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The arithmetic mean of the following data is 25, find the value of k. xi: 5, 15, 25, 35, 45

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The arithmetic mean of the following data is 25, find the value of k.

xi: 5 15 25 35 45
yi: 3 k 3 6 2
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 X y yx
5 3 15
15 k 15k
25 3 75
35 6 210
45 2 90
 N = 14 + k  \(\sum\)yx = 15k + 390

Given,

Mean = 25

\(\frac{\sum yx}{N}=25\)

\(\frac{15k+390}{14+k}=25\)

15k + 390 = 25 (14 + k)

15k + 390 = 350 + 25k

40 = 10k

k = 4

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