- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion

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**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.

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**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 |