**MEAN (AVERAGE):** Mean [Ungrouped Data] – Mean of n observations, x_{1}, x_{2}, x_{3} … x_{n}, is

**MEAN [Grouped Data]:** The mean for grouped data can be found by the following three methods:

**(i) Direct Mean Method:**

Class Mark =

Note: Frequency of a class is centred at its mid-point called class mark.

**(ii) Assumed Mean Method:** In this, an arbitrary mean ‘a’ is chosen which is called, ‘assumed mean’, somewhere in the middle of all the values of x

**(iii) Step Deviation Method:**

**MEDIAN:** Median is a measure of central tendency which gives the value of the middle-most observation in the data.

l = Lower limit of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of preceding class; h = Class size

(iii) Representing a cumulative frequency distribution graphically as a cumulative frequency curve, or an ogive of the less than type and of the more than type. The median of grouped data can be obtained graphically as the x-coordinate of the point of intersection of the two ogives for this data.

**Mode:**

(i) Ungrouped Data: The value of the observation having maximum frequency is the mode.

(ii) Grouped Data:

l = Lower limit of modal class; f_{1} = Frequency of modal class; f_{0} = Frequency of the class preceding the modal class; f_{2} = Frequency of the class succeeding the modal class; h = Size of class interval. c.f. = Cumulative frequency of preceding class; h = Class size

Mode = 3 Median – 2 Mean

ncert solution