### CFA Practice Question

There are 294 practice questions for this study session.

### CFA Practice Question

Listed below are two data sets: S and T. Which data set has the larger standard deviation? (Hint: you can answer this question by inspecting the two data sets. But if you are not sure after inspection, calculate the standard deviation.)

Data Set S: 1, 2, 3, 4, 5, 6, 7, 8, 9
Data Set T: 8, 9, 9, 9, 10, 11, 11, 12

On inspection, data set S has the larger sample standard deviation. By calculation: S(S) = 2.58, S(T) = 1.27.

User Comment
Lucho If it is a sample, you should use N instead of N-1 to calculate variance. It it is a population, then you should use N.
namie good question. I guess it is a population variance that's why it uses only N, instead of N-1. In this question we are not trying the sample the data buy actually trying the calculate the sd directly.
rfvo Here, i'll make it easy for ya....check the range
dravinskis Agree with rfvo.
AUAU I think no need to calculate.
Just observe the deviation from mean.
jayphx So when I use my hp12c:
1Σ+
2Σ+
3Σ+
4Σ+
5Σ+
6Σ+
7Σ+
8Σ+
9Σ+
the g and s I get 2.739. Can someone tell me what I'm doing wrong?
johntan1979 Range means nothing, especially if both sets have the same range. The key to solving this question fast is by observing the difference between each number. Set S is consistently at least 1, while Set T has a few zeros. Logic and common sense will tell you that Set S definitely has the higher sd.
jonan203 jayphx:
you have to calculate the mean of the population and add it as the nth sigma before calculating the population standard deviation

1 <sigma>
2 <sigma>
3 <sigma>
4 <sigma>
5 <sigma>
6 <sigma>
7 <sigma>
8 <sigma>
9 <sigma>
<g><mean><sigma>
<g><s> = 2.58199

you have to do this because hp12c defaults to sample statistics.
ascruggs92 Don't use a calculator for this. Standard Deviation is one of the measurement that establishes how much the observations in a population vary from the population mean. If the range of observations in the data set is bigger than that of another data set, it is said to have more variation. That can very literally be translation to "it has a larger variance", and because standard deviation is the square root of Variance, the standard deviation is higher as well.
pigletin numbers in set s are more variant? hence the higher variance
walterli No need to calculate... just compare the difference with the average for each number.... S has large difference than T