Liquid products were first obtained from coal in England during the 1700s. Lamp oil was produced from coal in the United States as early as 1850,...
1). Liquid products were first obtained from coal in England during the 1700s. Lamp oil was produced from coal in the United States as early as 1850, but the domestic coal chemicals industry did not develop until World War I. A modern coal - for - recovery system uses a battery of coke ovens to produce liquid products from coal feed. These observations are obtained on the random variable X, the number of gallons of liquid product obtained per coal feed: (insert data)
| 7.6 | 8.2 | 7.1 | 10.0 | 6.5 | 9.6 |
| 6.1 | 6.2 | 7.6 | 6.2 | 9.5 | 6.7 |
| 7.4 | 9.5 | 9.2 | 8.0 | 8.5 | 9.3 |
| 8.8 | 9.6 | 9.7 | 6.8 | 7.1 | 7.7 |
| 8.7 | 7.8 | 8.7 | 8.2 | 8.2 | 7.4 |
| 9.0 | 8.8 | 7.3 | 7.9 | 7.1 | 7.9 |
| 7.6 | 6.7 | 8.1 | 6.2 | 5.3 | 7.4 |
| 7.7 | 9.1 | 7.9 | 8.7 | 8.4 | 8.1 |
a). Construct a stem – and – leaf diagram for these data. Use the numbers 5,6,7,8,9,10 as stems.
b). Is the assumption that X is normally distributed justifiable? Explain.
c). Break these data into six categories
d). Construct a frequency table and relative frequency histogram for these data. Does the histogram exhibit the bell – shape characteristics of a normal density?
e). Construct a cumulative frequency table and relative cumulative frequency ogive for these data. Use the ogive to approximate the probability that a randomly selected ton of coal will yield les than 7 gallons of liquid product.
2). Temperature different between the warm upper surface of the ocean and the colder deeper level can be utilized to convert thermal energy to mechanical energy. This mechanical energy can in turn be used to produce electrical power using a vapor turbine. Let x denote the difference in temperature between the surface of the water and the water at a depth of 1 kilometer. Measurements are taken at 15 randomly selected sites in the gulf of Mexico. These data result in the following temperature:
| 22.5 | 23.8 | 23.2 | 22.8 | 10.1 |
| 23.5 | 24.0 | 23.2 | 24.2 | 24.3 |
| 23.3 | 23.4 | 23.0 | 23.5 | 22.8 |
a) Construct a double stem-and-leaf diagram for these data.
b) Find the sample mean, sample median, and sample standard deviation for these data.
c) Note that the starred observation in the data set is very different from the others. It is potential outlier. Construct a boxplot for these data to verify that the value 10.1 dose, in fact, qualify as an outlier.
d) To see the effect of this outlier, drop it from the data set and calculate the sample mean, median, and standard deviation for the remaining 14 observation. Which measure is least affected by the presence of the outlier? Do you see why it is desirable to report both the mean and median of a data set?
