class 10 maths chapter 14 statistics

1. Mean: The mean for grouped data can be found by :
   (i) The direct method =

(ii) The assumed mean method=
Where d_i = x_i-a. a = Provisional mean

(iii) The step deviation method=, where U₁ = ^X_i-a/_h

2. Mode: The mode for the grouped data can be found by using the formula :
   
   l = lower limit of the modal class.
   f₁= frequency of the modal class.
   f₀= frequency of the preceding class of the modal class.
   f₂ = frequency of the succeeding class of the modal class.
   h = size of the class interval.
   Modal class – class interval with highest frequency.
3. Median: Median of continuous series is:
   (i) (^N/₂)^th term (if number of terms are odd)

(ii) ½ [(^N/₂)^th term + (^N/₂ + 1)^th term] (if number of terms are even)

(iii) The median for the grouped data can be found by using the formula :

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

4.Empirical Formula: Mode = 3 median – 2 mean.
5.Cumulative frequency curve or an Ogive :
(i) Ogive is the graphical representation of the cumulative frequency distribution.
(ii) Less than type Ogive :
• Construct a cumulative frequency table.
• Mark the upper class limit on the x-axis.
(iii) More than type Ogive :
• Construct a frequency table.
• Mark the lower class limit on the x-axis.
(iv) To obtain the median of frequency distribution from the graph:
• Locate point of intersection of less than type Ogive and more than type Ogive :
Draw a perpendicular from this point on x-axis.
• The point at which it cuts the x-axis gives us the median.