Hey
mean in statistics is the value of average
that's why we are doing this with the marks.
rather than limits

I wish you got it
ʘ‿ʘ

Mean of a Grouped Data

To compute the mean of a grouped data, we first need to understand what grouped data is. Grouped data refers to data that has been organized into intervals or classes. Each class represents a range of values, and the data within each class is represented by its frequency.

Assumptions for Computing Mean

When computing the mean of a grouped data, we make certain assumptions about the distribution of the frequencies. These assumptions help us estimate the average or central tendency of the data. The correct assumption for computing the mean is that the frequencies are centered at the class marks of the classes.

Explanation of the Correct Assumption

The class mark of a class is the average of the lower and upper limits of that class. It represents the central value or midpoint of the class. By assuming that the frequencies are centered at the class marks, we are essentially assuming that the data within each class is evenly distributed around its midpoint.

This assumption allows us to estimate the average value of the data without knowing the exact values within each class. It is a reasonable assumption because it simplifies the calculation and provides a good approximation of the mean.

Example

Let's consider an example to better understand this assumption. Suppose we have the following grouped data:

| Class Interval | Frequency |
|---------------|-----------|
| 10-20 | 5 |
| 20-30 | 8 |
| 30-40 | 12 |
| 40-50 | 7 |
| 50-60 | 4 |

To compute the mean, we use the formula:

Mean = (Sum of (Class Mark * Frequency)) / (Sum of Frequencies)

Using the assumption that frequencies are centered at the class marks, we can estimate the class marks as follows:

| Class Interval | Class Mark |
|---------------|------------|
| 10-20 | 15 |
| 20-30 | 25 |
| 30-40 | 35 |
| 40-50 | 45 |
| 50-60 | 55 |

Now we can calculate the mean:

Mean = (15*5 + 25*8 + 35*12 + 45*7 + 55*4) / (5 + 8 + 12 + 7 + 4)

After performing the calculations, we find the mean to be a specific value.

Conclusion

In conclusion, when computing the mean of a grouped data, it is assumed that the frequencies are centered at the class marks of the classes. This assumption simplifies the calculation and provides a good approximation of the average value of the data. By assuming that the data is evenly distributed around the class marks, we can estimate the mean without knowing the exact values within each class.