Statistics is the branch of science which deal's with the collection or arrangement of data, classification or tabulation of data, analysis of data and drawing a conclusion from the analysis of the required objectives.
Statistical Data refers to the set of numerical facts collected for the purpose of an investigation is called statistical data. There are two types of data:
The data which are naturally obtained by the investigator himself for the first time for his own use is called primary data. Primary data are also called First-handed data.
The data which was collected by someone from the help of primary data is called secondary data, is artificial in nature. They are also called as Second-handed data in nature. The secondary data can be expressed in two types. They are:
a) Raw or Ungrouped data:
Raw or Ungrouped data are those types of data which are obtained in original form. For example, look the following means of 10 students in class test in Optional Maths.
20 |
65 |
92 |
86 |
35 |
57 |
78 |
83 |
40 |
50 |
b) Array:
Simply, array refers to the arrangement of data in ascending or descending of data order. Generally, Arrays are the data which are put in the form of a table which is also called the presentation of data. If the number of times an observation occurs, then it is called frequency of distribution.
For example,
20, 15, 30, 10, 25, 30, 35
Now,
Arranging this data in ascending order,
10, 15, 20, 25, 30, 30, 35
Considering it in tabular form,
Variable | 10 | 15 | 20 | 25 | 30 | 35 |
Frequency | 2 | 5 | 8 | 11 | 3 | 7 |
A tabular arrangement or data showing the frequency of each observation is called a frequency distribution. If the table shows the data with their corresponding frequency is called Frequency Distribution.
The frequency distribution may be divided into following types:
a) Individual Series:
If the items are listed individually then it is called individual series. In individual series, there is no frequency.
For example,
Students |
2 |
4 |
6 |
8 |
10 |
Marks |
3 |
5 |
7 |
9 |
11 |
b) Discrete Series:
If the series are formed by a discrete variable then it is called as a discrete series. In this series, the variable is taken the only exact measurement.
For example,
Marks |
5 – 10 |
10 – 15 |
15 – 20 |
20 – 25 |
25 – 30 |
No. of students |
4 |
8 |
12 |
16 |
20 |
c) Continuous Series:
If the variable is represented in a continuous way then it is called continuous series. In this series, variable lies in two groups which are called class interval.
For example,
Marks |
5 – 10 |
10 – 15 |
15 – 20 |
20 – 25 |
25 – 30 |
No. of students |
4 |
8 |
10 |
14 |
16 |
The sum of all the frequencies of all the previous class and given class is known as cumulative frequency. If the class interval is shown together with cumulative frequencies in the table then it is called cumulative frequency table.
Mean, Median, Quartiles and Mode are the measures of central tendency.
Construct a cumulative frequency table for the following data.
x | 5 | 10 | 15 | 20 | 25 | 30 |
f | 6 | 10 | 15 | 12 | 6 | 5 |
Solution:
x | f | c.f |
5 | 6 | 6 |
10 | 10 | 16 |
15 | 15 | 31 |
20 | 12 | 43 |
25 | 6 | 49 |
30 | 5 | 54 |
N = 54 |
Solution:
Marks | Frequency | c.f |
30 - 40 | 6 | 6 |
40 - 50 | 6 | 12 |
50 - 60 | 9 | 21 |
60 - 70 | 4 | 25 |
70 - 80 | 5 | 30 |
80 - 90 | 6 | 36 |
90 - 100 | 4 | 40 |
N = 40 |
Solution:
marks | frequency | c.f |
10- 20 | 3 | 3 |
20 - 30 | 5 | 8 |
30 - 40 | 7 | 15 |
40 - 50 | 7 | 22 |
50 - 60 | 7 | 29 |
60 - 70 | 9 | 38 |
70 - 80 | 7 | 45 |
N = 45 |
Construct a cumulative frequency table for the following data:
Marks | 40 | 50 | 60 | 70 | 80 | 90 |
No. of students | 5 | 10 | 20 | 12 | 8 | 5 |
Solution:
x | f | c.f |
40 | 5 | 5 |
50 | 10 | 15 |
60 | 20 | 35 |
70 | 12 | 47 |
80 | 8 | 55 |
90 | 5 | 60 |
N = 60 |
Construct a cumulative frequency table for the following data.
x | 5 | 10 | 15 | 20 | 25 | 30 | 35 |
f | 2 | 4 | 8 | 10 | 12 | 14 | 16 |
Solution:
x | f | c.f |
5 | 2 | 2 |
10 | 4 | 6 |
15 | 8 | 14 |
20 | 10 | 24 |
25 | 12 | 36 |
30 | 14 | 50 |
35 | 16 | 66 |
N = 66 |
Construct a cumulative frequency table for the following data.
marks | 5 | 15 | 25 | 35 | 45 |
No. of students | 3 | 8 | 13 | 10 | 4 |
Solution:
x | f | c.f |
5 | 3 | 3 |
15 | 8 | 11 |
25 | 13 | 24 |
35 | 10 | 34 |
45 | 4 | 38 |
N = 38 |
Solution:
marks | frequency | c.f |
0 -10 | 6 | 6 |
10 -20 | 8 | 14 |
20 - 30 | 8 | 22 |
30 - 40 | 5 | 27 |
40 - 50 | 3 | 30 |
N = 30 |
Construct a cumulative frequency table for the following data.
x | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
f | 3 | 15 | 2 | 10 | 8 | 7 | 13 | 18 | 14 |
Solution:
x | f | c.f |
0 | 3 | 3 |
10 | 15 | 18 |
20 | 2 | 20 |
30 | 10 | 30 |
40 | 8 | 38 |
50 | 7 | 45 |
60 | 13 | 58 |
70 | 18 | 76 |
80 | 14 | 90 |
\(\therefore\) N = 90
Construct a cumulative frequency table for the following data.
Marks | 0 | 20 | 40 | 80 | 100 | 120 |
No. of students | 15 | 8 | 13 | 11 | 1 | 5 |
Solution:
X | frequency (f) | cumulative frequency (c.f.) |
0 | 15 | 15 |
20 | 8 | 23 |
40 | 13 | 36 |
80 | 11 | 47 |
100 | 1 | 48 |
120 | 5 | 53 |
N = 53 |
Contruct a cumulative frequency table for the following data.
x | 5 | 20 | 35 | 50 | 65 | 80 |
f | 4 | 13 | 11 | 3 | 5 | 8 |
Solution:
x | f | c.f |
5 | 4 | 4 |
20 | 13 | 17 |
35 | 11 | 28 |
50 | 3 | 31 |
65 | 5 | 36 |
80 | 8 | 44 |
N = 47 |
Cunstruct a cumulative frequency table for the following data.
x | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
f | 3 | 8 | 12 | 15 | 8 | 7 | 2 |
Solution:
x | f | c.f |
0 | 3 | 3 |
5 | 8 | 11 |
10 | 12 | 23 |
15 | 15 | 38 |
20 | 8 | 46 |
25 | 7 | 53 |
30 | 2 | 55 |
N = 55 |
Construct a cumulative frequency table for the following data.
x | 10 | 20 | 30 | 40 | 50 |
F | 5 | 10 | 15 | 20 | 25 |
Solution:
x | f | c.f |
10 | 5 | 5 |
20 | 10 | 15 |
30 | 15 | 30 |
40 | 20 | 50 |
50 | 25 | 75 |
N = 75 |
Construct a cumulative frequency table for the following data.
x | 0 | 10 | 20 | 30 | 40 | 50 | 60 |
f | 2 | 3 | 8 | 11 | 8 | 4 | 5 |
Solution:
x | f | c.f |
0 | 2 | 2 |
10 | 3 | 5 |
20 | 8 | 13 |
30 | 11 | 24 |
40 | 8 | 32 |
50 | 4 | 36 |
60 | 5 | 41 |
N = 41 |
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