Question

The following is the number of minutes to commute from home to work for a group of 25 automobile executives.

31	29	28	34	38	35	18	39	35	30	50	32	29
35	24	48	29	37	13	18	28	28	31	37	41

1. How many classes would you recommend?
2. What class interval would you suggest?
3. Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution.
   1. It is not symmetric
   2. It is fairly symmetric, with most of the values between 26 and 41.
   3. It is not very symmetric, but most of the values lie between 26 and 41

Answer 1

a)

Here are total observations are 25

We will determine the number of classes using 2 to k rule

Since 16 is less than 25.

So four classes are not enough

Let us try the next highest number

Since 32 is greater than 25

So recommended number of classes are five

b)

Class interval is given as

where i is class interval

H is highest observed value

L is lowest observed value

k is no of classes

From above table

Lowest observed value =13

Highest observed value=50

k=5

So interval will be =50-13/5=37/5=7.4

Round upto then we will get the class interval is 8

So suggested interval will be eight

c)

frequency table is given as below and also graph is shown

Interval	Frequency
13 to 21	3
21 to 29	7
29 to 37	10
37 to 45	3
45 to 53	2

Graph is fairly symmetric and most of values are lying between 26 and 41