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Mid-value

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☼ Mid-value

= $\frac{\textup{Uppe r Limit + Lowe r Limit} }{2}$

= Lower Limit Point + $\frac{Class-Length }{2}$

= Upper Limit Point – $\frac{Class-Length }{2}$

■ Frequency : Number of observations falling in a particular class is called the frequency of that class.

■ Cumulative Frequency : The distribution of frequency in various classes is known as

$\large \mapsto$ Mean ( $\large \overline{x}$ ) : – $\large \overline{x}$ = $\frac{\sum f_{i}x_{i}}{n}$ ; n = $\sum f_{i}$

$\large \mapsto$ Median (M) [ ascending and cumulative ] : –

Median class = $\left (\frac{n}{2} \right )^{th}$ Observation & M = $L + \frac{\frac{n}{2}-cf}{f}\times C$

$\large \mapsto$ Mode (Z) [ First convert inclusive class to exclusive class ] :–

Modal Class = The class with highest frequency

Z = $L+ \frac{f_{m}-f_{1}}{2f_{m}-f_{1}-f_{2}}\times C$