mean of 5 observations is 15. if first,second,third,fourth and fifth observations are increased by 1,2,3,4,5 resp. then find the new mean .(1 mark )

Let a,b,c,d and e are the observations of the data.Now,mean of observations = sum of observationnumber of observations15 = a+b+c+d+e5a+b+c+d+e = 75     ------1When first observation is increased by 1, second  observation is increased by 2, third  observation is increased by 3fourth  observation is increased by 4 and fifth  observation is increased by 5, then new mean is given by,     new mean = a+1+b+2+c+3+d+4+e+55new mean = a+b+c+d+e + 155new mean = 75 + 155 = 905 = 18    using 1

  • 15

Mean = Sum of observations/ Number of observations

15 = x/5

x= 15 x 5 (Bringing 5 to the other side)

x= 75

x+ 15 = 75 + 15 ( Adding 15 to both sides, since 1+2+3+4+5 = 15)

x+15 = 90

(x+15)/5 = 90/5 (Dividing both sides by 5 since the number of observations is 5)

(x+15)/5 = 16

Therefore the new mean is 16.

  • 1
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