- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion
CFA Practice Question
There are 410 practice questions for this study session.
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
|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.|
f Σ i.e. f SST clears stat data
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
|bidisha||wow thanks jim|
|Shaan23||Stop using calculators...you 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|