Answer to Question #187369 in Statistics and Probability for John

Question #187369

 

Height Frequency

 ( to nearest cm)

 150-159 11

160-169 24

170-179 21

180-189 15


a. State any assumption you make if calculating the mean and standard deviation for this data sample.​

 

b. State the boundaries and the class limits for the class interval containing the median. ​​

 

c. Which is the modal class interval and why?​

 

d. Calculate an estimate for the mean height.​

 

e. Calculate an estimate for the standard deviation.

 

 



1
Expert's answer
2021-05-07T12:04:06-0400

The continuous data distribution is-





Mean "\\bar{x}=\\dfrac{\\sum xf}{\\sum f}=\\dfrac{12079.5}{71}=170.13"


(a) The given Height has a discontinuous data- So first we converted it into continous distribution by adding 0.5 to the upper limit and subtracting 0.5 from the lower limit.


(b) Here "N=71,\\dfrac{N}{2}=\\dfrac{71}{2}=35.5"


This frequency corresponds to the class (169.5-179.5)


The boundaries are "- (169.5-179.5)"


(c) Modal class interval corresponds to the maximum frequency class i.e. "f=24"

So Modal class is "(159.5-179.5)"


(d) Mean height "\\bar{x}=\\dfrac{\\sum xf}{\\sum f}=\\dfrac{12079.5}{71}=170.13"


(e) Standard deviation "=\\sqrt{\\dfrac{(x-\\bar{x})^2}{N}}=\\sqrt{\\dfrac{500.07}{71}}=\\sqrt{7.04}=2.65"


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