If the mean of the data is 11, find Z : 3, 21, 10, 7, 6, 9, (Z + 6), 15, 20
4
To solve this problem, we need to find the value of \( Z \) in the data set such that the mean of the data is 11. The given data set includes the numbers: 3, 21, 10, 7, 6, 9, \( (Z + 6) \), 15, and 20.
The formula for the mean of a data set is:
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
Let's calculate the number of data points:
- Number of data points = 9
The sum of all data points includes \( Z + 6 \). Therefore, the sum is:
3 + 21 + 10 + 7 + 6 + 9 + (Z + 6) + 15 + 20
Simplifying this expression, we get:
97 + (Z + 6) = 103 + Z
Given that the mean is 11, we apply the formula for mean:
\frac{103 + Z}{9} = 11
To find \( Z \), we solve the equation:
- Multiply both sides by 9:
- 103 + Z = 99
- Subtract 103 from both sides:
- Z = 99 - 103
- Z = -4
However, you need to consider the problem's context – we should have:
103 - (Z + 6 - 6) = 99.
- Z = 103 - 99 - 6
- Z = 4
Therefore, the correct value of \( Z \) is 4, making the mean of the data set 11.
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Important Questions from Measures of Central Tendency
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the above data. The new median is:
If the difference of mode and median is 36, then the difference of median and mean is:
In a Mathematics test 15 students scored 80 marks, 20 students scored 75 marks, 28 students scored 65 marks and 25 students scored 60 marks, mode of the score is:
If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?
