Let x i , i = 1, 2, ..., n be n observations and w i = px i + k, i = 1, 2, ..., n where p and k are constants. If the mean of x i 's is 48 and standard deviation is 12, whereas the mean of w i 's is 55 and standard deviation is 15, then the value of p and k should be

For \(w = px + k\): mean(w) = p·mean(x) + k and SD(w) = |p|·SD(x). \(15 = |p| × 12 |p| = 1.25\) \(55 = 48p + k\). With \(p = 1.25\): \(k = 55 - 60 = -5\). (\(p = -1.25\) would give \(k = 115\), which is not an option.) Answer: (A) p = 1.25, k = −5

Let xi, i = 1, 2, ..., n be n... - Solved

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Question 7

Mathematics Statistics Easy

Let xi, i = 1, 2, ..., n be n observations and wi = pxi + k, i = 1, 2, ..., n where p and k are constants. If the mean of xi's is 48 and standard deviation is 12, whereas the mean of wi's is 55 and standard deviation is 15, then the value of p and k should be

(A) p = 1.25, k = -5

(B) p = -1.25, k = 5

(C) p = 2.5, k = -5

(D) p = 25, k = 5

✓ Correct Answer: Option A Verified Solution