Q. 1. Define the following terms:

1. Arithmetic mean
2. Median
3. Mode
   

(i) Arithmetic mean
Ans. Arithmetic mean is used to represent the entire data by one value. Its value is obtained by adding together all the items and by dividing this total by the number of items. Symbolically:
= (X₁ + X₂ + X₃ +................. X_n)/N
or = å X/N
Where:
= Arithmetic mean
å X = Sum of all the values of variable X, i.e., X₁ + X₂ + X₃ +................. X_n
N = Number of observations

(ii) Median
Ans. The median by definition refers to the middle value in a distribution. According to Connor, " the median of a series is that value of the variable which divides the group into two equal parts, one part comprising values greater, and the other all values less than the median".

Calculation of Median – Individual Observations

• Arrange the data in ascending or descending order.
• If n is odd, median = value of [( N + 1)/2]th item.
• If it is even, then median = mean value of N/2 and [(N/2) + 1]th item.

(iii) Mode
Ans. Mode is that value in a series of observations which occurs with the greatest frequency. For example, the mode of the series 2, 4, 7, 4, 3, 4, 8, 1 would be 4, since this value occurs more frequently than any of the others.