CBSE Class 10 Maths Chapter 14 Statistics Notes

MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x₁, x₂, x₃ … x_n, is

MEAN [Grouped Data]: The mean for grouped data can be found by the following three methods:
(i) Direct Mean Method:

Class Mark = $\frac { Upper\quad Class\quad Limit+Lower\quad Class\quad Limit }{ 2 }$

Note: Frequency of a class is centred at its mid-point called class mark.

(ii) Assumed Mean Method: In this, an arbitrary mean ‘a’ is chosen which is called, ‘assumed mean’, somewhere in the middle of all the values of x.

…[where d_i = (x_i – a)]

(iii) Step Deviation Method:

….. [where ${ u }_{ i }=\frac { { d }_{ i } }{ h }$ , where h is a common divisor of d_i]

MEDIAN: Median is a measure of central tendency which gives the value of the middle-most observation in the data.

…where[l = Lower limit of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of preceding class; h = Class size]

(iii) Representing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type. The median of grouped data can be obtained graphically as the x-coordinate of the point of intersection of the two ogives for this data.

Mode:
(i) Ungrouped Data: The value of the observation having maximum frequency is the mode.
(ii) Grouped Data:

…where[l = Lower limit of modal class; f₁ = Frequency of modal class; f₀ = Frequency of the class preceding the modal class; f₂ = Frequency of the class succeeding the modal class; h = Size of class interval. c.f. = Cumulative frequency of preceding class; h = Class size]

Mode = 3 Median – 2 Mean
Median = $\frac { Mode+2Mean }{ 3 }$
Mean = $\frac { 3Median-Mode }{ 2 }$