Question

The following table shows the average distance, to the nearest mile, travelled per week to work by a random sample of 350 commuters.

Miles Travelled Frequency Midpoint Class Boundaries

6 - 11 43

12 - 17 32

18 – 23 80

24 - 29 120

30 - 35 75

(a) Complete the table above.

(b) What is the mean distance travelled per week by these commuters?

(c) Why is the answer for part (b) an estimate of the mean distance travelled?

(d) State one advantage and one disadvantage of using the mean as a measure of central tendency.

(e)What is the modal length of distance travelled by the commuters?

(f) Calculate the variance for the distance travelled per week by the commuters.

Answer 1

To find the boundary, you will subtract the upper class limit of the lower class from the lower class limit of the upper class, then divide the answer by 2, and finally add that answer back to the upper class limit of the lower class.

For example, if you have classes 6 - 11 and 12 - 17, you will:

Subtract 12 - 11 = 1

1 / 2 = 0.5

11 + 0.5 = 11.5

6-0.5= 5.5

mean= = 8087/350= 23.1057

variance=

Standard deviation= sqrt(57.2)= 7.56

Advantage :It is based on all observation.

Disadvantage: It is affected by outliers.

Estimated Mode = L + (f_m − f_m-1)/(f_m − f_m-1) + (f_m − f_m+1) × w

• L is the lower class boundary of the modal group
• f_m-1 is the frequency of the group before the modal group
• f_m is the frequency of the modal group
• f_m+1 is the frequency of the group after the modal group
• w is the group width

• L = 23.5
• f_m-1 = 80
• f_m = 120
• f_m+1 = 75
• w = 6

23.5 + (120 − 80)*6/(120 − 80) + (120− 75)

= 23.5+240/40+45

= 23.5+ 240/85

23.5+2.82

=26.32