Question:
For the following distribution, calculate mean using all suitable methods:
Solution:
Direct Method:
We may prepare the table as shown:
We know that mean, $\bar{X}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$=\frac{848}{64}$
$=13.25$
Hence, the mean is 13.25.
Short-Cut Method:
We may prepare the table as shown:
Let the assumed mean be A = 12.5.
We know that mean, $\bar{X}=A+\frac{\sum f_{1} d_{1}}{\sum f_{1}}$
$=12.5+\frac{48}{64}$
$=12.5+0.75$
$=13.25$
Hence, the mean is 13.25.
Step-deviation method cannot be used to evaluate the mean of the distribution as the width of the class intervals are not equal. Here, h is not fixed.
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