Question:
The mean of $100$ observations is $50$ and their standard deviation is $5$. The sum of all squares of all the observations is
The mean of $100$ observations is $50$ and their standard deviation is $5$. The sum of all squares of all the observations is
Updated On: Jun 23, 2023
- $50000$
- $250000$
- $252500$
- $255000$
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The Correct Option is C
Solution and Explanation
$\Sigma x_{i}^{2}=n\left\{\sigma^{2}+\left(\bar{x}\right)^{2}\right\}=100\left(5^{2}+50^{2}\right)=252500$
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution