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.
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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