Data Mining
Question 1:
Suppose that a hospital tested the age and body fat data for 18...
Suppose that a hospital tested the age and body fat data for 18 randomly selected adults
with the following results:
age 23 23 27 27 39 41 47 49 50
%fat 9.5 26.5 7.8 17.8 31.4 25.9 27.4 27.2 31.2
age 52 54 54 56 57 58 58 60 61
%fat 34.6 42.5 28.8 33.4 30.2 34.1 32.9 41.2 35.7
(a) Calculate the mean, median, and standard deviation of age and %fat.
(b) Draw the boxplots for age and %fat.
Solution:
a)
For Age:
Sorted values: 23, 23, 27, 27, 39, 41, 47, 49, 50, 52, 54, 54, 56, 57, 58, 58, 60, 61
Median= (50+52)/2=51
Items= N=18
Sum of all ages=Σx=836
Mean=μ= 836/14=46.44
Standard Deviation (σ):
σ2 = Σ(xi – μ)2/N
= (23 – 46.4)2 + … + (61 – 46.4)2 /18
= 2970.44/18
= 165.02
σ = √165.02
= 12.84
For Fat:
Sorted values= 7.8, 9.5, 17.8, 25.9, 26.5, 27.2, 27.4, 28.8, 30.2, 31.2, 31.4, 32.9, 33.4, 34.1, 34.6, 35.7, 41.2,
42.5
Median= (30.2+31.2)/2=30.7
N=18
Sum= Σx=518.1
Mean= μ=28.78
Standard Deviation (σ) :
σ2 = Σ(xi – μ)2/N
= (7.8 – 28.78)2 + … + (42.5 – 28.78)2 /18
= 1455.94
= 80.88
σ = √80.88
= 8.99
b)
Box plots: