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Chapter 2: Problem 32

Briefly explain the concept of cumulative frequency distribution. How are the cumulative relative frequencies and cumulative percentages calculated?

Short Answer

Expert verified
Cumulative Frequency Distribution describes how the number of data points that fall below a specific value in a data set add up. Cumulative Relative Frequency is the accumulation of relative frequencies, where the relative frequency of an observation is its frequency divided by the total number of data points. Cumulative Percentage is the cumulative frequency expressed as a proportion of total frequency in percentage form.

Step by step solution

01

Understanding Cumulative Frequency Distribution

Cumulative Frequency Distribution is a method of portraying a data set. In cumulative frequency distribution, the frequency of each data point is added to sums of the frequencies of all data points prior to it. This gives the total number of data points that fall below the upper limit of a specific class.
02

Calculation of Cumulative Relative Frequencies

The Cumulative Relative Frequency of a data set is the accumulation of the previous relative frequencies added to the relative frequency for the current observation. The relative frequency for an observation is the frequency of the data point divided by the total number of data points. So for a current observation, we add its relative frequency to the sum of relative frequencies of all previous observations.
03

Calculation of Cumulative Percentages

Cumulative percentage is a way of expressing cumulative frequency as a percentage of the total frequency. To find the cumulative percentage for a particular data point, we divide the cumulative frequency up to that data point by the total frequency and multiply the result by 100.

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Most popular questions from this chapter

The following data give the numbers of orders received for a sample of 30 hours at the Timesaver Mail Order Company. \(\begin{array}{llllllllll}34 & 44 & 31 & 52 & 41 & 47 & 38 & 35 & 32 & 39 \\\ 28 & 24 & 46 & 41 & 49 & 53 & 57 & 33 & 27 & 37 \\ 30 & 27 & 45 & 38 & 34 & 46 & 36 & 30 & 47 & 50\end{array}\) a. Construct a frequency distribution table. Take 23 as the lower limit of the first class and 7 as the width of each class. b. Calculate the relative frequencies and percentages for all classes. c. For what percentage of the hours in this sample was the number of orders more than 36 ?

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