Question

Mileage Ratings for 2016 Small Non-hybrid Cars 37 35 50 36 36 35 34 35 34 34 45 34 36 36 35 35 36 34 40 35 35 36 37 35 35 35 36 | 34 36 50 39 45 44 37 35 36

1.Construct a frequency distribution for the hybrid cars with a class width of 2.

2.Explain why a class width of 2 is too narrow for these data.

3.Construct a relative frequency distribution for the hybrid cars with a class width of 3, where the first class has a lower limit of 20.

4.Construct a histogram based on this relative frequency distribution. Is the histogram unimodal or bimodal? Describe the skewness, if any, in these data.

Answer 1

1)

Frequency distribution table is shown below

Mileage ratings	frequency
34-36	30
36-38	19
38-40	1
40-42	1
42-44	0
44-46	3
46-48	0
48-50	0
50-52	2
Total	56

2)

Number of observations = 56

Using Sturges' rule,

Number of class (K) = 1+3.322 log(n)

where n= number of observations

So, K= 1+ 3.322 log(56)

= 6.8075

~ 7

Therefore class width = Range / K

= (max - min) / 7

= (50 - 34) / 7

= 2.2857

~ 3

That is why class with of 2 is too narrow for these data.

3)

Relative frequency = given frequency / Total frequency

Mileage ratings	frequency(f)	Relative frequency
20-23	0	0
23-26	0	0
26-29	0	0
29-32	0	0
32-35	11	0.20
35-38	38	0.68
38-41	2	0.04
41-44	0	0.00
44-47	3	0.05
47-50	0	0.00
50-53	2	0.04
Total	56

4)

Histogram Relative frequency 1920 1988 ********** 20-23 23-26 26-29 29-32 41-44 44-47 47-50 50-53 32-35 35-38 38-41 Class interval

The mode of a data set is the value that appears the most frequently in the data set.

Unimodal is when the data set has a single mode.

Bimodal is when the data set has two different modes.

Therefore, the given histogran is unimodal.