Worksheet for practicing mean, median, mode, and range calculations with six data sets.

Let’s solve each problem step by step. We’ll find the mean, median, mode, and range for each set of numbers.

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Problem 1:

Data: {4.3, 5.2, 4.5, 5.1, 4.8, 5.4, 4.5, 4.7, 4.3, 5.2, 4.5, 4.8, 5.1}

Step 1: Order the data (smallest to largest)
→ 4.3, 4.3, 4.5, 4.5, 4.5, 4.7, 4.8, 4.8, 5.1, 5.1, 5.2, 5.2, 5.4

There are 13 numbers.

Mean: Add all numbers → divide by 13
Sum = 4.3+4.3+4.5+4.5+4.5+4.7+4.8+4.8+5.1+5.1+5.2+5.2+5.4
Let’s add in groups:
(4.3+4.3) = 8.6
(4.5×3) = 13.5
(4.7) = 4.7
(4.8×2) = 9.6
(5.1×2) = 10.2
(5.2×2) = 10.4
(5.4) = 5.4
Total = 8.6 + 13.5 = 22.1; +4.7=26.8; +9.6=36.4; +10.2=46.6; +10.4=57; +5.4=62.4
Mean = 62.4 ÷ 13 = 4.8

Median: Middle number in ordered list → 7th number → 4.8

Mode: Most frequent number → 4.5 appears 3 times → 4.5

Range: Max - Min = 5.4 - 4.3 = 1.1

✔ Final for #1: Mean=4.8, Median=4.8, Mode=4.5, Range=1.1

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Problem 2:

Data: {12.6, 12.8, 9.7, 10.4, 9.7, 10.8, 12.4, 12.8, 11.5, 10.4, 10.9, 12.8}

Order:
→ 9.7, 9.7, 10.4, 10.4, 10.8, 10.9, 11.5, 12.4, 12.6, 12.8, 12.8, 12.8
(12 numbers)

Mean: Sum ÷ 12
Add:
9.7+9.7 = 19.4
10.4+10.4 = 20.8
10.8 + 10.9 = 21.7
11.5
12.4 + 12.6 = 25.0
12.8×3 = 38.4
Total = 19.4+20.8=40.2; +21.7=61.9; +11.5=73.4; +25.0=98.4; +38.4=136.8
Mean = 136.8 ÷ 12 = 11.4

Median: Average of 6th and 7th numbers → 10.9 and 11.5 → (10.9+11.5)/2 = 22.4/2 = 11.2

Mode: 12.8 appears 3 times → 12.8

Range: 12.8 - 9.7 = 3.1

✔ Final for #2: Mean=11.4, Median=11.2, Mode=12.8, Range=3.1

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Problem 3:

Data: {-12, 7, 5, 1, 0, -2, -7, 0, -10, -3, -8, 7, 2, 4, -4, 3, -1, 0}

Order:
→ -12, -10, -8, -7, -4, -3, -2, -1, 0, 0, 0, 1, 2, 3, 4, 5, 7, 7
(18 numbers)

Mean: Sum ÷ 18
Add negatives first:
-12-10=-22; -8=-30; -7=-37; -4=-41; -3=-44; -2=-46; -1=-47
Positives: 0+0+0=0; 1+2+3+4+5+7+7 = let's do: 1+2=3; +3=6; +4=10; +5=15; +7=22; +7=29
Total sum = -47 + 29 = -18
Mean = -18 ÷ 18 = -1

Median: Average of 9th and 10th → both are 0 → 0

Mode: 0 appears 3 times → 0

Range: Max - Min = 7 - (-12) = 7 + 12 = 19

✔ Final for #3: Mean=-1, Median=0, Mode=0, Range=19

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Problem 4:

Data: {-6, -13, -8, -3, -7, -10, 2, 0, -3, -5, 5, 7, -6, 2, 1, -6, -18}

Order:
→ -18, -13, -10, -8, -7, -6, -6, -6, -5, -3, -3, 0, 1, 2, 2, 5, 7
(17 numbers)

Mean: Sum ÷ 17
Negatives:
-18-13=-31; -10=-41; -8=-49; -7=-56; -6×3=-18 → total so far: -56-18=-74? Wait — better to list:

List all:
-18, -13, -10, -8, -7, -6, -6, -6, -5, -3, -3 → that’s 11 negatives
Sum negatives:
-18-13 = -31
-31-10 = -41
-41-8 = -49
-49-7 = -56
-56-6 = -62
-62-6 = -68
-68-6 = -74
-74-5 = -79
-79-3 = -82
-82-3 = -85

Positives: 0, 1, 2, 2, 5, 7 → sum = 0+1+2+2+5+7 = 17
Total sum = -85 + 17 = -68
Mean = -68 ÷ 17 = -4

Median: 9th number in ordered list → count: 1(-18),2(-13),3(-10),4(-8),5(-7),6(-6),7(-6),8(-6),9(-5) → -5

Mode: -6 appears 3 times → -6

Range: 7 - (-18) = 25 → 25

✔ Final for #4: Mean=-4, Median=-5, Mode=-6, Range=25

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Problem 5:

Data: {0.24, 0.31, 0.43, 0.22, 0.34, 0.24, 0.35, 0.4, 0.18, 0.3, 0.29}

Order:
→ 0.18, 0.22, 0.24, 0.24, 0.29, 0.3, 0.31, 0.34, 0.35, 0.4, 0.43
(11 numbers)

Mean: Sum ÷ 11
Add:
0.18 + 0.22 = 0.40
+0.24 = 0.64
+0.24 = 0.88
+0.29 = 1.17
+0.3 = 1.47
+0.31 = 1.78
+0.34 = 2.12
+0.35 = 2.47
+0.4 = 2.87
+0.43 = 3.30
Mean = 3.30 ÷ 11 = 0.3

Median: 6th number → 0.3

Mode: 0.24 appears twice → 0.24

Range: 0.43 - 0.18 = 0.25

✔ Final for #5: Mean=0.3, Median=0.3, Mode=0.24, Range=0.25

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Problem 6:

Data: {-0.6, 0.4, 0.2, -0.3, 0.1, -0.5, 0.2, 0.4, 1.1, -0.6, 0.7, 0, 0.2, -1.3}

Order:
→ -1.3, -0.6, -0.6, -0.5, -0.3, 0, 0.1, 0.2, 0.2, 0.2, 0.4, 0.4, 0.7, 1.1
(14 numbers)

Mean: Sum ÷ 14
Negatives:
-1.3 -0.6 = -1.9; -0.6 = -2.5; -0.5 = -3.0; -0.3 = -3.3
Positives: 0 + 0.1 + 0.2×3 + 0.4×2 + 0.7 + 1.1
= 0 + 0.1 = 0.1
+0.6 (from three 0.2s) = 0.7
+0.8 (two 0.4s) = 1.5
+0.7 = 2.2
+1.1 = 3.3
Total sum = -3.3 + 3.3 = 0
Mean = 0 ÷ 14 = 0

Median: Average of 7th and 8th → 0.1 and 0.2 → (0.1+0.2)/2 = 0.15 → 0.15

Mode: 0.2 appears 3 times → 0.2

Range: 1.1 - (-1.3) = 1.1 + 1.3 = 2.4

✔ Final for #6: Mean=0, Median=0.15, Mode=0.2, Range=2.4

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Final Answer:
1) Mean=4.8, Median=4.8, Mode=4.5, Range=1.1
2) Mean=11.4, Median=11.2, Mode=12.8, Range=3.1
3) Mean=-1, Median=0, Mode=0, Range=19
4) Mean=-4, Median=-5, Mode=-6, Range=25
5) Mean=0.3, Median=0.3, Mode=0.24, Range=0.25
6) Mean=0, Median=0.15, Mode=0.2, Range=2.4