Question

rce department was interested in the average number of company's human resou years that a person works before retiring. The sample of size 11 follows 10 16 18 19 20 21 21 22 24 24 24 i. What is the mode? What does it signify? (2 Marks) b. A ii. What is the arithmetic mean? Interpret its meaning. (2 Marks) ii What is the median? Provide an interpretation to this value. (2 Marks) iv. Based on i, ii, and ii above, describe the shape of the distribution. State the reason. (2 Marks) c. The mean income for a sample of 75 part-time assistants at IIUM is RM800; the standard deviation is RM40. i. According to Chebyshev's theorem, at least what per cent of the income will lie between RM600 and RM1000? (2 Marks) ii. How many of the part-time assistants will receive the income between RM600 and RM1000? (2 Marks) ii. If we assume that the distribution of income is symmetrical, about 99.7 percent of the observations will be between what two values? (2 Marks)

Answer 1

1)

mode =24

highest frequency number =24

maximum times number of years a person works before retirement is 24

2)arithmetic mean = total sum/# terms = 19.9091

average number of years a person works before retirement = 19.9091 years

3) median=21

median year is  21

This midpoint value is the point at which half the observations are above the value and half the observations are below the value

c)

k1=(x-µ)/(σ/√n) = (600-800)/(40/sqrt75) = -43.3013

k2 = (1000-800)/(40/sqrt75) = 43.3013

according to chybeshev theorem

proportion = 1-1/k^2 = 1 - 1/43.30^2=0.9995

so, 99.95% of income lie between RM 600 and RM1000

c3)if distribution is normal ,then 99.7% observation lie within 3 std dev away from mean

so, values are µ+/-3σ

(800-120,800+120)

(680,920)