Averages is a topic that appears quite often in many important examinations.
So, what do you understand by the term Average? For any list (or set) of numbers, its average is simply the central value of that list (i.e., the mean value).
The simple formula:
Average = Total value / No. of values
Average = Total value / No. of values
Total value = Average * No. of values
Do note that the average would always be greater than the lowest value and smaller than the highest value among all numbers in a list. An average is simply the central value of a list. Thus, the average would always lie between the extreme values in a list.
For example, if the highest amount is Rs. 170 and the smallest amount is Rs. 120.
The average amount would be Rs. 150, which falls between Rs. 120 and Rs. 170.
Let us now look at example on averages.
A smuggler illegally transports drugs from Surat to Baroda in his car every day. While travelling to Baroda, his car is heavier due to all of the drugs. Hence, he is only able to drive at 20 kph and so takes 6 hours for this part of the journey (Surat to Baroda). While returning, he is able to drive at 30 kph and so takes only 4 hours. Can you figure out his average speed over the entire journey, i.e. the journey from Surat to Baroda and back to Surat?
20 + 30 = 50 kph and 50 kph/2 = 25 kph
Actually, 25 kph is not the right answer!
The right answer is 24 kph.
Let us see how we get this answer.
Distance from Surat to Baroda = 20 kph * 6 hours = 30 kph * 4 hours = 120 kms.
Hence, total distance covered while travelling from Surat to Baroda and back = 120 kms * 2 = 240 kms and Total time taken = 6 + 4 hrs = 10 hrs.
Thus, total distance covered = 240 kms and total time taken = 10 hrs
Hence, average speed = 240/10 = 24 kph
Weighted Averages:
Weighted average can be calculated in 2 steps:
Step 1: Total value = sum of (each value * number of times the value appears)
Step 2: Average = Total value / Total number of values
Example:
In a group of four top order batsmen, two scored 20 runs each in a certain match while the other two scored 60 and 40 runs respectively. What is the average runs scored by these four batsmen in this match?
Total runs scored = 1* 60 + 1*40 + 2*20 = 140
Total number of batsmen = 4
Thus, average runs = 140/4 = 35