- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 9. Symmetry and Skewness in Return Distributions

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**CFA Practice Question**

A reading test (conducted with a large sample of third graders) with 50 possible points yields a bell-shaped distribution with scores ranging from 5 to 48. If the same test was administered to fifth graders, what would we expect the form of the frequency distribution to be?

A. negatively skewed (skewed to the left)

B. symmetric, but not bell-shaped

C. positively skewed (skewed to the right)

**Explanation:**The frequency distribution would be negatively skewed because these students would be expected to score higher in general.

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**User Contributed Comments**
25

User |
Comment |
---|---|

gambary |
if they score more, that means there are more extreme scores to the right, that will lead to a further right tale.. Skewed to the right, right? |

jgelfand |
i still do not get it....they should be skewed to the right since mean becomes higher |

ckevin |
it should be skewed to the left: tail is to the left and mean is thus higher at the right side. |

kuan |
positively skewed. mean should go up! ans is confirm wrong. Just draw the normal distribution and imagine the mean goes up! |

alsd |
the answer depends on how many grades lies to the right from that point (48-5)/2+5 if there are many good grades (above that point) that's negative skew and reverse; so the answer A implies that there are more grades above that point and less grades below that point |

tenny45 |
so is the answer postive or negative skewed?? Did someone actually confirm the answer? |

CocaColas |
Negatively skewed means it has a long tail in the negative direction.. |

aroman21 |
It has to be negative skew. The reason is a negative skew has large negative outliers which tend to "pull" the mean downward, in other words, the 5th graders do better than the 3rd graders, so more 5th graders ace the exam, this is your large outliers which "pull" the mean downward. The large outliers cause a higher mode and median compared to the mean. In the case of a positive skew, you have many small losses and FEW EXTREME GRAINS, this is not the case with 5th graders compared to 3rd graders, 5th graders would DO BETTER than 3rd graders so your outliers would be HUGE (negative skew) not small in the case of a positive skew. |

mtcfa |
A good way to think of this is the mode, which is highest in a negative skew. Most 5th greaters would get very high scores, but there will undoubtedly be a few morons who score very low and pull the average (mean) down. |

dlhdang |
I am not an english speaker. I do not understand why the 5th grader do better than the 3rd grader. also, if 5 th grader have higher score than 3rd grader, distribution would skewed to the right. plz explain to me |

timbball |
It might be easier to think of the area (ie. probability) under the curve. If fifth graders take grade 3 level test, more are likely to score higher than the third graders, so the area above the mean would be larger compared to the area below, which is negatively skewed. |

gene80 |
go with the mode. The force is strong in that one. |

xavi |
We would expect the 5th graders to do better, on average, but there would be some outliers which would be negative. The large deviations from the mean would be negative, bringing the mean down, not up. |

pierreE14 |
This question is a 50/50 guess for all the candidates that are not US nor UK ... :( |

capitalpirate |
not 50/50? see, its bell-shaped now, i.e normally distributed. A sample of 5th graders is added, taking 5rd grade test - you would expect most to score close to 50. hence the skew would move to the left, with mean, median, mode higher. |

aakash1108 |
.....we can look at at it this way...as the test is an easy one - most of the students would get the score of 50 and one or two might get a score of 10 or 12 (just an example).....thus the bulge of the distribution would be on the righ hand side and the the distribution would have a tail on the left.....i.e. negative skewed. ......draw the frequecy distribution or a frequency polygon to get a clearer picture.. |

StanleyMo |
This is how i think, 0 - 100 points for the test, the 5th graders alot of scoring at high points, causing extremtly high points exist at right side, and shift the skewness to left. ( more mode at right side) |

serboc |
They may also ask: which of the following is positive skew? mean>median>mode |

kellyyang |
yes, the negative skew makes more sense. |

Rubbish |
more 5th graders score better means mode shift to right of mean.=negative skew |

rsanfo |
Imagine a string of rubber attached to a board with two tacks. stretch it upward with your finger in the middle for a normal distribution. Now move your finger to the right (better scores for fifth graders). The longer tail is on the left (negative skew). |

omya |
negatively skewed means- few extreme losses and many small gains |

something |
Mode will be higher than the mean, therefore negative skew |

something |
In positive skew, a few outliers move mean to the right of mode. In this case, many usuals i.e. mode is pushed to the right of mean, therefore negative skew. |

krispy4 |
This is a strange question/answer. But I suppose the mode will definitely be 48 (if a fifth grader got a 3rd grade test, there is no doubt that one or two people would ace the test), while the mean will be slightly less. |