 # Relative Frequency vs Cumulative Relative Frequency

I need help to understand this better. Below are the returns on 20 industry groups of stocks over the past year: 12%, -3%, 18%, 9%, -5%, 21%, 2%, 13%, 28%, -14%, 31%, 32%, 5%, 22%, -28%, 7%, 9%, 12%, -17%, 6% 1) What’s the range of the data? 2) Based on a frequency distribution with 12 intervals, what’s the Relative Frequency and Cumulative Relative Frequency of the 10th interval (ascending order)? Thanks.

range = -28 to + 32 = 60% based on 12 intervals Interval******Rel Freq****Cum Freq -28 to -23****1******1 -23 to -18****1******2 -18 to -13****1******3 -13 to -8*****0******3 -8 to -3******1******4 -3 to +2*****1****** 5 2 to 7*******3******8 7 to 12******3*****11 12 to 17****3******14 17 to 22****2******16 22 to 27****1******17 27 to 32****3******20 2 and 16 based on above

Thanks, CP. It’s a Schweser exercise. I checked the answer key and I believe Schweser’s take is wrong (or else I’m wrong). 1) Range = Max - Min (given data set) = 32% - (-28%) = 60% (Schweser shows 60) Should we include the percentage? I think so. 2) The tenth interval is the 3rd top down based on the acending order. Each interval should contain 5 numbers (60/12 = 5). Thus, the pertinent intervals we should focus are: 12th interval: 27<= x <=32 11th interval: 22<= x < 27 10th interval: 17<= x < 22 Relative Frequency = # of observation on target interval / total frequency -> 10th R. Freq. = 2/20 = 10% -> 10th Cumulative Relative Frequency = F (12th) + F(11th) + F(10th) = 3/20 + 1/20 + 2/20 = 3/10 = 30% Am I right or wrong??? ********************************************************************* Schweser solution: Since there are four observations are >= 22%, so the Cumulative Relative Frequency of the 10th interval is (20-4)/20 = 80%. Anyone understands this thinking?

This is not about an interval containing 5 numbers, but about a range, divided in the required number of intervals, determine the span of an interval and then see how many observations are in such an interval. The range is from -28 to 32, that is a range of 60. Divide the range to the number of intervals to obtain the length of an interval, that would be 60/12=5. Check with CPK’s work, each interval is 5 units length. The number of observations in the 10th interval is: 2. In relative terms, that is 2/20=10% frequency, or the 10th interval contains 10% of the observations. The cumulative number of observations from the first to the 10th interval is: 16. In cumulative relative terms, that is 16/20=80% frequency, or the first 10 intervals contain 80% of the observations. This could also be calculated as 1- relative frequency of the 12th - frequency of the 11th intervals = 1-3/20-1/20 = 1-4/20=1-20%=80%.

Thanks for your great explanation, map1. The alternative method (1- relative frequency of the 12th interval - relative frequency of the 11th interval) would be more handy in this case. By the way, still not sure about the range. Why you take the percentage about? 60 is obviously not equal to 60%. Should we use the given min and max values to calculate the range?

This is a relative measure, no need to be concerned with it being expressed as a % or not. But if you insist, on a scale from -28% to +32% there are 60 intervals of 1% each.

I see. Appreciate your help.