Calculation of Mode for Given Data Set

The mode is the value that appears most frequently in a data set. To calculate the mode for the given data set, we need to follow the below steps:

Step 1: Arrange the data in ascending order.

The data set given is already arranged in ascending order.

Step 2: Find the frequency of each value.

The frequency of each value is given in the table as follows:

| Class mark | Frequency |
|------------|-----------|
| 1 | 4 |
| 2 | 8 |
| 3 | 20 |
| 4 | 16 |
| 5 | 10 |
| 6 | 6 |

Step 3: Find the value with the highest frequency.

The value with the highest frequency in the given data set is 3, which appears 20 times.

Step 4: Calculate the mode.

The formula to calculate the mode is:

Mode = L + [(f1 - f0) / (2f1 - f0 - f2)] × h

Where:

L = Lower limit of the modal class
f1 = Frequency of the modal class
f0 = Frequency of the class preceding the modal class
f2 = Frequency of the class succeeding the modal class
h = Size of the class interval

In the given data set, the modal class is 2.5 - 3.5, which has a frequency of 20. The class preceding the modal class is 1.5 - 2.5, which has a frequency of 8, and the class succeeding the modal class is 3.5 - 4.5, which has a frequency of 16. The size of the class interval is 1.

Putting these values in the formula, we get:

Mode = 2.5 + [(20 - 8) / (2 × 20 - 8 - 16)] × 1
= 2.5 + (12 / 12) × 1
= 2.5 + 1
= 3.5

Therefore, the mode of the given data set is 3.5, which means that 3.5 is the value that appears most frequently in the data set.