Question

Statistic

Q2

A restaurant chain owner would like to know the sales of a certain signature dish in his restaurants. A random sample of 120 restaurants is selected and the sales of the dish in 2018 are summarized as follows.

Sales (in thousand ($))	Frequency
26 – 30	6
31 – 35	12
36 – 40	15
41 – 45	36
46 – 50	21
51 – 55	20
56 – 60	10

Q2(a) Calculate the mean, median and standard deviation of the sales.

Q2(b) Calculate the coefficient of skewness using results in (a) and interpret your result briefly.

Q2(c) Estimate, from the frequency distribution table, the number of restaurants who sales were between $38,500 and $54,500 in 2018.

Q2(d) Estimate, from the frequency distribution table, the sales amount that exceeded by 30% of the restaurants in 2018.

Answer 1

Sales (in thousand ($))	Frequency (f)	Mid value (=x)	x*f	x2*f	Cumulative frequency (< type)
26 – 30	6	28	168	4704	6
31 – 35	12	33	396	13068	18
36 – 40	15	38	570	21660	33
41 – 45	36	43	1548	66564	69
46 – 50	21	48	1008	48384	90
51 – 55	20	53	1060	56180	110
56 – 60	10	58	580	33640	120
Total=	120		5330	244200
Average=			44.41667	2035

(c)

The estimated number of restaurants who sales were between $38,500 and $54,500 in 2018=104-28=76.

(d) 30% of 120=0.30*120=36

The estimated sales amount that exceeded by 30% of the restaurants in 2018=$41000.