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.

### NCERT Books Free Pdf Download for Class 5, 6, 7, 8, 9, 10 , 11, 12 Hindi and English Medium

 Mathematics Biology Psychology Chemistry English Economics Sociology Hindi Business Studies Geography Science Political Science Statistics Physics Accountancy