1.3 |
| 6 | 5.5 | 5.5 | 6.2 | 1.9 |

You can now fill these into the worksheet! Let me know if you want a printable version or explanation for any specific step.