Practice sheet featuring five questions designed to test students' understanding of central tendency measures like mean, median, and mode.

Here are the step-by-step solutions for each problem on your worksheet.

Problem 1

Task: Determine the mean, median, and mode of: $8, 10, 12, 12, 10, 10, 12, 8, 12$.

Step 1: Organize the data.
First, let's put the numbers in order from smallest to largest to make it easier to see patterns.
Sorted list: $8, 8, 10, 10, 10, 12, 12, 12, 12$

There are 9 numbers in total.

Step 2: Find the Mean (Average).
Add all the numbers together and divide by the count (9).
Sum: $8 + 8 + 10 + 10 + 10 + 12 + 12 + 12 + 12 = 94$
Mean: $94 \div 9 = 10.44$ (rounded to two decimal places) or $10 \frac{4}{9}$.

Step 3: Find the Median (Middle Number).
Since there are 9 numbers (an odd number), the median is the exact middle one.
Count 4 numbers from the left and 4 from the right. The one in the center is the 5th number.
Sorted: $8, 8, 10, 10, \mathbf{10}, 12, 12, 12, 12$
The median is 10.

Step 4: Find the Mode (Most Frequent).
Look at which number appears the most times.
- 8 appears 2 times.
- 10 appears 3 times.
- 12 appears 4 times.
The mode is 12.

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Problem 2

Task: What is the median of: $2, 6, 7, 8, 2$?

Step 1: Order the numbers.
Put them from least to greatest:
$2, 2, 6, 7, 8$

Step 2: Find the middle.
There are 5 numbers. The middle one is the 3rd number.
$2, 2, \mathbf{6}, 7, 8$

The median is 6.

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Problem 3

Task: Five friends bought vegetables. Mike (12 kg), Suzanne (10 kg), Sara (10 kg), Olivia (16 kg), Sam (17 kg). What is the mean weight?

Step 1: Add the weights.
$12 + 10 + 10 + 16 + 17 = 65 \text{ kg}$

Step 2: Divide by the number of friends.
There are 5 friends.
$65 \div 5 = 13$

The mean weight is 13 kg.

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Problem 4

Task: A movie row has 23 seats. Which seat is the median position?

Step 1: Understand the concept.
The median position is the exact middle seat. This means there should be an equal number of seats to the left and to the right.

Step 2: Calculate.
Since 23 is an odd number, we can find the middle by adding 1 and dividing by 2.
$(23 + 1) \div 2 = 12$

Let's check: If you sit in seat 12, there are 11 seats before you (1–11) and 11 seats after you (13–23).

You would occupy seat 12.

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Problem 5

Task: What is the mode of the following sets?

Set a: $67, 65, 72, 76, 80, 74, 74, 74$
* Look for repeats.
* 74 appears three times. All other numbers appear only once.
* Mode: 74

Set b: $11, 4, 16, 16, 17, 12, 6, 7, 9$
* Look for repeats.
* 16 appears twice. All other numbers appear only once.
* Mode: 16

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Final Answer:

1. Mean: $\approx 10.44$, Median: $10$, Mode: $12$
2. Median: $6$
3. Mean: $13 \text{ kg}$
4. Seat $12$
5. a) Mode: $74$, b) Mode: $16$