Question

QUESTION 6 Student Age Question 6 On February 15, 2013, students in STT 201 at Michigan State University were asked "How old were you on your last birthday?" Their responses are tallied in the table below. 18 19 20 21 22 23 25 Frequency 109 243 108 111 29 57 43 Find the proportion of students with age within 0.7413*IQR of the median age. a. 0.6484 b. 0.6571 c. 0.6687 d. 0.6738 e. 0.6859

Answer 1

Let us construct the cumulative frequency table

Age	Frequency	cf
18	109	109
19	243	352
20	108	460
21	111	571
22	29	600
23	57	657
25	43	700

N=700 ( total freuency )

N/ 2= 350

Median is the 350th observation

Cumulative frequency just greater than 350 is 352

Corresponding age is 19

Median age = 19

We know that IQR= Q3-Q1

where IQR= interquartile range

Q1= first quartile ( value under which 1/4th that is 25% of the observation lie )

Q3 = third quartile ( value under which 3/4th that is 75% of the observation lie )

Let us find Q1 and Q3

N/4 = 175 , first quartile is the 175th observation  

cf just greater than 175 is 352

Q1= 19

3N/4 = 525 , third quartile is the 525th observation

cf just greater than 525 is 600

Q3 = 22

IQR= 22-19=2

age within 0.7413 IQR of the median age

= ( median - 0.7413*IQR, median +0.7413 *IQR)

= (19- 0.7413*2 , 19+0.7413*2)

= (17.52 , 20.48)

Number of students within age (17.52 , 20.48) is 109+243+108= 460

Proportion of students with age within 0.7413*IQR is 460/700= 0.6571

Thus , answer is (b) 0.6571