CBSE · Class 6-12

Class 10 · Mathematics (Standard)

Unit 13 · Class 10Mathematics (Standard)

Statistics

Measures of central tendency for grouped data: mean, median, mode and their empirical relationship.

Lessons

5 concepts

1
Mean of Grouped Data
For a frequency distribution with classes and midpoints $x_i$ and frequencies $f_i$ , direct method: $\bar x = \dfrac{\sum f_i x_i}{\sum f_i}$ . Assumed-mean method: pick $a$ near the middle; $d_i = x_i - a$ ; then $\bar x …
2
Median (Grouped Data)
The median class is the class where the cumulative frequency first reaches or exceeds $n/2$ . Then median $= l + \dfrac{n/2 - cf}{f}\cdot h$ , where $l$ = lower limit of median class, $cf$ = cumulative frequency before med…
3
Mode (Grouped Data)
The modal class is the class with the highest frequency. Mode $= l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\cdot h$ , where $l$ = lower limit of modal class, $f_1$ = frequency of modal class, $f_0$ = frequency of preceding c…
4
Empirical Relationship
For a moderately asymmetrical distribution: $\text{Mode} \approx 3\text{Median} - 2\text{Mean}$ . This lets you estimate one measure if the other two are known — useful when full data is unavailable.
5
Choosing the Right Measure
Mean is affected by extreme values; median is robust; mode is used for the most frequent value (often for categorical data). In skewed distributions, median is often preferred over mean.

Skills to practise

Skill · medium

Statistics — Practice