Statistics is a branch of mathematics that deals with the interpretation of data. Statisticians work in a wide variety of fields in both the private and the public sectors.

In real life statistics, we come across numerical data in the newspapers, magazines and television regarding different aspects like increase or decrease in population, profit made by a company in different years, weather report, etc. These numerical facts are also represented by graphs which are easy to understand.

The term statistics is derived from a Latin word status meaning condition. The branch of mathematics which deals with the collection, presentation, analysis and interpretation of the numerical data is called statistics.

Terms Related to Statistics

Data:

The collection of information in the form of numerical figures, regarding different aspects of life is called data. The data can be about population, birth, death, temperature of place during a week, marks scored in the class, runs scored in different matches, etc. We need to analyze this data.

The following table gives the data regarding the number of students opting for different activities.

Activities	Dance	Music	Art	Sports
No. of students	15	25	10	40

Raw data:

When some information is collected randomly and presented, it is called a raw data.

For Example:

Given below are the marks (out of 25) obtained by 20 students of class VII A in mathematics in a test.

18, 16, 12, 10, 5, 5, 4, 19, 20, 10, 12, 12, 15, 15, 15, 8, 8, 8, 8, 16

Observation:

Each entry collected as a numerical fact in the given data is called an observation.

Array:

The raw data when put in ascending or descending order of magnitude is called an array or arrayed data.

For Example:

The above data is arranged in ascending order and represented as:

4, 5, 5, 8, 8, 8, 8, 10, 10, 12, 12, 12, 15, 15, 15, 16, 16, 18, 19, 20

Range:

The difference between the highest and the lowest value of the observation is called the range of the data.

In the above data,

Highest marks obtained = 20

Lowest marks obtained = 4

Therefore, range = 20 - 4 = 16

Mean:

It is calculated by dividing the sum of all the observation by the total number of observations. If x, x1, x3, ……… xn are n observations then

Arithmetic mean = (x1 + x2 + xn, ……………. xn)/n = (∑xi)/n

[∑ is the Greek letter sigma and is used to denote summation]

For Example:

The heights of 10 girls were measured in cm and results are as follows:

142, 149, 136, 148, 129, 140, 148, 145, 150, 133

(i) What is the height of the tallest girl?

Solution:

The height of the tallest girl is 150 cm.

(ii) What is the height of the shortest girl?

Solution:

The height of the shortest girl is 129 cm

(iii) What is the range of the data?

Solution:

Range = 150 cm – 129 cm = 21 cm

(iv) Find the mean height.

Solution:

The mean height = (142 + 149 + 136 + 148 + 129 + 140 + 148 + 145 + 150 + 133)/10

= 1420/10

= 142 cm

(v) How many girls are there whose height is less than the mean height?

Solution:

There are 4 girls whose height is less than the mean height, i.e., the girl having heights 136 cm, 129 cm, 133 cm, 140 cm.

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