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Introduction to the Concept of Average

Average: Average is the sum of different terms (data) divided by the total number of terms.
Average = Sum of given terms)/(Total number of terms)

For example: Find the average of given terms 12, 16, 17, 19, 21.
Sol:
Total number of terms = 5
Average = (12 + 16 + 17 + 19 + 21)/5 = 17

Some Basic Formulae

The list given below, states the basic formulae for the concept of Average. Let us take a look at them before we learn some awesome tricks for average.

  • Average of first ‘n’ natural number = (n + 1)/2
  • Average of first ‘n’ even numbers = (n + 1)
  • Average of first ‘n’ odd numbers = n
  • Average of ‘n’ consecutive natural numbers = (First number + Last number)/2
  • Average of squares of first ‘n’ natural numbers = (n + 1)(2n + 1)/6

Some Important Tips and Tricks for Average

Here are some handy tricks for Average which will make your calculation faster and efficient with practice:

  • If the value of each number is increased by the same value ‘a’, then the average of all numbers will also increase by ‘a’.
  • If the value of each number is decreased by the same value ‘a’, then the average of all numbers will also decrease by ‘a’.
  • If the value of each number is multiplied by the same value ‘a’, then the average of all numbers will also get multiplied by ‘a’.
  • If the value of each number is divided by the same value ‘a’, then the average of all numbers will also get divided by ‘a’.

A few more Useful Shortcuts and Tricks for Average

(1) If the average of marks obtained by ‘n’ students in an exam is ‘m’. If the average marks of passed students is ‘p’ and total of failed students is ‘f’. Then the number of students who failed in the exam is equal to [n(p – m)/(p – f)].

Example 1: The average marks obtained by 125 students in an exam is 29. If the average marks of passed students is 36 and that of failed students is 11. What is the number of failed students?
Sol:
No. of failed students = 125(36 – 29)/(36 – 11) = 125 * 7/25 = 35


(2) If a batsman in his nth innings makes a score of ‘s’ and thereby increased his average by ‘t’, then the average after ‘n’ innings is equal to [s – t(n-1)].

Example 2: A batsman in his 44th innings makes a score of 86 and thereby increases his average by 1, Find the average after 44 innings?
Sol:
Average after 44th innings = [86 – 1 * (44 – 1)] = 86 – 43 = 43

The document Overview: Averages | Quantitative Techniques for CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
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FAQs on Overview: Averages - Quantitative Techniques for CLAT

1. What is the concept of average?
Ans. The concept of average, also known as mean, is a statistical measure that represents the central tendency of a set of numbers. It is calculated by adding up all the numbers in the set and dividing the sum by the total count of numbers.
2. How is the average calculated?
Ans. To calculate the average, you need to add up all the numbers in the set and then divide the sum by the total count of numbers. For example, if you have the numbers 5, 8, and 12, you would add them up (5 + 8 + 12 = 25) and then divide by the count of numbers (3). The average in this case would be 25/3 = 8.33.
3. Why is the concept of average useful?
Ans. The concept of average is useful because it provides a representative value for a set of numbers. It allows us to summarize and understand data in a meaningful way. Average is commonly used in various fields, such as finance, statistics, and sports, to analyze trends, compare values, and make informed decisions.
4. Can the average be influenced by extreme values?
Ans. Yes, the average can be influenced by extreme values in a data set. Extreme values, whether they are unusually high or low, can significantly impact the average. This is because the average takes into account all the values in the set, so extreme values have the potential to skew the overall result.
5. How can averages be used to compare different sets of data?
Ans. Averages can be used to compare different sets of data by calculating the average for each set and then comparing the values. By comparing the averages, you can gain insights into the relative values of the sets and identify any differences or similarities. This comparison can be helpful in various scenarios, such as comparing the performance of different products, analyzing the effectiveness of different strategies, or evaluating the progress of different groups.
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