Question

Q2 Suppose a hypothetical economy consists of 20 nonunionised private sector workers following annual earnings: $18,000, $9,000, $82,000, $12,000, $13,000, $76,000, $61,000, $14,000, $22,000, $23,000, $21,000, $46,000, $59,000, $26,000, $27,000, $37,000, $6,000, $41,000, $3,000, and $24,000.

Using annual earnings range of $10,000 (i.e. 0-$10,000, $10,000- $20,000, and so forth), construct a histogram (absolute frequency distribution) of this economy’s distribution of personal earnings. What is the mode of the histogram? What is the average (mean) level of earnings? What is the medium level of earnings? Characterize the distribution as being normal, skewed leftward, or skewed rightward. Explain.

Answer 1

A) HISTOGRAM AND DATA BELOW

B) MODE = 20000-30000 ~ 25000 (The class with highest frequency)

C) MEAN = 31000 ( TOTAL VALUE/ N no. of incomes = 620000/20 = 31000)

D) MEDIAN= 23500 (arrange data in ascending order - 3000 6000 9000 12000 13000 14000 18000 21000 22000
23000 24000 26000 27000 37000 41000 46000 59000 61000 76000 82000 = (n/2)+(n/2+1)/2 = 10 th and 11th term average = 23000+24000/2 =23500)

E) right skewed data (if we take a closer look over the histogram than we can see large lump of frequency in the starting class groups.)