Question

2. In a given sample data below, find the mean, median, mode, and standard deviation.22, 30,...

2. In a given sample data below, find the mean, median, mode, and standard deviation.22, 30, 26, 39, 40, 33, 26, 36.

Homework Answers

Answer #1

Solution:

x x2
22 484
30 900
26 676
39 1521
40 1600
33 1089
26 676
36 1296
∑x=252 ∑x2=8242



Mean ˉx=∑xn

=22+30+26+39+40+33+26+36/8

=252/8

=31.5


Median :
Observations in the ascending order are :
22,26,26,30,33,36,39,40

Here, n=8 is even.

M=Value of(n2)thobservation+Value of(n2+1)thobservation2

=Value of(82)thobservation+Value of(82+1)thobservation2

=Value of4thobservation+Value of5thobservation2

=30+332

=31.5


Mode :
In the given data, the observation 26 occurs maximum number of times (2)

∴Z=26


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√8242-(252)28/7

=√8242-7938/7

=√304/7

=√43.4286

=6.59

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