When it comes to statistics, there are plenty of things that you would need to learn before you can call yourself someone advanced. It would take an entire lifetime if you were to try and cover each and every single topic that existed under the heading of statistics. However, before you can go towards any of those, the first thing you need to familiarise yourself with are the basics.
There are several things that can be considered as the ‘basics’ of statistics. But the 3 main topics which fall under this category are:
These 3 terms are the basic foundations of understanding anything else in statistics. It wouldn’t be a stretch to state that you would not be able to calculate a single other advanced topic without knowing how to calculate the mean, median or mode.
They are existent in almost every sort of calculation and you will see that being the case once you begin to dig in as well. But enough about that, let’s just stay focused on the topic of discussion at hand. Here are 5 steps each to help you calculate the mean, median and mode of a given set of data.
The mean of a given set of data, also known as the mathematical average is basically the first measure of said data set. It gives us an idea about the tendencies of the current data set and which value it resides around. It may sound a bit complicated but it is really as easy as it can get. Finding the average can be summed up as follows:
- First, find the sum of all the given numbers in the data set. It does not matter in which order they are arranged since all you need to be concerned with is the sum total and nothing else.
- Next, you need to count the number of data existing within the set. So basically you need to find the total number of addends in the given problem.
- Once you have both of the above, simply divide the total sum by the total number of addends and you will find the average for the given data set. Keep in mind that the mean may not be a whole number at all times. In fact, it is likelier for the mean to not be a whole number.
- Things are a little bit different if you are given a frequency table to work with. In that case, you will have to find out the frequency scores of all the data given. Then you multiply this frequency with the corresponding data and add it with all of the rest.
- Then you follow the same step as before and you divide the total sum by the total frequency from the frequency table. The final result is the mean that you are looking for.
The Median of a data set is basically a reference to the middle element of the set so that one half of the set is on the left while exactly the other half is on the right. It gives you an idea about the gradient of change taking place in the data set from left to right. But before getting into such technical details, let’s just find out how we find the median of a given data set:
- The first and most important step of finding the median is to arrange the given numbers in ascending order from left to right. This is crucial since otherwise there would be no way to see which element falls in the ‘middle’.
- The next thing you want to do is to find the total number of elements that exist in the given data set. This really matters since the calculation depends on whether or not the total frequency is odd or even.
- If it is odd, the calculation is really simple. Divide the (total number of elements + 1) by 2 and the result gives you the position of the element that is the median for the data set.
- If it is even, divide the total number of elements by 2. Find the average of the element in the resulting position and the element in the next position. The resultant number is the median for this data set.
- The discrepancies between the 2 formulas for odd and even number of elements should be pretty intuitive in nature. You are looking for the exact middle element of an arranged data set. As such, the procedure mentioned above should make perfect sense.
The Mode of a data set is defined to be the most frequently occurring data element in that set. It is much simpler than any of the abovementioned things in terms of calculation. You will sometimes even be able to do it just by looking at the data set without any pen and paper. But if you have to define it formally, it would go something like:
- Start analysing the list from left to right. Find the frequency of the first number that you encounter while doing so.
- Move on to the next number and do the same for it. If it is greater than the previous frequency, consider the newer one to be your current mode.
- Repeat this process for the entire list as you go from left to right until you have exhausted the entire thing. The highest frequency item that you end with is the mode.
- For calculation of mode, it is recommended that you make a frequency table since it makes things much easier.
- Also keep in mind that if a data set has no elements that occur more than once, the mode for that list is considered to be non-existent.
The Things You Need to Know for Easily Calculating the Measures of Central Tendency in Statistics
You will find that in the present times, information can be found in all corners. Right from the number of students studying in a class to average monthly income of a citizen. These numbers are really important to study and know different facets of everyday life.
Information around you is vast, hence effective steps are required to be taken for calculating everything meaningfully and interpreting results. There are certain tools of statistics, such as mean, median and mode which helps in determining results more effectively.
When you are using these tools, you will gain a new insight regarding looking at the data. You will know for sure about how information behaves when different activities take place around you.
Occurrence of mode
When you are going through a specific set of information, mode will be a particular value which occurs the most number of times in a data set. Mode is often useful in giving us the correct value when certain number of outliers are present in the data set. For example, in a company, there might be a manager and certain number of workers.
The wages earned by these workers might be in thousands and that earned by their manager might be in millions. If you go about calculating the average salary of employees, then you will definitely get a wrongly interpreted data.
This is because of the huge salary taken the boss in comparison to the workers. The value which has maximum leverage in a data set is preferred over others here.
Average based mean
The mean of a data, is often known as an average. However, the mean is not the only type of average that is used during calculations. Mean is used for calculating the statistics in different arenas such as academics as well as sports.
For example, when you see the goal average of a footballer, that number would be representing the number of goals scored divided by the number of minutes that he has played football.
The final grade that students get while in school, is also of course a mean value. This kind of mean would be representing the number of marks you scored, divided by the total number of marks allotted in the paper. This is a really good example of mean as calculation gives a single number as result.
Median for showing average
The mean is considered to be a universal number for calculating averages. However, you will also find that the median is also often sued for expressing the average in a more transparent manner. Median is that value in the data set, where half of the numbers are above the median value and the other half is below the median value.
You may have often heard about the median salary being offered at the end of studying in a B school. This number represents the middle most value in the group. In case of using mean, there always exists a chance of very low values or very high values influencing the final outcome.
However, when you are using median for calculations, the chances of that happening is almost nil.
Find the perfect value
The mean, median and mode are considered to be the measures of central tendency used widely. From a collection of data, the question often arises regarding where a particular data would reside inside it. When you consider a certain collection of data, the centre point or the mid-point is something that everyone wants to know at first.
You need to consider the spread of the data or find its variance before you can proceed with making certain decisions. Conclusions from data sets are derived in this way.
To calculate the mean, the total number of data values, are divided by the number of data points in the set. If you consider data to be markings on a scale, then the mean would be a balance point with equal amount of weight or distance on both sides of data. If there was a center of that scale, then it would be called its mean. You do not require sorting data in any manner in order to calculate mean. Often you will find that it is more time consuming to calculate mean in comparison to calculating median or mode.
Calculation of median
Median is considered to be that middle value when you sort your values in either ascending or descending order. If there are odd number of values, then a median can be determined quite easily. If there are even number of values, then median would be calculated by taking into account two of the middle values. Sorting of data, actually gives you a definite edge when you undertake calculations or form assumptions.
Median is not really sensitive towards different extreme values in data sets. Not much calculation is required here except for arranging data, which gives a clear picture. Sometimes it becomes a little tedious to do sorting for a huge amount of data. Median values are often known to vary more than mean when moving from one sample to another.
As mentioned earlier, a value occurring the most number of times in a data set, would be its mode. It is very much possible for more than one mode to exist in a set of data. You simply need to identify a value occurring more than others in a set of data and you will have your mode. It is an actual value and can be identified by use of any kind of histogram plot. It is not mandatory for value of this mode to be close to that of median or mean.
When to use a measure?
Mean and median are used most often in calculations. You need to take a hard look at the data in front of you to determine which method is to be used for your calculation. Having some idea about variance and standard deviation will also help in extracting data from data sets easily. You cannot use mean or median in every situation of statistics.
Michelle Johnson is a name that you will find to be synonymous with a lot of students. She holds an MBA degree and hails from University of Pennsylvania. She is a really motivating author cum teacher and has 6 years of experience in this field. Statistics has got more interesting for students ever since she has taken over.