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Study the given table and answer the question that follows.
The table shows the demand of different shoe sizes as obtained in a survey.
| Shoe size | Number of pairs demanded |
|---|---|
| 5 | 44 |
| 6 | 48 |
| 7 | 58 |
| 8 | 46 |
| 9 | 39 |
| 10 | 37 |
Find the modal size of shoes demanded that one can obtain from the survey.
9
5
6
7
7
Simply scan the 'Number of pairs demanded' column for the largest number and identify the corresponding 'Shoe size'.
A frequency table showing shoe sizes 5, 6, 7, 8, 9, 10 and their respective demands: 44, 48, 58, 46, 39, 37 pairs.
Mode=value with highest frequency
Simply scan the 'Number of pairs demanded' column for the largest number and identify the corresponding 'Shoe size'.
Students often accidentally select the highest shoe size (10) or the highest frequency value (58) instead of the corresponding shoe size (7).
Identify frequencies
List the demands for each shoe size: size 5 has 44, 6 has 48, 7 has 58, 8 has 46, 9 has 39, and 10 has 37.
Frequencymax=58
Determine the mode
The modal value is defined as the observation that occurs with the maximum frequency in the given data set. Looking at the table, the maximum frequency is 58.
Mode=7
D is correct because the shoe size 7 has the highest number of pairs demanded (58), which defines it as the modal value.
This is a basic definition of mode. In grouped frequency distributions, you would use the formula Mode=L+(2f1−f0−f2f1−f0)×h.