- Statistics is branch of mathematics that deals with collection, presentation, analysis and interpretation of numerical data.
- Range of the data is obtained by the difference between the maximum and the minimum values of the observations.
Frequency distribution table
- A table that shows the frequency of different values in the given data is known a frequency distribution table
- A frequency distribution table that shows the frequency of each individual observation in the given data is called an ungrouped frequency distribution table.
Suppose a survey is conducted in
which we ask 15 households of a building about how many pets they have in their
home. The results are as follows:
1, 2, 4, 1, 2, 7, 3, 8, 6, 1,
3, 1, 5, 4, 2, 5 [Raw data]
1, 1, 1, 1, 2, 2, 2, 3, 3, 4,
5, 5, 6, 7, 8 [Arranged data]
Data arranged in ungrouped frequency
distribution table.
|
Number of pets (xi) |
Number of families (fi) |
|
1 |
4 |
|
2 |
3 |
|
3 |
2 |
|
4 |
1 |
|
5 |
2 |
|
6 |
1 |
|
7 |
1 |
|
8 |
1 |
- A table that shows the frequency of groups of observations in the given data is called a grouped frequency distribution table.
Data arranged in grouped frequency
distribution table.
|
Class interval |
Number of pets (fi) |
|
1 - 2 |
4 |
|
2 - 3 |
3 |
|
3 - 4 |
2 |
|
4 - 5 |
1 |
|
5 - 6 |
2 |
|
6 - 7 |
1 |
|
7 - 8 |
1 |
|
8 - 9 |
1 |
- The groupings used to group the values in given data are called classes or class-intervals.
- The number of values that each class contains is called the class size or class width. The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit.
- Class mark of a class is the mid value of the two limits
of that class.
- A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.
- A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution.
Mean of Data:
The mean, is called the average, of a
numerical set of data.
It is obtained simply the sum of the data values
divided by the number of values.
It is also referred to as the arithmetic mean. The
mean is the balance point of a distribution.
If the values of the observations are x
x̄ = (x
x̄ = ∑x
Examples:
Nikkei has been working on programing and updating
a Web site for his company for the past 15 months. The following numbers
represent the number of hours Nikkei has worked on this Website building for
each of the past 7 months:
24, 28, 31, 50, 53, 66, 78
We have to find the mean (average) number of hours
that Nikkei worked on this Web site each month?
Step 1: Add the numbers to determine the total
number of hours he worked.
24 + 28 + 37
+ 50 + 53 + 66 + 78 = 336
Step 2: Divide the total by the number of
months.
Mean=>336/7=48
Thus, Nikkei worked on this Web site each month=48
hours
Mean – Ungrouped
Data:
Suppose a survey is conducted in which we ask 15 households of a building
about how many pets they have in their home. The results are as follows:
1, 2, 4, 1, 2, 7, 3, 8, 6, 1, 3, 1, 5, 4, 2, 5 [Raw data]
1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8 [Arranged data]
|
Number of pets (xi) |
Number of families (fi) |
|
1 |
4 |
|
2 |
3 |
|
3 |
2 |
|
4 |
1 |
|
5 |
2 |
|
6 |
1 |
|
7 |
1 |
|
8 |
1 |
|
Number of pets (xi) |
Number of families (fi) |
xifi |
|
1 |
4 |
4 |
|
2 |
3 |
6 |
|
3 |
2 |
6 |
|
4 |
1 |
4 |
|
5 |
2 |
10 |
|
6 |
1 |
6 |
|
7 |
1 |
7 |
|
8 |
1 |
8 |
|
|
∑fi = 15 |
∑xifi = 51 |
Therefore, mean = ∑xifi / ∑fi = 51 / 15 = 3.4
Mean – Grouped
Data:
Suppose a survey is conducted in which we ask 15 households of a building
about how many pets they have in their home. The results are as follows:
1, 2, 4, 1, 2, 7, 3, 8, 6, 1, 3, 1, 5, 4, 2, 5 [Raw data]
1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8 [Arranged data]
|
Class interval |
Number of pets (fi) |
|
1 - 2 |
4 |
|
2 - 3 |
3 |
|
3 - 4 |
2 |
|
4 - 5 |
1 |
|
5 - 6 |
2 |
|
6 - 7 |
1 |
|
7 - 8 |
1 |
|
8 - 9 |
1 |
|
Class interval |
Number of pets (fi) |
Class marks (xi) |
xifi |
|
1 - 2 |
4 |
1.5 |
6 |
|
2 - 3 |
3 |
2.5 |
7.5 |
|
3 - 4 |
2 |
3.5 |
7 |
|
4 - 5 |
1 |
4.5 |
4.5 |
|
5 - 6 |
2 |
5.5 |
11 |
|
6 - 7 |
1 |
6.5 |
6.5 |
|
7 - 8 |
1 |
7.5 |
7.5 |
|
8 - 9 |
1 |
8.5 |
8.5 |
|
|
∑fi = 15 |
|
∑xifi = 58.5 |
Therefore, mean = ∑xifi / ∑fi = 58.5 / 15 = 3.9