Question

Hii friends

Please answer me this question..

1) The mean of 10 observation is 15.5. By an error, one observation 23 is added instead of 32. Find correct mean.

2) If the mean of the following data is 25, find k.
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x 5 15 25 35 45

f 3 k 3 6 2

Please answer these two questions

Answer 1

1)Mean =15.5
No. of observations=10
Sum of observations=Mean ×No. of observations(since Mean =Sum of observations/No. of observations)
=15.5×10
=155
No subtract the wrong observation from Sum of observations
155-23=132==>eq.1
Now add the correct observations to eq.1
132+32=164
Correct Mean=Sum of observations/No. of observations
=164/10
=16.4
2)Sum of frequencies(Sigma f)=3+k+3+6+2=14+k
x-fx
5-15
15=15k
25-75
35-210
45-90
Sum of fx(Sigma fx)=15+15k+75+210+90=390+15k
Mean=25
Sigma fx/Sigma f=25
390+15k/14+k=25
390+15k=25(14+k)
390+15k=350+25k
15k-25k=350-390
10k=40
k=40/10
k=4