hapter 14 : STATISTICS

Chapter 14 : STATISTICS

KEY POINTS

The three measures of central tendency are :
i. Mean
ii. Median
iii. Mode
• Mean Of grouped frequency distribution can be calculated by the following methods.

Direct Method

Where Xi is the class mark of the ith class interval and fi frequency of that class

Assumed Mean method or Shortcut method

Where a = assumed mean
And di = Xi - a

Step deviation method

Where a = assumed mean
h = class size
And ui = (Xi – a)/h

• Median of a grouped frequency distribution can be calculated by

Where
l = lower limit of median class
n = number of observations
cf = cumulative frequency of class preceding the median class
f = frequency of median class
h = class size of the median class.

• Mode of grouped data can be calculated by the following formula.

Where
l = lower limit of modal class
h = size of class interval
f1 = Frequency of the modal class
fo = frequency of class preceding the modal class
f2= frequency of class succeeding the modal class

•Empirical relationship between the three measures of central tendency.
3 Median = Mode + 2 Mean
Or, Mode = 3 Median – 2 Mean

• Ogive
Ogive is the graphical representation of the cumulative frequency distribution. It is of two types:
(i) Less than type ogive.
(ii) More than type ogive

• Median by graphical method
The x-coordinated of the point of intersection of ‘less than ogive’ and ‘more than ogive’ gives the
median.

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