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

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

$\displaystyle 1019+x=1140$

$\displaystyle x=121$ IQ

Quote:

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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?

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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