Terms Related to Statistics
Meaning
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
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:
Primary 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 Firsthanded data.
Secondary 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 Secondhanded data in nature. The secondary data can be expressed in two types. They are:
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 
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 
Frequency Distribution
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:
 Individual Series
 Discrete Series
 Continuous Series
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 
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 
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 
Cumulative Frequency
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.
Measures of the Central Tendency
Mean, Median, Quartiles and Mode are the measures of central tendency.
 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. They are primary data and secondary data.
 A tabular arrangement or data showing the frequency of each observation is called a frequency distribution.
 The median is a variate value which divides the given data into two equal parts.
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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