Question

5. The following data show the yearly salaries of a random sample of Worcester residents Resident Salary (In $1,000) 97 48 69 85 92 48 79 74 For the above sample, determine the following measures (give your answer in dol- lars): a. The mean yearly salary b. The median. c. The mode. d. The 20th percentile. e. The 40th percentile. f. The 60th percentile. g. The 80th percentile.

Answer 1

Solution:

a. Mean yearly salary = sum of all salaries/number of residents

= (97+48+69+85+92+48+79+74)/8 = 74 = $74,000

b. Arranging the data in ascending order: 48,48,69,74,79,85,92,97

Median will be average of 4th and 5th number. Hence median = (74+79)/2 = 76.5 = $76500

c. Mode is the number which occurs the most. Hence mode = 48 = $48000

d.For calculating 20th percentile, multiply 0.20 by number of observation i.e 8 which comes 1.6. Rounding up to nearest whole number we get 2. The 20th percentile will be the second number in the data arranged in the ascending order. Hence, the 20th percentile is 48 or $48000.

e. Similarly for calculating 40th percentile, 0.40*8 = 3.2. Thus 3rd number will be 40th percentile which is 69 or $69000.

f. Similarly for calculating 60th percentile, 0.60*8 = 4.8. Thus 5th number will be 60th percentile which is 79 or $79000.

g. Similarly for calculating 80th percentile, 0.80*8 = 6.4. Thus 6th number will be 80th percentile which is 85 or $85000.