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Descriptive statistics describes precise with reference to a collection of information.

1.1 Measures Of Central Tendency:

The measures of central tendency are defined as a “statistical constants which enable us to comprehend in a single effort significance of the whole” by Professor Bowley. The measures of central tendency are also called as averages or measures of location. The measures of central tendency are:

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  • Arithmetic mean or simply mean
  • Median
  • Mode
  • Geometric mean
  • Harmonic mean

1.1.1 Arithmetic mean:

Arithmetic mean for a set of observations is the sum of the observations over the number of observations. The arithmetic mean is denoted by (X bar).

The arithmetic mean formula for the frequency, fi of the variables, xi is given as,

N is the number of observations

The formula for the grouped or continuous frequency, fi of the variables, xi with the number of observations, N and A, the arbitrary point is given as,

Where h is the common magnitude

1.1.2 Median:

The median is the value of the variable divides the observations into two equal parts. The median is called as the positional average.

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The median for a discrete frequency observation is

Step1: Find N/2, where

Step2: Cumulative frequency (c.f.)

The median is the value which is just greater than N/2 in the Cumulative frequency

The median for the grouped or continuous frequency distribution is

Where l is the lower limit of the median class, f is the frequency of the median class, h is the magnitude of the median class, c is the c.f. of the class preceding the median class and N is the number of observations.

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