Frequency shows how often the data occurred.
Frequency measures the numbers of times that the event occurred in an experiment or a study. It shows how often something occurred during a certain period of time.
The three most frequently used methods to measure frequency are:
1. MODE
2. FREQUENCY DATA
3. GROUPED FREQUENCY DATA
1. MODE
What is mode? It is the item that occurs the most frequently in a dataset.
How to calculate mode? Firstly, organize all the items in the dataset into ascending or descending order. Then, it will immediately become clearly obvious which item(s) occur the most often.
Uses of mode in business management: Mode can identify the most frequently occurring item in the dataset. The result could be used for identifying the most popular product, the most typical inventory reorder level, the most common wage paid to the workers, etc.
Example 1: The table below shows all the shoes sold in the shoe shop this month and last month.
| Shoe sizes sold (in ascending order): | |
|---|---|
| This month: | 36, 36, 36, 36, 38, 40, 41, 41, 42, 42, 44, 45 |
| Last month: | 35, 36, 36, 36, 40, 41, 42,43, 45 |
The mode of this month’s results is size 36 shoes. And, the mode of last month’s results is size 36 shoes as well. This means that the shoe shop should hold more pairs of size 36 shoes than any other size. Size 36 was the most frequently occurring size among all of the shoes sold this month and last month.
Example 2: A convenience store records the number of sales of Pepsi bottles at its store in the last month.
| Number of bottles (x): | Frequency (f): |
|---|---|
| 20 | 3 |
| 29 | 1 |
| 30 | 2 |
| 31 | 5 |
| 15 | 1 |
| 25 | 15 |
| 37 | 1 |
| 20 | 1 |
| 40 | 1 |
On 15 of the 30 days, the retailer sold 25 bottles of Pepsi. This number occurs more times than any other number in the set of data, so 25 is the mode value for the retailer.
For retailers if color, size or style is the basis of customer choice, the frequency of occurrence is going to determine the level of stock-holding decisions.
Advantages of mode: It can be easily observed, no calculation is necessary and it is very easy to understand. The result is a whole number that is not affected by extreme values. When mode is analyzed together with the arithmetic mean and the median, it can show the overall central tendency of the dataset.
Disadvantages of mode: Mode is of limited value when the dataset contains results that only occur once as there is no the most frequently occurring items. And, when there is more than one modal result, it might create confusion which number to choose.
2. FREQUENCY DATA
What is frequency? Frequency of data in the dataset is usually expressed in a table. The table shows how many times each individual item appears in the data. Frequencies for all items can be clearly seen and the average frequency for all the items can be calculated.
How to calculate frequency data? The frequency data can be calculated using the following formula for mean frequency:
Mean frequency = ∑fx / ∑f
Where:
x – Variable, or each individual item
f – Frequency for one individual variable
∑x – Sum of Variables
∑f – Sum of frequencies for all individual variables
∑fx – Sum of Variables x Frequency
Uses of frequency data in business management: Frequency data is primarily used to show the average value that appears the most frequently among all values.
Example 1: The following table shows the sizes of the female shoes sold in a shoe shop last month. The middle column shows how often each size was sold (frequency). The third column on the right was added and the calculations were made to show the sum of all items (shoe size) multiplied by their frequencies.
| Shoe size (x): | Frequency (f): | fx: | |
|---|---|---|---|
| 36 | 5 | = | 180 |
| 37 | 8 | = | 296 |
| 38 | 4 | = | 152 |
| 39 | 9 | = | 351 |
| 40 | 11 | = | 440 |
| 41 | 10 | = | 410 |
| 42 | 2 | = | 84 |
| 43 | 6 | = | 258 |
| 44 | 4 | = | 176 |
| TOTAL: | ∑f = 59 | = | ∑fx = 2,347 |
Now, frequency data can then be calculated in the following way:
Mean frequency = 2,347 / 59
Mean frequency = 39.77
This result shows that the arithmetic mean shoe size is 39.77 which is the average shoe size sold the most frequently. This information helps the shoe shop manager to determine that size 40 is the most frequently sold shoe size in the shop.
How to calculate cumulative frequency data? Cumulative frequency data can help to find the median item in the dataset. To figure it out, add each frequency to the total of the preceding frequencies. Cumulative frequency is necessary to find the median item. The median will be the middle item of an ordered set of data – the 30th item (Median = (50+1)/2).
| Shoe size (x): | Cumulative frequency (f): |
|---|---|
| 36 | 5 |
| 37 | 13 |
| 38 | 17 |
| 39 | 26 |
| 30th item is somewhere here | |
| 40 | 37 |
| 41 | 47 |
| 42 | 49 |
| 43 | 55 |
| 44 | 59 |
The median item will be the shoe size within the shoes size group 39.
Advantages of frequency data: It is fairly easy to calculate the average frequency and interpret the results for small sets of data. When results of frequency data are analyzed together with mode, it can provide more accurate calculations of frequency.
Disadvantages of frequency data: The result of mean frequency may not be a whole number such as the shoe size 39.77 (which is neither size 39 nor 40 per se) which can create confusion. Also, sale of products in one day, week, month or year do not give any real evidence on which to base conclusions about stock-holding levels for the same period in the future.
3. GROUPED FREQUENCY DATA
What is grouped frequency data? Grouped frequency data shows how items appear within different groups of data in the dataset. Groups are also called classes or class intervals.
How to calculate grouped frequency data? Grouped frequency data is usually displayed as a table where the numbers are grouped together into different classes. These groups then show how many times items from within each group appear in the list.
Uses of grouped frequency data in business management: It is a useful way of organizing very large datasets into more manageable smaller groups. This will help researchers to analyze data and draw graphs. Grouped frequency tables can also be used to find averages.
Example 1: The following table shows grouped data for monthly salaries of managers earning between USD$2,000 and USD$4,000 working for a business producing exclusive fish tanks in Canada.
| Salary in USD$ (x): | Midpoint (x): | Managers (f): | fx: | Cumulative frequency: |
|---|---|---|---|---|
| $2,000 to $2,500 | $2,250 | 5 | USD$11,250 | 5 |
| $2,501 to $3,000 | $2,750 | 7 | USD$19,250 | 12 |
| $3,001 to $3,500 | $3,250 | 8 | USD$26,000 | 20 |
| $3,501 to $4,000 | $3,750 | 3 | USD$11,250 | 23 |
| TOTAL: | ∑f = 23 | ∑fx = 67,750 |
The averages can be calculated in the following ways.
1. MEAN: The arithmetic mean can be calculated by dividing the sum of all groups multiplied by their respective frequencies by the sum of all managers.
Mean frequency = USD$67,750 / 23 = USD$2.945.65
The mean frequency in this business is USD$2,945.65. It means that the average monthly salary paid the most frequently to a manager is USD$2,945.65.
2. MEDIAN: The median manager is the person who is in the middle of the pay scale.
Median frequency (odd) = (23 + 1) / 2
Median frequency (odd) = 12
The median worker is the 12th worker and his salary is USD$3,000 per month. To find out the median manager’s approximate salary, cumulative frequency needs to be calculated and is added in the right-hand side column. This person divides the whole group of managers into 50% of the highest-paid workers and 50% of the lowest-paid workers. It means that 11 managers earn less than USD$3,000 per month and 11 managers earn more than USD$3,000 per month.
3. MODE: The modal group is the third group with 8 managers earning between USD$3,000 and USD$3,500. Modal group is the group with the highest frequency among all groups in the dataset. For many business decisions, it is enough to just identify this group.
Advantages of grouped frequency data: Large amounts of data can be presented in this way making long lists of numbers grouped together for better clarity.
Disadvantages of grouped frequency data: It is complicated to calculate the exact numbers as what is presented is not a whole number, but a range of possible answers. Especially for the mode which lies somewhere within the modal group.
This article showed in details how numerical data might be summarized using the statistical techniques for calculating frequency. While the mode shows the value that appears the most frequently in the data sample, the frequency data shows the average value that appears the most frequently and the grouped frequency shows how often values appear within different groups of data.
You can find out more about statistical analysis of market research results here.
