## Statistics and its applications

The scientific methods of collection of data, its classification and application to commerce and everyday life is called
statistics. A list of some important terms as follows:

• ungrouped data

• tabulation of data

• Range: the difference between maximum and minimum value in a given set.

• frequency

• frequency distribution

• Mean :Sum of all the events divided by the total number of events

• Median: The Median is the 'middle value' in your list

• Average is the same as mean in statistics

• Mode : The mode in a list of numbers refers to the number that occur most frequently

#### EXAMPLES

Example 1.

Given a table of debtors and creditors, comment on the growth of the company.

 Year Debtors Creditors 2000 10 15 2001 4 8 2002 7 9 2003 11 14 2004 16 20 2005 17 14 2006 12 13

Sundry creditors are more than the sundry debtors. Hence, the company's growth is very slow and declining.

Example 2.

In the above table, find out the average number of debtors the company has.

Average/ Mean = Sum of total number of debtors/ total number of years

= 77/7 = 11 debtors in an average for the years from 2000 through 2006

Example 3.

Find the median of the above table of creditors.

Step 1 given numbers in the creditors list: 15, 8, 9, 14, 20, 14 and 13

Step 2 Arrange numbers in increasing order: 8, 9, 13, 14, 14, 15 and 20

Step 3 Count the number of terms, it is 7

Step 4 the median here is the middle number = 14

Example 4.

Find the mode of the above table of debtors and creditors.

Mode is the value that occurs most frequently.

In the creditors list, 14 occurs twice while other values occur once hence 14 is the mode.

#### Try these questions

1. John wants to know how long he can dance without stopping, and decides to record how long he can dance (in minutes). The following is a graph he made to record the data. Based on the data, answer questions 1 and 2. 1. Find the longest time period for which he danced.

A. 15

B. 25

C. 30

D. 20

Solution

It is the bar with maximum height.

2. Find the average time for which he can dance.

A. 15.7 minutes

B. 20 minutes

C. 15 minutes

D. 17.5 minutes

Solution

Average = (10 + 5 + 15 + 20 +25 + 20 + 15)/7 = 15.7 minutes approx.

3. Mean for the numbers 2, 3, 4, 5, 6, 1 is ------------.

A. 2.8

B. 3.5

C. 4.6

D. 5.4

Solution

Add all the numbers and divide it by 6

Mean = 3.5

4. The range of numbers 12, 23, 45, 67, 78, 89 is ----------.

A. 65

B. 77

C. 87

D. 98

Solution

Range = maximum value – minimum value

=89 – 12 =77

5. Find the median of: 23, 53, 32, 77, 87, 98, 12, 54, 76, and 53

A. 54

B. 53

C. 53.5

D. 55

Solution

Step 1: Arrange numbers: 12, 23, 32, 53, 53, 54, 76, 77, 87, 98

Step 2: Since there are even number of events, median will be = (5th number + 6th number)/2

=(53 +54)/2 = 107/2 = 53.5

6. Find the mode for the above sequence.

A. 53

B. 23

C. 45

D. 40

Solution

53, as it is repeated twice.

7. Find the mean in the above sequence.

A. 56.5

B. 45.5

C. 34.4

D. 30.5