Question

the mean of a set of 30 observations is 75. If each observation is multiplied by a non zero number lemda and then each of them is decreased by 25, their mean remains the same. Then lemda is equal to

Answer 1

The λ is equal to $\frac{4}{3}$.

• Let us consider the sum of 30 observations to be 'x'.
• Now the mean of 30 observations is 75.
• Therefore the sum of 30 observations(x) will be equal to 75 × 30.
• Now that each observation is multiplied by 'λ' and decreased by 25, the sum of those observations will be x.λ that is (75 × 30)λ -25 ×30
• According to the given condition, both the means are equal.
• AS the number of observations are equal there sum will also be equal.

(75 × 30)λ -25 ×30 = 75 × 30

75λ - 25 = 75

75λ = 100

λ = $\frac{4}{3}$