Sta301 Ass Sol

Question 2: (Marks: 4+8=12)
a) Show that the range is greatly affected by the extreme values; interpret the result.
996 999 9 997 995 1000 1014 1002 1001


Solution

range = greatest value-smallest value
=1014 - 9
= 1005

if we calculate without the vaule "9" then

range = 1014 - 995
= 19

interpretation
there is a big difference between the 19 and 1005
so its proved that range is affected by extreme values.

According to shebycheys thoremand according imperical rule 95%(for 2S.D) and 100%(for 3S.D) must lies between the interval.
Data is not provided here then how can we prove it??????????????????

Question 3: (Marks: 5+5=10)

Find the first two moments about mean from the following data.
X= 34, 70, 42, 54, 40, 68, 56, 38, 36, 72


Solution



Mean= 50.9 x x-mean (x-mean)^2
34 -16.9 285.61
70 19.1 364.81
42 -8.9 79.21
54 3.1 9.61
40 -10.9 118.81
68 17.1 292.41
56 5.1 26.01
38 -12.9 166.41
36 -14.9 222.01
71 20.1 404.01
total 0 1968.9

M1 = 0

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