**Statistics**

The words ‘Statistics’ appears to have been derived from the latin word ‘status’ meaning a (political) state. In its origin, Statistic was simply the collect of data on different aspects of the life of the people.

Statistics deals with data collected for specific purposes. We can make decisions about the data by analysing and interpreting it.

**Mean**: The mean or average of a number of observation is the sum of the value of all the observation divided by the total number of the observations.

It is denoted by the symbol, read as x bar

Here n is a number of observation.

**Example-** people were asked about the time in a week they spend indoing social work in their community. They said 10, 7, 13, 20 and 15 hours respectively.Find the mean (or average) time in a week devoted by them in social work.

**Sol. **The mean =(Sum of all the observations)/(Total number of observations)

=(10 + 7 + 13 + 20 + 15)/5=65/5=13

So, the time spent by these 5 people in doing social work is 13 hours in a week.

**The median**- the median is that value of the given number of observations, which divide it into exactly two parts. when the data is arranged in ascending or decreasing order.

**The median of ungrouped data is calculated as follows:**

**(i)** When the number of observation (n) is odd, the median is the value of the ((n+1)/2)ith observation.

**Example:** If n = 15, the value of the ((15+1)/2)ith i.e. the 8^{th} observation will be median

**(ii)** When the number of observation (n) is even, the median is the mean of the (n/2)ith and (n/2+1)ith observations.

**Example:** If n = 16 the mean of the value of the (16/2)ith and (16/2+1)ith observations.

**Example:** The height (in cm) of 9 students of a class follows.

155, 152, 160, 144, 145, 148, 150, 147,149

Find the median of the data

**Sol.** Arrange the data in ascending data

144, 145, 147, 148, 149, 150, 152, 155, 160

Since the number of students is 9, an odd number.

Median is the height of the = 5^{th} student which is 149 cm

So, median = 149 cm

**Modes**: The mode is that value of the observation which occurs most frequently i.e. an observation with the maximum frequency is called the mode.

**Example: **Find the mode of the following marks (out of 10) obtained by 20 students.

4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9

**Sol. **We arrange this data in the following form:

2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 9, 9, 9, 9,10, 10

Here 9 occurs most frequently i.e. four times. So, the mode is 9.