Statistics Mean

STATISTICS
Statistics was simply the collection and presentation of data on different aspects of the life of people, useful to
the State. Statistics deals with collection, organization, analysis and interpretation of data.
Frequency Distribution
When observations, discrete or continuous are available on a single characteristic of a large number of
individuals
Consider the marks obtained by 10 students in a biostatistics test as given below:
55 36 95 73 60 42 25 78 75 62
The data in this form is called raw data.

Consider the marks obtained (out of 100 marks) by 30 students of Class of a Collage:
10 20 36 92 95 40 50 56 60 70
92 88 80 70 72 70 36 40 36 40
92 40 50 50 56 60 70 60 60 88
Table 1
Marks Number of students
(i.e., the frequency) Cumulative Frequency(c.f.)
10 1 1
20 1 2
36 3 5
40 4 9
50 3 12
56 2 14
60 4 18
70 4 22
72 1 23
80 1 24
88 2 26
92 3 29
95 1 30
Total 30
Table 1 is called an ungrouped frequency distribution table, or simply a frequency

distribution table
The representation of the data as above is known as frequency distribution.

Marks are called the variable (x) and the 'number of students' against the marks
is known as the frequency (f) of the variable.
100 plants each were planted in 100 schools during Van Mahotsava. After one month, the
number of plants that survived were recorded as :
95 67 28 32 65 65 69 33 98 96
76 42 32 38 42 40 40 69 95 92
75 83 76 83 85 62 37 65 63 42
89 65 73 81 49 52 64 76 83 92
93 68 52 79 81 83 59 82 75 82
86 90 44 62 31 36 38 42 39 83
87 56 58 23 35 76 83 85 30 68
69 83 86 43 45 39 83 75 66 83
92 75 89 66 91 27 88 89 93 42
53 69 90 55 66 49 52 83 34 36
Table 2
Number of plants Number of schools Cumulative
survived (frequency) Frequency(c.f.)
20 - 29 3 3
30 - 39 14 17
40 – 49 12 29
50 - 59 8 37
60 – 69 18 55
70 – 79 10 65
80 - 89 23 88
90 - 99 12 100
Total 100
Mean
(i) For raw data
Mean = X   
x Sum of all the observations
N Total number of observations
(ii) For Ungrouped data
X
 fx
f
(iii) When A is assumed mean
X  A
 fd where d  X  A
f
(iv) For grouped data
X  A
 fu  i where u 
X A
f i
Example 1 : 5 people were asked about the time in a week they spend in doing
social work in their community. They said 10, 7, 13, 20 and 15 hours, respectively.
Find the mean (or average) time in a week devoted by them for social work.
Solution : the mean of a certain
number of observations is equal to Sum of all the observations
Total number of observations
Example 2 : Find mean of the temperature during a week

38.4, 40.7, 42, 41, 39.9, 40.2, 39.1
Solution :
x
 x  38.4  40.7  42  41  39.9  40.2  39.1
N 7
281.3

7
 40.2C
Example 3 : Find the average marks in statistics from the data given below
Marks 18 25 31 34 38 40 44 48 50
No. of student 7 6 4 5 11 5 1 4 2
Solution :
Marks No. of student

X f f x
18 7 126
25 6 150
31 4 124
34 5 170
38 11 418
40 5 200
44 1 44
48 4 192
50 2 100
Total 45 1524
Mean  x 
  f  x   1524
f 45
 33.87
Example 4 : Find the mean from the data given below

x 35 45 55 60 75 80
f 12 18 10 6 3 11
Solution :
Let assumed mean A = 55
X f d  x  55 f d
35 12 -20 - 240
45 18 -10 -180
55 10 0 0
60 6 5 30
75 3 20 60
80 11 25 275
Total 60 -55
Mean  x  A 
 f  d 
f
55
 55 
60
 55  0.92
 54.08
Example 5 : The weekly observations on Cost of Living Index in a city for a year
Cost of Living Index No. of weeks
272-280 6
280-288 10
288-296 16
296-304 10
304-312 8
312-320 2
Find the average weekly cost of living Index

Solution :
Let assumed mean A = 292
Cost of No. of weeks Mid Value x  A x  292 fu
Living Index x
u 
f h 8
272-280 6 276 -2 -12

280-288 10 284 -1 -10
288-296 16 292 0 0
296-304 10 300 1 10
304-312 8 308 2 16
312-320 2 316 3 6
Total 52 10
Mean  x  A 
 f u i
f
10
 292  8
52
 292  1.54
 293.54
Exercise
Q.1 The blood groups of 30 students of Class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Represent this data in the form of a frequency distribution table. Which is the most
common, and which is the rarest, blood group among these students?
Q.2 The distance (in km) of 40 engineers from their residence to their place of work were
found as follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
Construct a grouped frequency distribution table with class size 5 for the data given
above taking the first interval as 0-5 (5 not included). What main features do you
observe from this tabular representation?
Q.3 In a statistics test given to 15 students, the following marks (out of 100) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean
Q.4
Q.5 The marks obtained by 30 students of a certain Pharmacy college in a

Biostatistics paper consisting of 100 marks are presented in table below. Find the
mean of the marks obtained by the students.
Q.6
Consider the following distribution of daily wages of 50 workers of a factory
Find the mean daily wages of the workers of the factory by using an appropriate method

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STATISTICS

Consider the marks obtained by 10 students in a biostatistics test as given below:

The data in this form is called raw data.

Table 1 is called an ungrouped frequency distribution table, or simply a frequency

The representation of the data as above is known as frequency distribution.

(ii) For Ungrouped data

Example 2 : Find mean of the temperature during a week

Marks No. of student

Example 4 : Find the mean from the data given below

Let assumed mean A = 55

Find the average weekly cost of living Index

272-280 6 276 -2 -12

Q.5 The marks obtained by 30 students of a certain Pharmacy college in a

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