Question

A random sample of 100 customers was chosen in a market between 3:00 and 4:00 PM on a Thursday afternoon. The frequency distribution below shows the distribution for checkout time, in minutes.
Checkout Time
1.0-1.9
2.0-2.9
3.0-3.9
4.0-5.9
6.0-6.9
Frequency
8
22
Missing
Missing
Missing
Cumulative Relative Frequency
Missing
Missing
0.84
0.98
1.00

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to two decimal places

(b) What percentage of checkout times was less than 3 minutes?

(c) Which of the following checkout time groups does the median of this distribution belong to? 1.0-1.9, 2.0-2.9, 3.0-3.9, 4.0-5.9, 6.0-6.9

Answer 1

Relative Frequency = Frequency for the corresponding group / Total Frequency

Cumulative relative frequency = Cumulative relative frequency till the prev corresponding group + Relative freq for the corresponding group

a) Let us fill the relative frequency and cumulative relative frequency for the first 2 groups.

Relative frequency = Cumulative relative frequency of the group - Cumulative relative frequency of the previous group

Given relative frequency, frequency of group= Total frequency * relative frequency

Check out times	Frequency	Relative Frequency	Cumulative relative frequency
1.0-1.9	8	8/100=0.8	8/100 = 0.80
2.0-2.9	22	22/100=0.22	0.80 + 0.22 = 0.3
3.0-3.9	0.54 * 100 = 54	0.84 - 0.22= 0.54	0.84
4.0-5.9	0.14 * 100 = 14	0.98 - 0.84 =0.14	0.98
6.0-6.9	0.02 * 100 = 2	1 - 0.98 = 0.02	1

Check out times	Frequency	Cumulative relative frequency
1.0 - 1.9	8	0.08
2.0-2.9	22	0.3
3.0-3.9	54	0.84
4.0-5.9	14	0.98
6.0-6.9	2	1
Total	100

b) No. of checkouts with less than 3 minutes = 8 + 22 = 30

Percentage of checkouts with less than 3 minutes = 30 /100 =0.3 or Cumulative relative frequency of group "2 - 2.9" = 0.3

c) Median is the middle element in a sorted list thus the middle value in the given distribution would be the 50th/51th value

Thus, for the given distribution median would belong to 3.0 - 3.9 group