# Thread: Average,Chebyshevs theorem,skewness

1. ## Average,Chebyshevs theorem,skewness

please solve following quesitons

Q#1The average IQ of 10 students in a mathematics course is 114.If 9 of the students have IQs of 101, 125, 118, 128, 106, 115, 99,118 and 109. What must be the other IQ? Feeling

Q#2
The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:
3.2,1.9,2.7,2.4,2.8,2.9,3.8,3.0,2.5,3.3,1.8,2.5,3. 7,2.8,2.0,3.2,2.3,2.1,2.5,1.9
Calculate the percentage of grade point averages falling in the intervals X_+2S and_+3S . Do these results agree with Chebyshevs theorem?

Q3

Calculate skewness from the following distribution by

a.the Bowleys formula
b.the Pearsonian method
data
Groups: 35-39,40-44,45-49,50-54,55-59,60-64,65-69.
Frequency: 13,15,17,28,12,10,5 respectively.

Groups
frequency
35-39
40-44
45-49
50-54
55-59
60-64
65-69
13
15
17
28
12
10
5
Thanks

2. 1.
$\displaystyle \frac{101 + 125 + 118 +128 +106 + 115+ 99 + 118 + 109+x}{10}=114$

$\displaystyle 1019+x=1140$

$\displaystyle x=121$ IQ

3. Originally Posted by nisoo-1 Q#2
The grade-point averages of 20 college seniors selected at random from the graduating class are as follows:
3.2,1.9,2.7,2.4,2.8,2.9,3.8,3.0,2.5,3.3,1.8,2.5,3. 7,2.8,2.0,3.2,2.3,2.1,2.5,1.9
Calculate the percentage of grade point averages falling in the intervals X_+2S and_+3S . Do these results agree with Chebyshev’s theorem?
Calculate the mean and standard deviation, In both cases all but one
the data points fall in the intervals, thus the proportion out side the
interval is 1/21.

Chebyshev’s inequality tells us that the proportion out side the two intervals
should be less than 1/2^2=1/4 and 1/3^3=1/9 respectivly, so Chebyshev's
inequality is satisfied.

RonL

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