FRM Part I · FRM Exam Part I · Sample Moments
For a sample of n = 10 observations, the sum of the values is 50 and the sum of the squared values is 400. What is the unbiased sample variance?
The unbiased sample variance is 16.67. The sum of squared deviations equals 400 minus 50 squared over 10, which is 150, and dividing by n-1 = 9 gives 16.67. Dividing by 10 would give 15, which is the biased figure.
- A15.00
- B16.67
- C17.78Correct
- D15.56
Explanation
Sum of squared deviations = 400 - (50^2)/10 = 400 - 250 = 150. Dividing by n-1 = 9 gives 16.67. Check: 150/9 = 16.67. The value 15.00 results from dividing by n, and 17.78 is wrong because it uses a mistaken subtraction.
Did you get it right without looking?
One question tells you little. A timed set on Sample Moments shows your real accuracy, how long you take and where you lose marks.
More Sample Moments questions
- A sample of 4 monthly returns (in percent) is 1, 3, 5, 7. The sample standard deviation using n-1 is closest to which of the following?
- An analyst records five monthly returns for a fund: 2%, 4%, 6%, 8% and 10%. What is the sample standard deviation of these returns (using th…
- Which statement about the sample mean of i.i.d. observations is correct?
- A risk analyst estimates the kurtosis of a portfolio's daily returns as 5.2. Which statement is the most accurate description relative to a …
- A risk manager observes the following sample of 4 daily P&L figures (in $ thousands): -2, 0, 2, 4. Using the sample estimator with n-1 in th…
- An analyst estimates the population mean of i.i.d. returns using the sample mean. Which set of properties makes the sample mean the best lin…