SOCI 250 Healey 3 (Chapter 4) 1. A college polled their 2010 graduates recently

Question

SOCI 250 Healey 3 (Chapter 4)

1. A college polled their 2010 graduates recently to find out their incomes after graduating from their programs. Below are the results of the poll.
Incomes of Recent College Graduates (in $)
14000

14500

15500

16000

16350

19500

20900

21000

22900

23000

24500

25000

25000

28760

29500

29650

32000

34450

35450

39800

a. Identify and write down the formula for calculating the interquartile range (Q).
b. Calculate the interquartile range.
c. Write your results regarding the interquartile range (Q) in a sentence.
d. Identify and write down the formula for calculating the range (R).
e. Calculate the range (R).
f. Write your results regarding the range (R) in a sentence.

Explanation / Answer

a) IQR: Q3-Q1 in box plot

b) Q1: (n+1)/4 th observation= 21/4=5.25th observation= 16350+ 0.25( 19500-16350)

Q1= 17137.5

Q3: 3*(n=1)/4 th observation= 15.75th observation= 29500+0.75(29650-29500) = 29612.5

IQR= Q3-Q1 = 29612.5- 17137.5 =12475

c) Inter quantile range covers 50% data with in the data set. In a box plot middle 50% will be from 25% to 75% data will be called as Inter quantile range.

d) R= Max-Min

e) Maximum= 39800

Minimum=14000

Range= 39800-14000 =25800

f) The data set has been distributed with in interval range of 14000 to 39800.

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