What is 'loss of information' in classified data?
Loss of information is an inherent shortcoming of classifying data into a frequency distribution. While this process summarises raw data to make it concise and comprehensible, it does not display the specific details present in the original data. Once the data is grouped into classes, individual observations lose their significance for further statistical calculations.
For example, if a class interval 20–30 contains six observations (25, 25, 20, 22, 25, and 28), the frequency distribution only shows the frequency as 6, not the actual values. In further analysis, all values in the class are assumed to be equal to the class mark. Since calculations are based on the class mark rather than the actual values of the observations, it results in a considerable loss of information.
Explanation
The answer is derived directly from the 'Loss of Information' section of the provided text. It highlights the trade-off between summarising data and retaining specific details. The textbook explains that while classification makes data easier to handle, the grouping process hides the actual values of individual observations. The example of the 20–30 class interval is used in the text to illustrate how using the class mark (mid-value) for calculations instead of the actual diverse values (like 20, 22, 25, 28) leads to a loss of precision or 'information'.