How To Calculate Averages? Mean, Median, Mode 📟
Big data can be complex and confusing to the mind . Additionally, analysing them is challenging. The several figures that are being compared must all be reduced to just one single figure in order to simplify the data and make it comparable.
If, for example, a comparison is made between the marks obtained by 100 students of B.Com. II class of a college and the marks obtained by 100 students belonging to B.Com. II class of another college, it would be impossible to arrive at any conclusion, if the two series relating to these marks are directly compared.
On the other hand, comparison and understanding would be much simpler if each of these series were represented by a single figure. An average is a single number that sums together all the data in a set. Averages are also referred to as measurements of location or measures of central tendency.
How To Calculate Averages?
Meaning of an average ⌛️
An average is a single value that sums up the entire set of data, with each individual item centred around it. An average, then, is a single value within the data range that is used to represent each value in the series as a whole. Since this average falls somewhere in the data’s range, it is known as a measure of central tendency.
Formula 💡
How To Calculate Averages?
Average: Sum of Values / Number of Values
TYPES OF AVERAGES
There are different kinds of averages. The three main types of averages are =
- Arithmetic Mean
- Median
- Mode
LET’S UNDERSTAND THEM IN BRIEF,
ARITHMETIC MEAN 💰
Arithmetic Mean:
~ An average of all elements in a series is called the arithmetic mean.
~It is the simplest measure of central tendency.The arithmetic mean of a series is called ‘Mean’.
- ARITHMETIC MEAN:
Formula:
Arithmetic mean is generally written as X.
( INDIVIDUAL SERIES )
DIRECT METHOD
i) Formula – Σf/ N
Where, Σf is sum of frequencies,
N is the number of observations.
ii) Find the sum of frequencies, i.e., f or N.
iii) Divide the total obtained Σf by the number of observations. The result would be the value of arithmetic mean.
Σ is a sign called sigma.It refers to the sum total of the values of different items in the series.
SHORT-CUT METHOD 🪚
When the number of observations are large, the arithmetic mean can be calculated by using short-cut method or assumed mean method. When deviations are taken from an assumed mean, the following formula is used
overline X = A + (Σ d)/N
Where, d-Deviations of the items from the assumed mean, ie, X-A Assumed Mean
Steps for Calculation
i)Any one of the items in the series is taken as assumed mean A.
ii) Take the deviations of the items from the assumed mean, ie, X-A and denote these deviations by d.
iii) Obtain the sum of these deviations.
(iv) Substitute the values of A, Σd and N in the above formula.
Therefore, the result will give the value of mean.
2. MEDIAN ⛓️
Median is another important measure of central tendency. It is an average based on position. The middle value in a series when it is arranged either in ascending or descending order is known as the median. It is a value that splits the ordered series into two equal portions so that the number of observations below and above the median are equal. Therefore, median is a positional average.
A point to be noted is that median is always determined by first arranging the series in an ascending or descending manner.
Calculation of Median
• Individual Series
The formula used for calculating the median in individual series is:
M=Size of (N+1)/2 th item.
Here, M is the median, and N is the total number of items in the series.
Steps for Calculation
i) Arrange the data in ascending or descending order of the size.
ii) Locate the median item by using the formula N+1/2
iii) The value or size of this item is the median.
3. MODE 📱
Mode is another important measure of central tendency. It is a value which has the greatest frequency in a distribution. For example, the mode of the series 20, 21, 23, 23, 23, 23, 25, 26, 26 would be 23, since this value occurs most frequently than any of other values. The above description indicates that mode is the value around which there is in greatest concentration of items. So, the symbol for mode is “Z”. Calculation of Mode
• Individual Series
In case of individual series, mode can be computed by inspection method. Inspection method involves an inspection of the items. Therefore, one needs to simply look for the value that occurs in series the maximum number of times. Such a value is called mode.
Example . Find the mode from the following data: 8, 12, 6, 8, 2, 7, 8, 9, 10, 7
Solution:
The value 8 is the one amongst the following that occurs most frequently in the series.
Hence, Mode (7) = 8.
So , that’s all about How To Calculate Averages? Mean, Median and Mode. We hope this math factoid will help improve your mathematical thinking and logic skills.
