Answers
From the histogram , we observe that the it is not symmetric , the distribution is positively skewed.
First find the mean and sample standard deviation s of the given data set using the functions mean() and sd() in R respectively.
= 8.34 and s = 4.92
Therefore
- s = 8.34 - 4.92 = 3.42 and
+ s = 13.26
- 2*s = 8.34 - 9.84 = -1.50 and
+ 2*s = 8.34 + 9.84 = 18.18
- 3*s = 8.34 - 14.76 = -6.42 and
+ 3*s = 8.34 + 14.76 = 23.10
So locate -6.42,-1.50, 3.42, 13.26,18.18,23.10 on the histogram
In the range ( 3.42,13.26 ) there are 24 numbers in the data set are lies , so % of data numbers lies in interval ( - s ,
+ s ) is 24/40 = 0.6 or 60%
According to Empirical rule approximately 68% of the observations fall within ( - s ,
+ s )
In the range ( -1.50,18.18 ) there are all 40 numbers in the data set are lies , so % of data numbers lies in interval ( -2*s ,
+2* s ) is 40/40 = 1 or 100%
According to approximately 95% of the observations fall within ( -2 *s ,
+2* s )
In the range ( -6.42,23.10 ) there are all 40 numbers in the data set are lies , so % of data numbers lies in interval ( -3*s ,
+3* s ) is 40/40 = 1 or 100%
According to approximately 99.7% of the observations fall within ( -3*s ,
+3* s )
Empirical rules stated for the symmetric distribution, therefore from the above result we can say that the given distribution of the radon concentration is not symmetric.
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