Question

The following data represent the lifetimes (in hours) of a sample of 40 transistors: 112, 121, 126, 108, 141, 90, 136, 134, 121, 118, 108, 143, 108, 122, 127, 140, 113, 117, 126, 130, 134, 120, 131, 133, 118, 125, 151, 147, 137, 140, 132, 119, 110, 124, 132, 162, 135, 130, 136, 128

a) Give a cumulative relative frequency plot of these data.

b) Treating the cumulative relative frequency plot as the Cumulative Probability Distribution of an unknown continuous random variable, estimate the median of this random variable from the plot.

Answer 1

it is convention that number of class should be between 5 and 20, taking the lowest side let the number of class=k=5

(a) the following is frequency distribution for this given data

lower	upper	frequency	cumulative frequency
90	105	1	1
105	120	10	11
120	135	18	29
135	150	9	38
150	165	2	40

(b) please find the requied plot in the given image

median x such that the P(X<x)=0.5 and from the given image the median is about x=127.5 ,

as the perpendicular line from the given point touches between 120 and 135.