- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Statistical Measures of Asset Returns
- Subject 2. Measures of Dispersion
CFA Practice Question
A sample of 5 persons with hypertension underwent a special blood-pressure-reducing treatment program that resulted in the following values of reduction in systolic blood pressure (i.e., the scores give SBP after treatment - SBP before treatment): -5, 10, 20, 5, 10.
Suppose, for a second sample of 5 persons, the sample mean is 10 and the sample variance is 25. Which of the following statements about this second sample is not correct?
A. A person with a SBP reduction of -5 units is 3 standard deviations below the sample mean.
B. The sum of the squared deviations of SBP reduction scores from the sample mean, i.e., SUM((X - XBAR)2) = 100.
C. Any SBP reduction score between 0 and 20 is within one standard deviation of the sample mean.
Explanation: 10 ± SQRT(25) is the interval from 5 to 15.
User Contributed Comments 13
User | Comment |
---|---|
Carol1 | Why is equation (SUM((...) correct? I will say this equation exist when the the left side need to divide the sample size. |
wollogo | It says "SUM of squared deviations" so you are not dividing by the sample size. |
stevelaz | Can someone please explain all the options |
sunilcfa | It says 5 and 15 lie between the range 0 to 20 |
mchu | it is n-1, rather than n |
Andrewua | A is true: 10-3*SQRT(25)=-5. |
u0302638 | SUM((X - XBAR)2) = 100. why is this correct? |
Gooner7 | @u0.... I have same question, but through knew 3rd choice was wrong |
bhavini | how does the sum of squared deviations add up to 100 |
Nando1 | Answer B is correct because if you work backwards from the variance [25 * 4 (n-1) = 100] you will see that the sum of the squared deviations has to be 100. (x-xbar)^2 is the result before dividing by n-1 to get the variance. |
RAustin | A is right: SD = 5 (Sq. rt. of Var. of 25), so 3 SDs to left of 10 would be -5. C is wrong: Any score between 0 & 20 is NOT 1 SD away from the mean of 10; -5 is 3 SDs away, 0 is 2 SDs away, etc. |
dream007 | best to guess a question like this and move on...:) |
birdperson | well said @Nando1 | variance = (xi - xbar)^2/(n-1) | 25 = (xi - xbar)^2/(5-1) | 25 * 4 = (xi - xbar)^2.... B is correct. A is correct as stated by@andrewua |