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1 , 5, 6 ,5 ,8 ,7 ,5 ,10 ,0 , 2
1 ,2 , ,3,10 ,22, 8 ,7 ,9 ,15
The above are the marks obtain by the students of class 7 in math in dictation . The numerical figures are called data. Statistics is a branch of mathematically related with the collection of different thing which is shown by figures . It analysis the data. The data should be always shown proper order so that it will be easier to get the important and necessary information for which they are collected . The data are always arranged in ascending or descending order , which is known as a proper order.
The data which arranged properly are called arrayed data. If the data are not arranged properly then they are said raw data . Data are always can be present in a bar graph or in a line graph.
8 6 7 9 8 6 7 8
8 6 8 8 7 8 7 9
6 6 6 7 7 7 7 8
8 8 8 8 8 8 9 9
Here ,
Wages (in Rs ) | Tally marks | Frequency |
6 | ||| | 3 |
7 | |||| | 4 |
8 | \(\enclose{horizontalstrike}{||||}\) || | 7 |
Total | 14 |
The data and their frequencies can be shown in the table called frequency table . So, the above wages of 14workers in the frequency table . It is the system of showing frequencies by using diagonal lines grouped in five when each time five is reached , there is a horizontal line is drawn with the tally marks to make a group of five . For example :
1 | | |
2 | | | |
3 | ||| |
4 | |||| |
5 | \(\enclose{horizontalstrike}{||||}\) |
6 | \(\enclose{horizontalstrike}{||||}\) | |
7 | \(\enclose{horizontalstrike}{||||}\) || |
8 | \(\enclose{horizontalstrike}{||||}\) ||| |
9 | \(\enclose{horizontalstrike}{||||}\) |||| |
10 | \(\enclose{horizontalstrike}{||||}\) \(\enclose{horizontalstrike}{||||}\) |
Bar graph
There are mainly two types of a bar graph . They are described below :
Simple bar graph : The data which is presented single or the graph which is drawn to present single type of data is called simple bar graph . In a simple bar, data are equally wide . The height of the bars represents the frequency at the data.
Multiple bar graph : Multiple bar graph is drawn to or more than two related components of the given data.
Average ( or mean )
The single number which represents the central value of a set of data is known as average . It indicated or show the quality of the data . It is calculated by adding them together and dividing the sum by the number of data.
Average = \(\frac{Total sum of data}{Number of data}\)
If x is used to represent the data and n is used to represent the number of data , then,
Average = \(\frac{∑x}{n}\)
Here , the symbol '∑' means the summation of whole data.
Mean or average of ungrouped repeated data
Following are the steps given below to calculate the mean of ungrouped repeated data .
Solution:
Let's present the above data of 16 workers in frequency table:
Wages () | Tally Marks |
Frequency |
60 | ||| | 3 |
70 | |||| | 4 |
80 |
|||| || |
7 |
90 | || | 2 |
Total | 16 |
The data which are presented properly are called ______ data .
A ______ is drawn to show two or more related components of the given data.
A ______ is drawn to present a single type of data.
The systematical numerical figures are called ______ .
A ______ is the number of times of a value occurs.
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