- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 3. Frequency Distributions

###
**CFA Practice Question**

The figures below describe the total return rates (in percentages) for the past three years for 15 top-performing utilities mutual funds.

Smallest return: 3.1

Median return: 9.5

Biggest return: 15.1

Smallest return: 3.1

Median return: 9.5

What interval length should be used, if one is desired, to construct a frequency distribution with four equally spaced intervals?

A. 4

B. 3.75

C. 3

**Explanation:**1. Determine how many classes we need. Since 2

^{4}> 15, we need 4 classes.

2. Interval: (15.1 - 3.1)/4 = 3

###
**User Contributed Comments**
7

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

wollogo |
Where do they get the 2^4 from? It says in the question that their are "four equally spaced intervals"! |

chamad |
step 1 is just an extra explanation for more complicated cases |

haosheng |
4 equally interval: 0,3,6,9,12 make sense? I chose A. Hope anyone could explain this a bit |

StanleyMo |
3.1 to 15.1 is 12, with 4 same space interval, we pick the length as 3. |

Daddykay |
Wollog, the best way to look at it is to take to calculate the range which is highest value less lowest value (15.1-3.1=12). Now you wanna spread out 12 into four equally spaced distributions which means they must have intervals of 12/4=3 |

mpapwa22 |
Thanks Daddykay...tht is the best explanation you get here. Find the range first. |

Shaan23 |
No guys. THere's a rule and it states that the for the smallest value of k where 2^k > 15 select that number for the number of intervals. The first k value is 4 ---- 16 > 15 Its just memorization |