Question

Marks of six students are tabulated below:

Name : Raj Anil Amit Om Rita Renu

Marks : 54 50 52 48 50 52

From the population, tabulated above, you are supposed to choose a sample of size two.

(a) Determine, how many samples of size two are possible

(b) Construct sampling distribution of means by taking samples of size 2 and organize the data.

Answer 1

We have given the population,

54, 50, 52, 48, 50, 52.

Sample size $n = 2.$

a.) Number of possible samples of sample size 2 without replacement $= ^6C_2 = 15$

b.)

Sampling Distribution of sample mean,

$P(X=52) = \dfrac{3}{15}$

$P(X=53) = \dfrac{2}{15}$

$P(X = 51) = \dfrac{5}{15}$

$P(X=49) = \dfrac{2}{15}$

$P(X =50) = \dfrac{3}{15}$

Mean of sampling distribution $= \dfrac{156+106+255+98+150}{15} = \dfrac{765}{15} = 51$