AVERAGES
Content
• Average
• Weighted Average
Average
The Average of the number is a measure of the central tendency of a set of numbers. In other words, it is an estimate of where the centre point of a set of numbers lies.
The basic formula of average is
Average = sum of observations / number of observations
The average is also known as arithmetic mean
Ex. The average of the four numbers 101, 204, 305 and 407
= 101 + 204 + 305 + 407 / 4
= 254
Average Speed:
Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey [2xy/(x+y)]
Average speed: if both the time taken are equal i.e t1 = t2 = t, then, t1 + t2 / 2.
The average of odd numbers from 1 to n is = [Last odd no. + 1] / 2.
The average of even numbers from 1 to n is = [Last even no. + 2] / 2.
Key Points to remember
1. Average always lies between the lowest and the highest value of the observations.
2. If all the observations equal, the average value equal to the observation value.
3. If the value of each of the observations are increased / decreased by the same quantity X, then average will also increase / decrease by X.
4. If the value of half the observation increased by same quantity X and the value of other half of the observation decreased by the same quantity X, then the value of average doesn’t change.
5. If the value of each of the observations is multiplied by same quantity X, then average will also be multiplied by X.
6. If the value of each of the observations is divided by same quantity X, then average will also be divided by X.
7. If the number are in an arithmetic progression, then the middle value is the average of the entire series. If there are two middle values their average will be the average of all observations.
8. Use simple average only if the contribution of all the observation is same. If the contribution is different then use weighted average.
Weighted Average
When we have two or more groups whose individual averages are known, then to find the combine average of all the elements of all the groups we use weighted average.
Thus, if we have k groups with average A1, A2 … Ak and having N1, N2 … Nk elements then the weighted average is given by the formula:
Aw = (A1 N1) + (A2 N2) + … + (Ak Nk) / (N1 + N2 + … + Nk)
So, if you have weights are equal, the weighted average become a simple average. Instead of knowing the absolute values of the weights, we can calculate weighted average even by using the ratio of weights.
All The Best!!!
