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Consider the following distribution of daily wages of 50 workers of a factory.

Daily wages

100-120

120-140

140-160

160-180

180-200

No. of workers

12

14

8

6

10

Find the mean daily wages of the workers.


Daily wages (C.I.)

No. of workers (fi)

Class-Mark (xi)

fi xi

100 - 120

12

110

1320

120 - 140

14

130

1820

140 - 160

8

150

1200

160 - 180

6

170

1020

180 - 200

10

190

1900

 

Σfi = 50

 

Σfi xi = 7260


Now,

top enclose straight x space equals space fraction numerator begin display style sum from blank to blank of end style f subscript i x subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction equals 7260 over 50 equals 145.2

Hence, the mean daily wages of the workers be 145.2.
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A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as shown below, find the median marks obtained by the students of the class.


Solution not provided.

Ans.  45 Marks

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The marks obtained by 40 students of class X of a certain school in Science paper consisting of 10 marks are presented in the table below. Find the mean marks obtained by the students.

Marks obtained(xi)

5

6

7

8

9

Number of students (fi)

4

8

14

11

3


Marks Obtained (xi)

Number of students (fi)

fixi

5

4

20

6

8

48

7

14

98

8

11

88

9

3

27

 

Σfi = 40

Σfixi = 281


Now,

top enclose straight x space equals fraction numerator begin display style stack sum f subscript i x subscript i with blank below and blank on top end style over denominator begin display style sum from blank to blank of end style f subscript i end fraction equals 281 over 40 equals 7.025

Hence, the mean marks obtained is 7.025.
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What is the value of the median of the data using the graph in figure, of 'less than' ogive and 'more than ogive'?


Solution not provided.

Ans.   Median = 6
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Write the formula for finding the mode for grouped data.

Mode space equals space l italic space plus open square brackets fraction numerator straight f subscript 1 minus straight f subscript 0 over denominator 2 straight f subscript 1 minus straight f subscript 0 minus straight f subscript 2 end fraction close square brackets cross times straight h
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