Measures of Central Tendency Worksheet - Free Printable

Let's solve each problem step by step using the definitions provided in the image.

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Problem 1:

Data set: 1, 5, 6, 10, 7, 2, 2, 6, 2, 5

#### Step 1: Arrange the data in numerical order
We sort the numbers from smallest to largest:

Data set in order:
1, 2, 2, 2, 5, 5, 6, 6, 7, 10

#### Step 2: Find the sum of the numbers
Add all values:

1 + 2 + 2 + 2 + 5 + 5 + 6 + 6 + 7 + 10 =
= (1) + (2×3) + (5×2) + (6×2) + 7 + 10
= 1 + 6 + 10 + 12 + 7 + 10 = 46

✔ Sum of the numbers: 46

#### Step 3: Find the Mean
Mean = Sum / Number of items
There are 10 numbers.

Mean = 46 ÷ 10 = 4.6

#### Step 4: Find the Median
Since there are 10 numbers (even count), the median is the average of the 5th and 6th numbers.

Ordered list:
1, 2, 2, 2, 5, 5, 6, 6, 7, 10

5th number = 5
6th number = 5
Median = (5 + 5) ÷ 2 = 5

#### Step 5: Find the Mode
The mode is the number that appears most frequently.

- 1 → once
- 2 → three times ✔
- 5 → two times
- 6 → two times
- 7 → once
- 10 → once

So, 2 appears most often → Mode = 2

#### Step 6: Find the Range
Range = Largest value – Smallest value
= 10 – 1 = 9

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✔ Problem 1 Answers:

| Mean = | 4.6 |
|--------|-----|
| Median = | 5 |
| Mode = | 2 |
| Range = | 9 |

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Problem 2:

Data set: 5, 5, 6, 9, 4, 3, 4, 8, 10, 4

#### Step 1: Arrange the data in numerical order
Sort from smallest to largest:

3, 4, 4, 4, 5, 5, 6, 8, 9, 10

✔ Data set in order: 3, 4, 4, 4, 5, 5, 6, 8, 9, 10

#### Step 2: Find the sum of the numbers
Add all values:

3 + 4 + 4 + 4 + 5 + 5 + 6 + 8 + 9 + 10
= (3) + (4×3) + (5×2) + 6 + 8 + 9 + 10
= 3 + 12 + 10 + 6 + 8 + 9 + 10 = 58

✔ Sum of the numbers: 58

#### Step 3: Find the Mean
Mean = Sum / Number of items
= 58 ÷ 10 = 5.8

#### Step 4: Find the Median
Even number of data points (10), so median = average of 5th and 6th numbers.

Ordered list:
3, 4, 4, 4, 5, 5, 6, 8, 9, 10

5th = 5
6th = 5
Median = (5 + 5) ÷ 2 = 5

#### Step 5: Find the Mode
Look for most frequent value:

- 3 → once
- 4 → three times ✔
- 5 → two times
- 6 → once
- 8 → once
- 9 → once
- 10 → once

4 appears most often → Mode = 4

#### Step 6: Find the Range
Range = Max – Min = 10 – 3 = 7

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✔ Problem 2 Answers:

| Mean = | 5.8 |
|--------|-----|
| Median = | 5 |
| Mode = | 4 |
| Range = | 7 |

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✔ Final Answer Summary:

#### 1) Data Set: 1, 5, 6, 10, 7, 2, 2, 6, 2, 5
- In order: 1, 2, 2, 2, 5, 5, 6, 6, 7, 10
- Sum: 46
- Mean: 4.6
- Median: 5
- Mode: 2
- Range: 9

#### 2) Data Set: 5, 5, 6, 9, 4, 3, 4, 8, 10, 4
- In order: 3, 4, 4, 4, 5, 5, 6, 8, 9, 10
- Sum: 58
- Mean: 5.8
- Median: 5
- Mode: 4
- Range: 7

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