CFA Practice Question

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CFA Practice Question

A sample of the salaries of 4 employees from a large company was taken. The following are their salaries (in thousands of dollars) for this year: 33, 31, 24, 36. The variance of their salaries is ______.
Correct Answer: 26

The mean of these numbers is 31, and the four deviations from the mean are 2, 0, -7, and 5. Squaring these deviations and adding them gives the sum of 78 (squared deviations). Divide by m - 1 = 3 to get the variance.

User Contributed Comments 18

User Comment
kaliokale This is the sample variance not the population variance
willeen what number is m in the explanation above? thanks! F
Cooltallgal m is 4 in this case as it stands for the 4 employee's salaries.
bwbarksdale remember that the sample variance divides by "1" less than the population variance in order to achieve an "unbiased" measure of dispersion.
janetse What are the steps in BAII?
JimM Steps in BAII:
1) 2nd - DATA
2) enter the four data points as X values, leaving Y values alone (defaults to 1.0000)
3) 2nd - STAT
4) down arrow to read Sx (5.0990)
5) Variance is square of Sx, so hit x^2 button (26.0000)
albert2008 Thanks for the calc instructions!!!
JanLani Yeah, the calculator trick is greatly appreciated.
morek Anyone know instructions for HP12C? Thanks.
czim HP12c ; enter the data values using E+ in the stats function. Then key g s Enter to give you the standard deviation of the sample. simply square this to get sample variance.
tschorsch for HP12c
f Σ i.e. f SST clears stat data
33 Σ+
31 Σ+
24 Σ+
36 Σ+
g s i.e g .
g x² or enter x
DonAnd Thanks for the steps using BA11. These are one set of formulas that I made sure that I knew well so I just use the formula but the calculator steps will definitely save me some time.
harpalani Guys, can someone please explain the logic of reducing 1 from number of samples for calculating sample variance. How does the sample variance become biased when sample size is not reduced by 1?
ThomasDess Steps in BAII' - cf JimM post
3) 2nd - Stat
3') 2nd - SET - press repeatedley until the CALCULATION METHOD you want is displayed; for one-variable data set 1-V; !! - for this case we would find the same results for Sx for Lin and Exp methods but not for Ln and PWR
4) down arrow to read Sx etc
2014 Thanks Jim
bidisha wow thanks jim
Shaan23 Stop using dont understand anything and its fast without it...just find the average of the numbers 31+33+24+36/4 = 31

now just use each value and subtract the mean and square it -- Just use your head...for the first value 0 then second 2^2=4 then 7^2 =49 and 5^2 = 25....then 0 + 4 + 49 + 35 = 78

divide that by 3....

only section you need to ever use the calculator is time value calculations and stuff...
Kennyk11 Man, need to be careful with that N - 1 denominator, always gets me.... :p
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