Let's find the mode of the given data on savings. The data shows how many people saved a certain amount of money. To find the mode, we need to identify the value that appears most frequently in the data set. In this case, the data is presented in a frequency distribution table, where the 'Number of people' represents the frequency of each 'Savings (in Rs.)' amount.

Understanding Mode in Statistics

The mode is a measure of central tendency. It represents the value that has the highest frequency in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode if all values appear with the same frequency.

Analyzing the Savings Data to Find the Mode

The provided data gives us pairs of savings amounts and the number of people who saved that amount. We can list these frequencies:

• Savings of Rs. 5: Frequency = 1
• Savings of Rs. 15: Frequency = 3
• Savings of Rs. 20: Frequency = 4
• Savings of Rs. 25: Frequency = 2
• Savings of Rs. 30: Frequency = 1
• Savings of Rs. 35: Frequency = 1
• Savings of Rs. 40: Frequency = 2

Let's put this data into a table for clarity:

To find the mode of this data, we look for the highest frequency in the 'Number of People' column. The frequencies are 1, 3, 4, 2, 1, 1, and 2. The highest frequency among these is 4.

Now, we need to identify the 'Savings (in Rs.)' value that corresponds to this highest frequency (4). Looking at the table, the savings amount corresponding to a frequency of 4 is Rs. 20.

Therefore, the mode of the given data is Rs. 20, as this is the savings amount saved by the largest number of people.

Evaluating the Options

Let's check our answer against the given options:

• Option 1: Rs. 20. This matches our calculated mode, which has the highest frequency (4).
• Option 2: Rs. 30. The frequency for Rs. 30 is 1, which is not the highest.
• Option 3: Rs. 25. The frequency for Rs. 25 is 2, which is not the highest.
• Option 4: Rs. 15. The frequency for Rs. 15 is 3, which is not the highest (4 is higher than 3).

Based on the frequencies, Rs. 20 is indeed the mode of the data.

Conclusion

The mode of the given data set is the value that appears with the highest frequency. By examining the number of people for each savings amount, we found that 4 people saved Rs. 20, which is the highest frequency. Therefore, the mode is Rs. 20.

Revision Table: Measures of Central Tendency

Here's a quick recap of common measures of central tendency:

Additional Information: Types of Data and Mode

Data can be broadly classified into qualitative (categorical) and quantitative (numerical).

• Mode for Qualitative Data: The mode is the only measure of central tendency suitable for nominal qualitative data (like colors, types of cars), as you can only count frequencies.
• Mode for Quantitative Data: The mode can also be used for numerical data, as seen in this problem, especially to identify the most common value or peak in the distribution.
• Mode for Grouped Data: For data presented in class intervals (like 0-10, 10-20), the mode is calculated using a specific formula:
  Mode $$= L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h$$ Where:
  • $L$ is the lower limit of the modal class (the class with the highest frequency).
  • $f_1$ is the frequency of the modal class.
  • $f_0$ is the frequency of the class preceding the modal class.
  • $f_2$ is the frequency of the class succeeding the modal class.
  • $h$ is the class size.
  The problem here uses discrete values with frequencies, not class intervals, so the formula for grouped data is not needed. We simply find the value with the highest frequency.