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RD Chapter 7 Statistics Ex 7.1 Solutions

Question - 11 : - The arithmetic mean of the following data is 14, find the value of k. (C.B.S.E. 2002C)

X

5

10

15

20

25

f

7

k

8

4

5

Answer - 11 : -


⇒ 14 (24 + k) = 360 + 10k
⇒ 336 + 14k = 360 + 10k
⇒ 14k- 10k- 360 -336 24
⇒ 4k = 24
⇒ k= 24/4 = 6 
Hence k = 6

Question - 12 : - The arithmetic mean of the following data is 25, find the value of k. (C.B.S.E. 2001)

X

5

15

25

35

45

f

3

k

3

6

2

Answer - 12 : -

Mean =25
 
⇒ 25 (14 + k) = 390 + 15k
⇒ 350 + 25k= 390 + 15k
⇒ 25k- 15k = 390 -350
⇒ 10k = 40 ⇒ k = 40/10 = 4
Hence k = 4

Question - 13 : - If the mean of the following data is 18.75. Find the value of p.

X

10

15

P

25

30

f

5

10

7

8

2

Answer - 13 : -


⇒ 460 + 7p = 32 (18.75)
⇒ 460 + 7p = 600
⇒ 7p = 600 – 460 = 140
⇒ p =  140/7 = 20
∴ p = 20

Question - 14 : - Find the value of p, if the mean of the following distribution is 20.

X

15

17

19

20 + p

23

f

2

3

4

5p

6

Answer - 14 : -


⇒ 5p2 +100p + 295 = 20 (15 + 5p)
⇒ 5p2 +100p + 295 = 300 + 100p
⇒ 5p2 +100p – 100p = 300 – 295
⇒  5p2 =5 ⇒  p2 =  5/5  = 1
⇒ P= ±1
P = -1 i s not possible
∴ p= 1

Question - 15 : - Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.

Answer - 15 : -


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