Selina solutions

Selina solutions

Grade 7

Data Handling | Exercise 21(B)

Question 12

Q12) The mean of six numbers :x-5,x- 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.

Solution:

The mean of six numbers are x – 5, x – 1, x, x + 2, x + 4 and x + 12 is 15

Mean=\frac{Sumofallobservations}{No.ofobservations}

Mean=\frac{((x-5)+(x-1)+(x)+(x+2)+(x+4)+(x+12))}{6}

=\frac{(x-5+x-1+x+x+2+x+4+x+12)}{6}

=\frac{(12+6x)}{6}=15

12 + 6x = 90

6x = 90 – 12

6x = 78

x=\frac{78}{6}=13

x = 13

∴ The six numbers are (13 – 5), (13 – 1), 13, (13 + 2), (13 + 4), (13 + 12) i.e. 8, 12, 13, 15, 17, 25

Now, mean of first four numbers = \frac{(8+12+13+15)}{4}=\frac{48}{4}=12

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Question 12

Q12) The mean of six numbers :x-5,x- 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.

Solution:

The mean of six numbers are x – 5, x – 1, x, x + 2, x + 4 and x + 12 is 15

Mean=\frac{Sumofallobservations}{No.ofobservations}

Mean=\frac{((x-5)+(x-1)+(x)+(x+2)+(x+4)+(x+12))}{6}

=\frac{(x-5+x-1+x+x+2+x+4+x+12)}{6}

=\frac{(12+6x)}{6}=15

12 + 6x = 90

6x = 90 – 12

6x = 78

x=\frac{78}{6}=13

x = 13

∴ The six numbers are (13 – 5), (13 – 1), 13, (13 + 2), (13 + 4), (13 + 12) i.e. 8, 12, 13, 15, 17, 25

Now, mean of first four numbers = \frac{(8+12+13+15)}{4}=\frac{48}{4}=12

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