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 |
Answer :
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.
Answer :
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.
Answer :
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.
Answer :
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
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.
Find the longest time period for which he danced.
A. 15
B. 25
C. 30
D. 20
Answer B
Solution
It is the bar with maximum height.
Find the average time for which he can dance.
A. 15.7 minutes
B. 20 minutes
C. 15 minutes
D. 17.5 minutes
Answer A
Solution
Average = (10 + 5 + 15 + 20 +25 + 20 + 15)/7 = 15.7 minutes approx.
Mean for the numbers 2, 3, 4, 5, 6, 1 is ------------.
A. 2.8
B. 3.5
C. 4.6
D. 5.4
Answer B
Solution
Add all the numbers and divide it by 6
Mean = 3.5
The range of numbers 12, 23, 45, 67, 78, 89 is ----------.
A. 65
B. 77
C. 87
D. 98
Answer B
Solution
Range = maximum value – minimum value
=89 – 12 =77
Find the median of: 23, 53, 32, 77, 87, 98, 12, 54, 76, and 53
A. 54
B. 53
C. 53.5
D. 55
Answer C
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
Find the mode for the above sequence.
A. 53
B. 23
C. 45
D. 40
Answer A
Solution
53, as it is repeated twice.
Find the mean in the above sequence.
A. 56.5
B. 45.5
C. 34.4
D. 30.5
Answer A
Solution
Step 1: Add all the numbers = 565
Step 2: Divide it by the total numbers = 10
Step 3: The mean is 56.5