3 Give a brief note of the measures of central tendency together with their merits and Demerits Which is the best measure of central tendency and why?

Answer 1

ANS: Measures of central tendency will quantify the middle of the distribution. The measures in case of population are the parameters and in case of sample, the measures are statistics that are estimates of population parameters. The three most common ways of measuring the centre of distribution is the mean, mode and median.

In case of population, the measures of dispersion are used to quantify the spread of the distribution. Range, interquartile range, mean absolute deviation and standard deviation are four measures to calculate the dispersion.

The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features.

i. With respect to nature of data to cluster around a central value

ii. With respect to their spread from their central value

Arithmetic mean is defined as the sum of all values divided by number of values.

Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.

Mode is the value which has the highest frequency

The measures of variations are:

i. Range (R)

ii. Quartile Deviations ( Q.D)

iii. Mean Deviations (M.D)

iv. Standard Deviations (S.D)

Coefficient of variation is a relative measure expressed in percentage and is defined as:

CV in %=