I remember from my childhood memory that whenever our teacher used to show our test papers in class and I and my friends used to find the average of our marks to see who got how much and also to prepare ourselves for the result day. But what actually is an average? The average is the middle value that we get when we calculate anything by adding all the numbers first and then divide the result by the total quantity of the figures that were added.
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Many of us have been called an average student by our teachers in the class or by our friends from our sports club. Most of us have experienced this. So what is being average means? What does the word average itself means? Why do we use it and where should we use it? Well, here are the answers. We use an average to generalize the information that we are provided with. This makes the calculation easy and very understandable. Can we just by looking at the students tell them their average height? Or maybe their age? We can surely calculate them. So why wait? Here is how we use the average value formula to calculate the average.
There is a simple formula with the help of which we can calculate the average. The formula to calculate an average is:
Average = Sum of All The Numbers / Total Numbers
The average value formula helps us to calculate the average in a very simple and easy way. Average is also known as mean. In fact, mean median and mode are the types of averages that we usually use in Mathematics. For calculating the average, we just have to add up all the given numbers and then divide it by the total number of the numbers that we have. For example, if we are given numbers like 22, 18, 6, 25, 39, 42, 66, 13, 52, and asked to take out the average then we just have to go according to the average value formula.
Average = Sum of All The Numbers / Total Numbers
= 22 + 18 + 6 + 25 + 39 + 42 + 66 +13 + 52
= 283 9
Therefore, 31.4 is the average.
Often in our daily lives, we face problems that deal with the average calculation frequently such as the average runs of Sachin Tendulkar in his test matches, the average temperature, the average age of a family, or a member of the family. On the basis of these calculations, we can find out who might live longer on an average: men or women. Or we can say that on average, healthier people are the ones who don’t smoke than the people who do. There are numerous average related problems that we are usually asked in our aptitude exams.
Question 1) There are 7 boys and the mean weight of all of them together is 56 kgs. If we know the weight of six of them as 52, 57, 55, 60, 59, and 55. What will be the weight of the seventh boy?
Solution 1) We know the mean weight of 7 boys is 56 kgs (that is 56 kgs x 7 = 392) and we also know the individual weight of six of the boys that we will add up together.
So, 52 + 57 + 55 + 60 + 59 + 55 = 338 kgs.
Therefore, the weight of the seventh boy = total weight of the 7 boys - the total weight of 6 boys.
= 392 - 338 kgs
= 54 kgs
Hence the total weight of the 7th boy is 54 kgs.
Question 2) If a cricketer has a mean score of 58 runs in 9 innings. So, how many runs can the cricketer score in the 10th innings to get the mean score of 61?
Solution 2) The mean score of 9 innings were 58 runs.
Therefore the total score of the 9 innings will be 58 x 9 = 522 runs.
The mean score required in 10 innings is 61 runs.
The total score required in 10 innings is 61 x 10 = 610 runs.
Therefore the total number of runs to be scored in 10 innings will be:
The scores of 10 innings - the scores of 9 innings = 610 - 522 = 88 runs.
Question 3) There are 5 numbers whose mean is 28. If one number gets excluded and the mean reduces by 2 then what is the excluded number?
Answer 3) the mean of 5 numbers are 28.
Sum of the five numbers are 28 x 5 = 140
So if the mean is reduced by 2 the means of the rest 4 will be 28 - 2 = 26
The sum of these 4 numbers will be 26 x 4 = 104
Therefore, the excluded number will be the sum of 5 numbers - the sum of 4 numbers
140 - 104 = 36.
1. What Is The Relationship Between Average And Mean, Median, And Mode?
Average is very closely related to mean, median, and mode. We find the mean by adding all the numbers together and then dividing it by the total number of numbers that is almost like how we calculate average. The median is basically the middle value of the list of numbers. We find the median by first arranging all the numbers in numerical order that is from smallest to largest. The mode is the value occurring frequently. Mean, median, and mode are usually the measures of central tendency used in statistical data.
2. Why Do We Calculate The Average?
Often in our life, we face problems where we fail to predict the exact value of a quantity, therefore, calculating an average helps us to get to an approximate value. For example, there is a family who is about to cross a river. In such a situation we must be aware of two things. First, how deep is the river and secondly our own height so that we don’t get drowned. The river’s depth is 4 feet and the members of the family have the following heights: The father is six feet tall the mother is 5.5 feet tall, the daughter is 5 feet tall and the son is 3.5 feet tall. So what do you think? Who all will be able to cross the river? This is where we need the application of average.