Arithmetic Mean in the most common and easily understood measure of central tendency. We can define mean as the value obtained by dividing the sum of measurements with the number of measurements contained in the data set and is denoted by the symbol x¯x¯.
We're going to discuss methods to compute the Arithmetic Mean for three types of series:
· Individual Data Series
· Discrete Data Series
· Continuous Data Series
When data is given on individual basis. Following is an example of individual series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
When data is given alongwith their frequencies. Following is an example of discrete series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
0 |
5 |
7 |
When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
|
Items |
0-5 |
5-10 |
10-20 |
20-30 |
30-40 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
Arithmetic Median is a positional average and refers to the middle value in a distribution. It divides the series into two halves by first arranging the items in ascending or descending order of magnitude and then locating the middle value and is denoted by the symbol X~X~ or M.
We're going to discuss methods to compute the Arithmetic Median for three types of series:
· Individual Data Series
· Discrete Data Series
· Continuous Data Series
When data is given on individual basis. Following is an example of individual series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
When data is given alongwith their frequencies. Following is an example of discrete series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
0 |
5 |
7 |
When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
|
Items |
0-5 |
5-10 |
10-20 |
20-30 |
30-40 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
Arithmetic Mode refers to the most frequently occurring value in the data set. In other words, modal value has the highest frequency associated with it. It is denoted by the symbol MoMo or Mode.
We're going to discuss methods to compute the Arithmetic Mode for three types of series:
· Individual Data Series
· Discrete Data Series
· Continuous Data Series
When data is given on individual basis. Following is an example of individual series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
When data is given alongwith their frequencies. Following is an example of discrete series:
|
Items |
5 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
0 |
5 |
7 |
When data is given based on ranges alongwith their frequencies. Following is an example of continous series:
|
Items |
0-5 |
5-10 |
10-20 |
20-30 |
30-40 |
|
Frequency |
2 |
5 |
1 |
3 |
12 |
The Arithmetic Range of a set of data is the difference between the highest and lowest values in the set.
Arithmetic Range is defined and given by the following function:
Range=L−SRange=L−S
Where −
· LL = Largest item
· SS = Smallest item
This is an absolute measure. The relative measure called as coefficient of range is given by
Coefficient of Range=L−SL+SCoefficient of Range=L−SL+S
Problem Statement:
Cheryl took 7 math tests in one marking period. What is the range of her test scores and coeff.of range?
|
89 |
73 |
84 |
91 |
87 |
77 |
94 |
Solution:
Ordering the test scores from least to greatest, we get:
|
73 |
77 |
84 |
87 |
89 |
91 |
94 |
Range = Largest − Smallest =94−73=21Range = Largest − Smallest =94−73=21
Largest + Smallest =94+73=167Coefficient of Range=L−SL+S=21167=0.1257Largest + Smallest =94+73=167Coefficient of Range=L−SL+S=21167=0.1257
The Range of these test scores is 21 points and coeff. of range is 0.1257 points.