Question

Ashish studies for 4 hours, 5 hours and 3 hours respectively on three consecutive days. How many hours does he study daily on average?

Answer 1

Hint: To solve this question, we will take addition of numbers given in question and then we will divide that sum by the total numbers given in question. In other words, we have to find the arithmetic mean of numbers given in question. The arithmetic mean or average of any data is calculated from the formula shown below:
Average \( = {\rm{ }}\dfrac{{{x_1}{\rm{ + }}{{\rm{x}}_2}{\rm{ + }}{{\rm{x}}_3}{\rm{ + }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. + }}{{\rm{x}}_4}}}{n}\)
where \({x_1}{\rm{ + }}{{\rm{x}}_2}{\rm{ + }}{{\rm{x}}_3}{\rm{ + }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. + }}{{\rm{x}}_4}\)are the entities and n is the total number of entities.

Complete step-by-step answer:
Before we solve the question, we must know what an average is and how it is calculated. An average is a single number taken as representative of a list of different numbers. In other words, we can say that an ‘average’ is the arithmetic mean which is the sum of numbers divided by how many numbers are being averaged. An average can be said to be the central number of list. To calculate the average of numbers, we add up all the numbers then we divide the sum by how many numbers there are. Thus average of any data can be calculated by the formula shown below:
Average \( = {\rm{ }}\dfrac{{{x_1}{\rm{ + }}{{\rm{x}}_2}{\rm{ + }}{{\rm{x}}_3}{\rm{ + }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. }}{\rm{. + }}{{\rm{x}}_4}}}{n}\)
In our case, we have only 3 entities (hours) so the value of \[{\rm{n}} = {\rm{3}}\]. So the average number of hours in our case will be:
Average \( = {\rm{ }}\dfrac{{3{\rm{ hours + 4 hours + 5 hours}}}}{3}\)
\(\begin{array}{l} \Rightarrow {\rm{ Average = }}\dfrac{{12{\rm{ hours}}}}{3}\\ \Rightarrow {\rm{ Average = 4 hours}}\end{array}\)
So, Ashish studies 4 hours daily on average. The unit of average will be the same as the unit of individual entities.

Note: The alternative method to find the average of the given numbers without any calculation is as follows. If the number of entities are odd in number and they differ by the same amount when they are arranged in increasing order then the middle entity will be equal to the average of the numbers. In our case, the numbers are: 3, 4, 5. So the middle number is 4 and hence it will be the average.