Find the mode for the following frequency distribution:

by

Points to Remember:

  • Mode is the value that appears most frequently in a data set.
  • For grouped data, the mode is estimated using the modal class (the class with the highest frequency).
  • There can be more than one mode (multimodal data) or no mode (if all values appear with equal frequency).

Introduction:

The question asks to find the mode of a frequency distribution. The mode is a measure of central tendency, indicating the most common value in a dataset. Unlike the mean (average) and median (middle value), the mode is not sensitive to extreme values. It’s particularly useful for nominal data (categories) where mean and median are not applicable. Finding the mode for a frequency distribution involves identifying the data point or class interval with the highest frequency.

Body:

Unfortunately, the question is incomplete. It does not provide the frequency distribution itself. To illustrate how to find the mode, let’s consider two examples:

Example 1: Ungrouped Data

Let’s say we have the following ungrouped data: 2, 3, 4, 4, 4, 5, 5, 6, 7.

In this case, the mode is 4 because it appears three times, more frequently than any other value.

Example 2: Grouped Data

Consider the following grouped frequency distribution:

| Class Interval | Frequency |
|—|—|
| 10-20 | 5 |
| 20-30 | 8 |
| 30-40 | 12 |
| 40-50 | 7 |
| 50-60 | 3 |

Here, the modal class is 30-40 because it has the highest frequency (12). To estimate the mode for grouped data, we can use the following formula:

Mode ≈ L + (fm – f1) / (2fm – f1 – f2) * w

Where:

  • L = lower limit of the modal class (30)
  • fm = frequency of the modal class (12)
  • f1 = frequency of the class before the modal class (8)
  • f2 = frequency of the class after the modal class (7)
  • w = width of the class interval (10)

Substituting the values, we get:

Mode ≈ 30 + (12 – 8) / (2 * 12 – 8 – 7) * 10 ≈ 30 + 4/9 * 10 ≈ 34.44

Therefore, the estimated mode for this grouped data is approximately 34.44.

Conclusion:

The mode is a valuable measure of central tendency, particularly useful when dealing with categorical data or when extreme values might skew the mean. For ungrouped data, the mode is simply the most frequent value. For grouped data, the modal class is identified, and the mode is estimated using a formula that considers the frequencies of the surrounding classes. To accurately determine the mode, the frequency distribution data is crucial. Without the specific data from the original question, we can only provide a methodological explanation of how to calculate the mode for different types of data. A clear understanding of data representation and the appropriate statistical measure is essential for accurate data analysis and informed decision-making.

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