Question

a random sample of 40 hotel reviews is drawn from a large population of hotel customers. It’s known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation

of the hotel’s star rating.

Answer 1

Solution:

The formula for mean and standard deviation for probability distribution are given as below:

Mean = ∑ XP(X)

SD = Sqrt[∑ P(X)*(X - mean)^2]

The required calculation table is given as below:

X	P(X)	XP(X)	P(X)*(X - mean)^2
1	0.3	0.3	0.675
2	0.2	0.4	0.05
3	0.2	0.6	0.05
4	0.3	1.2	0.675
Total	1	2.5	1.45

Mean = ∑ XP(X)

Mean = 2.5

SD = Sqrt[∑ P(X)*(X - mean)^2]

SD = Sqrt(1.45)

SD = 1.204159458

Required standard deviation = 1.2042