For the data in our example, the minimum is 65 and the maximum is , a range of about We can therefore choose intervals of size 5, and have ten of them. Our classes are 65 - 70, 70 - 75, etc. This version of the course is no longer available. The ages of the participants were recorded as follows:. If a variable takes a large number of values, then it is easier to present and handle the data by grouping the values into class intervals.
Continuous variables are more likely to be presented in class intervals, while discrete variables can be grouped into class intervals or not. To illustrate, suppose we set out age ranges for a study of young people, while allowing for the possibility that some older people may also fall into the scope of our study. The frequency of a class interval is the number of observations that occur in a particular predefined interval.
So, for example, if 20 people aged 5 to 9 appear in our study's data, the frequency for the 5—9 interval is The endpoints of a class interval are the lowest and highest values that a variable can take. So, the intervals in our study are 0 to 4 years, 5 to 9 years, 10 to 14 years, 15 to 19 years, 20 to 24 years, and 25 years and over. The endpoints of the first interval are 0 and 4 if the variable is discrete, and 0 and 4.
The endpoints of the other class intervals would be determined in the same way. Class interval width is the difference between the lower endpoint of an interval and the lower endpoint of the next interval. Thus, if our study's continuous intervals are 0 to 4, 5 to 9, etc.
The intervals could also be written as 0 to less than 5, 5 to less than 10, 10 to less than 15, 15 to less than 20, 20 to less than 25, and 25 and over. In summary, follow these basic rules when constructing a frequency distribution table for a data set that contains a large number of observations:.
In deciding on the width of the class intervals, you will have to find a compromise between having intervals short enough so that not all of the observations fall in the same interval, but long enough so that you do not end up with only one observation per interval. It is also important to make sure that the class intervals are mutually exclusive and collectively exhaustive. Thirty AA batteries were tested to determine how long they would last.
The results, to the nearest minute, were recorded as follows:. Use the steps in Example 1 and the above rules to help you construct a frequency distribution table.
Using the given data and a class interval of 10, the interval for the first class is to and includes the lowest value. Remember, there should always be enough class intervals so that the highest value is included. An analyst studying the data from example 3 might want to know not only how long batteries last, but also what proportion of the batteries falls into each class interval of battery life.
The percentage frequency is found by multiplying each relative frequency value by Use the data from Example 3 to make a table giving the relative frequency and percentage frequency of each interval of battery life.
As previously shown for example 2, cumulative frequency is used to determine the number of observations that lie below a particular value in a data set. The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
The last value will always be equal to the total for all observations, since all frequencies will already have been added to the previous total. The daily number of rock climbers in Lake Louise, Alberta was recorded over a day period. The results are as follows:. The number of rock climbers ranges from 4 to In order to create a frequency table, the data are best grouped in class intervals of Each interval can be one row in the frequency table.
The Frequency column lists the number of observations found within a class interval. For example, there are only two values in the interval from 10 to 20, then its frequency is 2 in the table accordingly. The other entries in the table can be calculated similarly.
Results are presented in the table 4. Cumulative relative frequency is another way of expressing frequency distribution. It is obtained by calculating the percentage of the cumulative frequency within each interval. The fourth column in the table 4. The cumulative relative frequency distribution can be visualized with a bar chart or a line chart, like in chart 4. The following data represents the number of runs per innings a player has scored in a season.
Construct an ordered stemplot to display the data. An ordered stemplot for the scores that range from 4 to is given below. Stems 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are formed by the tens digits; whereas, the stems 10, 11 and 12 are formed by the hundreds and tens digits. The leaves are formed by the unit digits of the values. We notice that the scores 4, and are separated from the main body of the data.
So, 4, and are outliers. The stemplot for the data consisting of outliers can be displayed as follows:. The value of 4 is listed at the top of the table as an outlier and the values of and are listed below the table as outliers. All rights reserved. Australian Business Number 53 If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number. A table helps us to organise and analyse a set of data values.
In this section we will consider frequency tables and stemplots i. Frequency Tables A frequency table is a tabular representation of a data set in an ascending order of magnitude with their corresponding frequencies. Note: The word 'frequency' means 'how often'. Example 7 The scores awarded to 25 students for an assignment were as follows: 4 7 5 9 8 6 7 7 8 5 6 9 8 5 8 7 4 7 3 6 8 9 7 6 9 Present this information in a frequency table and find the mode.
Solution: The frequency table is as follows: The score that occurs most often is 7. Class Intervals The data is grouped into class intervals if the frequency table becomes too large to help us organise, interpret and analyse the data.
Frequency Tables with Class Intervals A frequency table for a data set containing a large number of data values is constructed as follows: Determine the data range of the data set. Decide the width of the class intervals.
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