create a histogram of with the data. One relatively easy way to do this is to...

create a histogram of with the data. One relatively easy way to do this is to divide the counts into 10 groups, say, each of length: (max length - min length)/10. Then compute the frequency of the data in each bin, and plot.

data: 143.344, 178.223, 165.373, 154.768, 155.56, 163.88, 178.99, 145.764, 174.974, 136.88, 173.84, 174.88, 197.091, 183.222, 138.233

please show work

Expert Solution

Maximum value of observation = 197.091

Minimum value of observation = 136.88

k = number of classes = 10

class width of each class =length of each class = (197.091 - 136.88) /10 = 6.0211 =6 (approximately)

Classes are 137-143, 143-149, 149-155,155-161,161-167,167-173,173-179,179-185,185-191,191-197

X	Approximate X
136.88	137
138.233	138
143.344	143
145.764	146
154.768	155
155.56	156
163.88	164
165.373	165
173.84	174
174.88	175
174.974	175
178.223	178
178.99	179
183.222	183
197.091	197

Frequency distribution is

Class	Frequency
137-143	2
143-149	2
149-155	1
155-161	1
161-167	2
167-173	0
173-179	5
179-185	1
185-191	0
191-197	1
Total	15

By using R

> l=seq(137,191,6)
> u=seq(143,197,6)
> x=(l+u)/2
> f=c(2,2,1,1,2,0,5,1,0,1)
> y=rep(x,f)
> b=seq(137,197,6)
> hist(y,breaks=b,xlab="Class interval",ylab="f(x)")

Histogram

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