Average

Quantitative Aptitude is a vital component of various competitive exams, including the Common Law Admission Test (CLAT). Among the topics tested, the concept of “averages” holds significant importance. Averages, often referred to as mean, are fundamental in understanding data distribution, making predictions and drawing conclusions. In this article, we will delve into the concept of averages, explore examples and discuss strategies to solve average-related problems in the quantitative aptitude section of CLAT.

Concept of Averages

An average or mean, is a measure that represents the central value of a set of data. It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. The average is used to represent a typical value in a dataset, helping to analyse the overall trend.

Examples

Let’s explore a few examples to better understand the concept of averages:

Example 1: Suppose we have the following test scores of a student in five subjects: 85, 78, 92, 70 and 88. To find the average score, we add up all the scores and divide by the total number of scores:

Average=85+78+92+70+885=4135=82.6Average=585+78+92+70+88​=5413​=82.6

So, the average test score is 82.6.

Example 2: Consider a scenario where a team of cricket players scored the following runs in five consecutive matches: 45, 60, 75, 80 and 95. The average runs can be calculated as:

Average=45+60+75+80+955=3555=71Average=545+60+75+80+95​=5355​=71

Hence, the average runs scored by the team are 71.

Solving Average Problems: Strategies

When facing average-related problems in the CLAT quantitative aptitude section, it’s essential to approach them methodically. Here are some strategies to tackle such problems effectively:

• Understand the Question: Read the problem carefully to understand what type of average is required (simple average, weighted average, etc.). Pay attention to the given data and the context of the question.
• Summarise the Data: Organise the given data in a clear format. Make sure you’ve identified all the values and their corresponding weights (if applicable).
• Calculate the Sum: Calculate the sum of the given values. This is a crucial step as averages are calculated based on the sum of values.
• Identify the Count: Determine the total number of values in the dataset. This will be used as the denominator when calculating the average.
• Apply the Average Formula: Apply the average formula: Average=Sum of ValuesTotal CountAverage=Total CountSum of Values​. Plug in the calculated sum and count to find the average.
• Solve Weighted Averages: In cases of weighted averages, where different values have varying weights, multiply each value by its weight, calculate the sum of the weighted values and then divide by the total weight.
• Interpret the Result: Once you’ve calculated the average, interpret it in the context of the problem. Understand what the average represents and how it can be used to draw conclusions.

Example Problems

Let’s work through a couple of example problems to solidify the strategies discussed:

Problem 1: The ages of a group of friends are 25, 28, 30, 22 and 27 years. Calculate the average age of the group.

Solution: Sum of ages = 25+28+30+22+27=13225+28+30+22+27=132 Total count = 5

Average = 1325=26.45132​=26.4

So, the average age of the group is 26.4 years.

Problem 2: The scores of a student in three subjects are as follows: Mathematics – 90, English – 85 and Science – 92. If the weights of these subjects are 4, 3 and 5 respectively, calculate the weighted average score.

Solution: Weighted sum = 4×90+3×85+5×92=360+255+460=10754×90+3×85+5×92=360+255+460=1075 Total weight = 4+3+5=124+3+5=12

Weighted average = 107512=89.58121075​=89.58

The weighted average score is approximately 89.58.