The average mark obtained by Saloni in four papers is 51, and in the fifth paper, she gets 56 marks. Find her new average in all five papers.
52
Calculating New Average Marks
The question asks us to find the new average mark obtained by Saloni over five papers, given her average in the first four papers and her score in the fifth paper.
To find the new average, we first need to determine the total marks Saloni scored in the first four papers. Then, we add the marks she got in the fifth paper to find the total marks over all five papers. Finally, we divide the total marks by the total number of papers (which is 5) to calculate the new average.
Step-by-Step Average Calculation
-
Find the total marks in the first four papers:
The average mark in four papers is 51.
Total marks in 4 papers = Average mark × Number of papers
Total marks in 4 papers = \(51 \times 4\)
Total marks in 4 papers = \(204\)
-
Find the total marks in all five papers:
Marks obtained in the fifth paper is 56.
Total marks in 5 papers = Total marks in 4 papers + Marks in the 5th paper
Total marks in 5 papers = \(204 + 56\)
Total marks in 5 papers = \(260\)
-
Calculate the new average mark over five papers:
New average = Total marks in 5 papers ÷ Total number of papers
New average = \(260 \div 5\)
New average = \(52\)
So, Saloni's new average mark in all five papers is 52.
Formula Used
The fundamental formula for calculating average is:
\(\text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}}\)
From this, we can also derive the sum of values:
\(\text{Sum of all values} = \text{Average} \times \text{Number of values}\)
Summary of Calculation
| Item | Value |
|---|---|
| Average (4 papers) | 51 |
| Number of papers (initial) | 4 |
| Total Marks (4 papers) | \(51 \times 4 = 204\) |
| Marks in 5th paper | 56 |
| Total Marks (5 papers) | \(204 + 56 = 260\) |
| Number of papers (final) | 5 |
| New Average (5 papers) | \(260 \div 5 = 52\) |
Revision Table: Average Concepts
| Concept | Description | Formula |
|---|---|---|
| Average | A measure of the central tendency of a set of numbers. | Sum of values / Number of values |
| Sum of Values | The total obtained by adding all the numbers in a set. | Average × Number of values |
| Calculating New Average | Finding the average after adding new values to the set. Requires calculating the new total sum and dividing by the new count of values. | (Old Sum + New Value) / (Old Count + 1) |
Additional Information: Understanding Averages
The average, also known as the mean, is a very common statistical tool used to represent a typical value in a dataset. It helps us understand the general performance or characteristic of a group. In this problem, the average mark gives us an idea of Saloni's overall performance across her papers. When a new data point (the fifth paper's score) is added, the average changes because the total sum of marks and the number of papers both increase.
Understanding how to calculate and update averages is useful in many real-life situations, such as calculating average speed over a journey, average income, or average temperatures.
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