Example 1. Find the mean of 4, 7, 9, 12 and 8.
- Sum = .
- Mean = .
Answer: 8
Mean, median and mode
Mean, median and mode are three ways to describe the "middle" of a data set. The mean is the average, the median is the middle value when the data is in order, and the mode is the value that occurs most often.
Formulas
Mean
Median
Mode and range
Worked examples
Example 2. Find the median of 5, 3, 9, 7, 2 and 8.
- Write them in order: 2, 3, 5, 7, 8, 9.
- There are 6 values, so average the middle two: .
Answer: 6
Example 3. Find the mode of 3, 5, 5, 2, 5, 3, 7.
- Count each value: 5 appears three times, 3 twice, the others once.
Answer: 5
Example 4. The mean of five numbers is 12. A sixth number, 18, is added. What is the new mean?
- The original sum is .
- The new sum is , shared among 6 numbers: .
Answer: 13
Common mistakes
- Finding the median without putting the numbers in order first.
- Using the middle position of the unsorted list instead of the middle value of the sorted one.
- Dividing the sum by the wrong count, especially after adding or removing a value.
Practice questions with answers
1. What is the arithmetic mean of 4, 6 and 8?
- A6
- B9
- C18
- D5
Show answer
Answer: A) 6
Mean = (4 + 6 + 8) / 3 = 18 / 3 = 6.
2. What is the mode of the data: 2, 3, 3, 4, 5?
- A2
- B3
- C4
- D5
Show answer
Answer: B) 3
The mode is the value that occurs most often. 3 appears twice, all others once, so the mode is 3.
3. Find the mean of 4, 6, 8, 10 and 12.
- A8
- B10
- C40
- D6
Show answer
Answer: A) 8
Mean = sum ÷ number of values = 40 ÷ 5 = 8. (40 is the sum, not the mean.)
4. In a colony in Nagpur, the mean monthly electricity bill of 25 houses is ₹600.
The mean bill of 10 of these houses is ₹720.
Find the mean bill of the remaining 15 houses.
The mean bill of 10 of these houses is ₹720.
Find the mean bill of the remaining 15 houses.
- A₹520
- B₹500
- C₹540
- D₹480
Show answer
Answer: A) ₹520
Total of . Total of . Remaining 15 total = 15000 - 7200 = 7800. Mean = 7800 / 15 = ₹520.
5. Over 8 days a juice stall sold these many glasses:
40, 55, 40, 60, 40, 55, 70, 40.
The owner reports the mode as the 'usual' day's sale.
What is the mode?
40, 55, 40, 60, 40, 55, 70, 40.
The owner reports the mode as the 'usual' day's sale.
What is the mode?
- A36
- B44
- C80
- D40
Show answer
Answer: D) 40
40 occurs 4 times, 55 occurs twice, others once. The most frequent value is 40, so the mode is 40.
6. Rohit's marks are 65, 70, 75, 80 and , where is more than 80. If the mean equals the median, what is ?
- A90
- B100
- C75
- D85
Show answer
Answer: D) 85
With > 80, the median is 75. Mean = 75 means total = 375, so .
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Practice by class
- Class 7 · Arithmetic Mean60 practice questions with answers
- Class 7 · Mode and Median60 practice questions with answers
- Class 8 · Mean and Median50 practice questions with answers
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the total divided by the count, the median is the middle value in order, and the mode is the most common value.
When is the median better than the mean?
When a few very large or very small values would pull the mean away from the typical value, as with incomes or house prices.
Can a data set have more than one mode, or none?
Yes. If two values tie for most frequent there are two modes. If every value occurs once, there is no mode.
How do you find the missing value if the mean is known?
Multiply the mean by the number of values to get the total, then subtract the values you already have.