Question

As director of human resources you have collected data on college major and commuting time (in minutes) between home and work from 20 employees. Your sample information is given in the table below.

Employee   College Major   Commuting Time
1 English 75.0
2 Math/Physics 34.2
3 Psychology 20.8
4 Economics 59.5
5 Economics 15.1
6 Math/Physics   43.3
7 English 37.9
8 Math/Physics   62.0
9 Psychology   18.6
10 Economics   16.1
11 Psychology   51.9
12 Psychology   8.0
13 Math/Physics   34.2
14 Economics   30.1
15 Math/Physics   28.7
16 Math/Physics   42.4
17 English 18.9
18 Psychology   26.0
19 Economics   14.1
20 Economics   30.5

5. Calculate the range of Commuting Time in your sample.

-Using the rule-of-thumb discussed in the learning area, how many bins do you propose to use for grouping Commuting Time?

-Create and fill in a table with columns for (1) bin, (2) absolute frequency, and (3) relative frequency.

-Draw a histogram of the relative frequency distribution of Commuting Time in your sample. How would you characterize the shape of your histogram (e.g. uniform, symmetric, etc.)?

Answer 1

Question 5

Part (i)

As per the table,

Maximum value = 75

Minimum value = 8

Step 1: Count the Number of Data Points

No. of data points in the table = 20 (sample number)

Step 2: Calculate the # of Bins, then round up

Calculation of bins = = = 4.47 5 (max round up)

Step 3: Calculate the Bin Width

Bin width = Range/number of bins = (Max-Min value)/ no. of bins = (75-8)/ 5 = 13.4 .

Part (ii)

Absolute Frequency = No. of frequency

Relative Frequency = each bin frequency/ total frequency

	Bin
Max = 75	8
Min = 8	21.4
Ban width = 13.4	34.8
	48.2
	61.6
	75

As per excel:

Bin	Absolute Frequency	Relative Frequency	Cummulative Percentage
8	1	0.05	5%
21.4	6	0.30	35%
34.8	6	0.30	65%
48.2	3	0.15	80%
61.6	2	0.10	90%
75	2	0.10	100%
Total	20	1.00

Part (iii)

The histogram is a positively skewed (or right-skewed) distribution where most values are clustered around the left tail of the distribution while the right tail is longer. Moreover, as per the central tendency measure, mean > median > mode.