Question

Students at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have to commute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in the school newspaper, contains the following histogram summarizing the commute distances for a sample of 60 students at the university: Frequency 30+ 10 10 4 8 12 Commute distance (in miles) 16 Based on this histogram, estimate the standard deviation of the sample of 60 distances. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place. (If necessary, consult a list of formulas.) x 6 ?

Answer 1

answer)

To find the standard deviation we will first consider the mid point

2 with frequency 5

6 with frequency 5

10 with frequency 30

14 with 10

18 with 10

First we need to estimate the mean

Mean = (sum of midpoint*frequency)/(sum of frequencies)

Mean = (2*5 + 6*5 + 10*30 + 14*10 + 18*10)/(5+5...)

Mean = 11

Now we need to subtract mean from each and every observations and take the square

(2-11)^2, (6-11)^1...

Now we need to multiply them with their respective frequencies and add them

(2-11)^2*5 + (6-11)^2*5....

= 1140

Now we need to divide 1140 by n-1 (sum of frequencies - 1) and take the square root

S.d = 4.396