Question

 

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.

 

 

Answer 1

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 $=\sqrt{\dfrac{(x-\bar{x})^2}{N}}=\sqrt{\dfrac{500.07}{71}}=\sqrt{7.04}=2.65$