Analyzing Monthly Income Data from a Table

The question provides a table showing the cumulative frequency distribution of monthly incomes for 100 families in a locality. The data is presented in a "more than" format, indicating the number of families whose income exceeds a certain threshold.

Understanding the Provided Income Data Table

Here is the data given in the problem:

This table tells us, for example, that 100 families have an income more than Rs. 10,000, and 85 families have an income more than Rs. 13,000, and so on.

Finding the Number of Families in a Specific Income Range

We are asked to find the number of families whose monthly income is in the range of Rs. 19,000 - 22,000. To find the number of families in a specific range from a "more than" cumulative frequency table, we can use the following logic:

• The number of families with income more than the lower limit of the range includes all families in the range plus all families with income more than the upper limit of the range.
• So, the number of families strictly within the range is the number of families with income more than the lower limit minus the number of families with income more than the upper limit.

In this case, the range is Rs. 19,000 - 22,000.

• Lower limit of the range: Rs. 19,000
• Upper limit of the range: Rs. 22,000

From the table:

• Number of families with income more than Rs. 19,000 is 50.
• Number of families with income more than Rs. 22,000 is 33.

The number of families with income in the range Rs. 19,000 - 22,000 is the number of families with income more than Rs. 19,000 minus the number of families with income more than Rs. 22,000.

Calculation:

\text{Number of families in range } 19000 - 22000 = (\text{Families with income } > 19000) - (\text{Families with income } > 22000)

\text{Number of families in range } 19000 - 22000 = 50 - 33

\text{Number of families in range } 19000 - 22000 = 17

Therefore, the number of families having an income range of Rs. 19,000 - 22,000 is 17.

Conclusion on Income Range Frequency

Based on the cumulative frequency data provided in the table, we determined that 17 families fall within the monthly income bracket of Rs. 19,000 to Rs. 22,000.

Revision Table: Key Concepts

Additional Information: Frequency Distribution Types

Data can be presented in various frequency distribution formats to make it easier to understand and analyze. Two common types are:

• Simple Frequency Distribution: This table shows the number of times each observation or group of observations occurs in a dataset. For example, the number of families exactly in the range 19000-22000 would be listed directly.
• Cumulative Frequency Distribution: This table shows the running total of frequencies. It can be "less than" or "more than".
  • "Less Than" Cumulative Frequency: Shows the total number of observations less than or equal to a certain value.
  • "More Than" Cumulative Frequency: Shows the total number of observations greater than a certain value (as seen in this problem).

Converting between these forms is a common task in statistics. To get the simple frequency for a class from a "more than" table, you subtract the cumulative frequency of the upper boundary from the cumulative frequency of the lower boundary.