and standard deviation ( ) σ = = . EXERCISE . Find the mean and variance for each of the data in Exercies to . .
, , , , , , , . First n natural numbers . First multiples of . x i f i .
x i f i . Find the mean and standard deviation using short-cut method. x i f i Find the mean and variance for the following frequency distributions in Exercises and . .
Classes - - - - - - - Frequencies MATHEMATICS . Classes - - - - - Frequencies . Find the mean, variance and standard deviation using short-cut method Height - - - - - - -105105- - in cms No. of children .
The diameters of circles (in mm) drawn in a design are given below: Diameters - - - - - No. of circles Calculate the standard deviation and mean diameter of the circles. [ Hint First make the data continuous by making the classes as . - .
and then proceed.] . Analysis of Frequency Distributions In earlier sections, we have studied about some types of measures of dispersion. The mean deviation and the standard deviation have the same units in which the data are given. Whenever we want to compare the variability of two series with same mean, which are measured in different units, we do not merely calculate the measures of dispersion but we require such measures which are independent of the units.
The measure of variability which is independent of units is called coefficient of variation (denoted as C.V.) The coefficient of variation is defined as C.V. σ × , ≠ , where σ and x are the standard deviation and mean of the data. For