Question

please help me in maths class 10 chapter 14 ​

Answer 1

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Compute the missing frequencies f

1

and f

2

in the following data if the mean is 166

26

9

and the sum of the frequencies is 52

C.I 140-150 150-160 160-170 170-180 180-190 190-200 Total

Freq. 5 f

1

20 f

2

6 2 52

Easy

Solution

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Class−Interval Class−Mark

x

i

f

i

f

i

x

i

140−150 145 5 725

150−160 155 f

1

155f

1

160−170 165 20 3300

170−180 175 f

2

175f

2

180−190 185 6 1110

190−200 195 2 390

∑f

i

=33+f

1

+f

2

∑f

i

x

i

=5525+155f

1

+175f

2

⇒ ∑f

i

=52 [ Given ]

⇒ 33+f

1

+f

2

=52

∴ f

1

+f

2

=19

∴ f

1

=19−f

2

----- ( 1 )

⇒ Mean=

∑f

i

∑f

i

x

i

⇒ 166

26

9

=

52

5525+155f

1

+175f

2

⇒

26

4325

×52=5525+155(19−f

2

)+175f

2

⇒ 8650=5525+2945−155f

2

+175f

2

⇒ 180=20f

2

∴ f

2

=9

⇒ f

1

=19−9=10

∴ f

1

=10 and f

2

=9