Question

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample Size 50 18 10 17 Sample Mean 32 36 42 48The overall mean (the grand mean) for all treatments is: a. 37.3 b. 36.7 c. 48.3 d. 37.0

Answer 1

Option (b) 36.7

Explanation:

Data provided in the question:

Treatment 1 Treatment 2 Treatment 3 Treatment 4

Sample Size 50 18 10 17

Sample Mean 32 36 42 48

Now,

The overall mean is calculated as

=
`\frac{\sum_(i = 1)^(4) n_i X_i}{\sum_(i = 1)^(4) {n_i}}`

Here, Xi = Sample mean

n = sample sizes

Thus,

Overall mean

= [ (50 × 32) + (18 × 36) + (10 × 42) + (17 × 48) ] ÷ [ 50 + 18 + 10 + 17 ]

= [ 1600 + 648 + 420 + 816 ] ÷ 95

= 36.67 ≈ 36.7

hence,

Option (b) 36.7