Arithmetic Mean Property for Adding Constants
We are given that the arithmetic mean of 100 observations is 50.
A key property of the arithmetic mean is that if a constant value is added to every observation in a dataset, the mean of the dataset increases by that same constant value.
In this case:
- Original Mean (\(\bar{x}\)) = 50
- Constant Added to Each Observation = 10
Calculating the New Arithmetic Mean
Using the property mentioned above, the new arithmetic mean can be calculated directly:
\(\text{New Mean} = \text{Original Mean} + \text{Constant Added}\)
\(\text{New Mean} = 50 + 10\)
\(\text{New Mean} = 60\)
Therefore, the new arithmetic mean will be 60.
Similar Questions
- All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E ?
Important Questions from Average
The average height of 20 students of class 8 is 152 cm and the average height of 15 students of class 9 is 168 cm. What is the average height (to the nearest cm) of the students of both classes?
The average of 4, 6, 8, 12 and x is 7 and the average of x, 9, 13, 15 and y is 9. What is the value of 2x - 3y?
The average weight of 20 girls in a school was 52 kg. Two new students of weight 54 kg and 50 kg were admitted. The ratio of this new average to the old one is:
If the average of two numbers is 13 and the square root of their product is 12, then the difference between the numbers is:
If the average of 5 consecutive odd integers in increasing order is 11 , then the average of the last 3 of them is:
