Question

Parts B and C

11 14 20 23 31 36 39 44 47 50 59 61 65 67 68 71 74 76 78 79 81 84 85 89 91 93 96 99 101 104 105 105 112 118 123 136 139 141 148 158 161 168 184 206 248 263 289 322 388 513 a. Why can a frequency distribution not be based on the class intervals 0-50, 50-100, 100-150, and so on? b. Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100,..., and then comment on interesting characteristics. c. Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics. d. What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?

Answer 1

b)

Frequency table:

Freq % 0-49 50-99 100-149 150-199 200-249 250-299 300-349 潔诽.ittpe> 500-549 Total 15) 22% 4% 4% 2% 2% 50

From the above histogram, we can conclude that the graph is skewed to the right.

Also, maximum points (19) lie in the class 50-99.

c)

We take the natural log of the given data points and construct class with interval of 1 units. Then we plot the frequency table and histogram.

The above histogram shows normal behaviour as the graph follows bell curve. So, natural log data points will show normal properties.