Question

1. A survey was conducted to investigate motor fuel octane ratings of several blends of gasoline, and the following data is presented:

88.5	98.8	89.6	92.2	92.7	88.4	87.5	90.9
94.7	88.3	90.4	83.4	87.9	92.6	87.8	89.9
84.3	90.4	91.6	91.0	93.0	93.7	88.3	91.8
90.1	91.2	90.7	88.2	94.4	96.5	89.2	89.7
89.0	90.6	88.6	88.5	90.4	84.3	92.3	92.2
89.8	92.2	88.3	93.3	91.2	93.2	88.9
91.6	87.7	94.2	87.4	86.7	88.6	89.8
90.3	91.1	85.3	91.1	94.2	88.7	92.7
90.0	86.7	90.1	90.5	90.8	92.7	93.3
91.5	93.4	89.3	100.3	90.1	89.3	86.7
89.9	96.1	91.1	87.6	91.8	91.0	91.0

1. Construct stem-and-leaf diagram for these data and compute the sample quartiles. (10 pts)
2. Compute sample median, mode, mean, variance and standard deviation. (5 pts)
3. Construct a frequency distribution and histogram for the ratings by using eight bins. What is the shape of the distribution? (10 pts)

On Excel

Answer 1

Ans a ) the stem and leaf plot is

			Stem-and-Leaf Display
			Stem unit:	1
Statistics		83	4
Sample Size	82		84	3 3
Mean	90.52561		85	3
Median	90.4		86	7 7 7
Std. Deviation	2.905202		87	4 5 6 7 8 9
Minimum	83.4		88	2 3 3 3 4 5 5 6 6 7 9
Maximum	100.3		89	0 2 3 3 6 7 8 8 9 9
			90	0 1 1 1 3 4 4 4 5 6 7 8 9
			91	0 0 0 1 1 1 2 2 5 6 6 8 8
			92	2 2 2 3 6 7 7 7
			93	0 2 3 3 4 7
			94	2 2 4 7
			95
			96	1 5
			97
			98	8
			99
			100	3

using minitab>stat>basic stat>descriptive stat

we have

Descriptive Statistics: data

Variable Mean StDev Variance Q1 Median Q3 Mode  
data 90.526 2.905 8.440 88.575 90.400 92.200 90.1

the sample quartiles are Q1,Q2,and Q3 are  88.575 90.400 and 92.200 respectively

Ans b ) sample median = 90.4

mode= 90.1

mean=90.526

variance = 8.44

standard deviation. =2.905

Ans c ) using excel

histogram is

the shape is approximately normally distributed