Question

A Sample of 50 Mileages for a New Midsize Model is given below.

30.8	30.8	32.1	32.3	32.7
31.7	30.4	31.4	32.7	31.4
30.1	32.5	30.8	31.2	31.8
31.6	30.3	32.8	30.7	31.9
32.1	31.3	31.9	31.7	33.0
33.3	32.1	31.4	31.4	31.5
31.3	32.5	32.4	32.2	31.6
31.0	31.8	31.0	31.5	30.6
32.0	30.5	29.8	31.7	32.3
32.4	30.5	31.1	30.7	31.4

Develop a stem-and-leaf display

Develop Class-Intervals, Frequency, Relative Frequency and Cumulative Frequency Numbers and percentages for the above data.

From data in Part b. Construct a histogram and OGIVE Chart

Calculate the 5 Metrics needed for a BOX-PLOT and construct a BOX Plot

For the data given in table above calculate Mean, Median, Mode, Range, Variance, Standard Deviation

Using Z Tables and data from part e, show detailed steps in calculating the following;

i.     Calculate Z value for 30, 31 and 32 Miles per gallons

ii.    Using Z-tables What is the probability of a car picked at random that the mileage will be above 32.5

iii.   Using Z-tables What is the probability of a car picked at random that the mileage will be below 30.5

Answer 1

A. The Stem And leaf plot as

2	9
3	0 0 0 0 0 0 0 0 0 0 0
3	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3	2 2 2 2 2 2 2 2 2 2 2 2 2 2
3	3 3

B.

Frequency Table
Class	Count	Relative frequency	Commulative Frequency
29.8-30.3	2	4	2
30.4-30.9	9	18	11
31-31.5	13	26	24
31.6-32.1	13	26	37
32.2-32.7	9	18	46
32.8-33.3	3	6	49
Total	50

Histogram as

OGIVE Chart as

Five point summary as

Population size: 50
Median: 31.55
Minimum: 29.8
Maximum: 33.3
First quartile: 30.95
Third quartile: 32.125
Interquartile Range: 1.175
Outliers: none

Mean calculated as 31.56 and Sample standard deviton as 0.80

1.Hence Z value calculated as

2.Z at 32.5

Hence the probability at above 32.5 as 0.118 as computed from table shown below.

3.Z at 30.5

Hence below 30.5 as

0.0926

Table below