In our everyday life, we came across a lot of data collection and representation. Whether we discuss our country’s population, the number of students in our class, our bills, or bank statement.
In fact, we are surrounded by data in many forms and collections. But the concern right now is, can it be possible to represent a collection of data by any specific figure or quantity of the data collection? Averages or measures of central tendencies are the simple solutions to this question.
Mean, Median and Mode are the basic measures of central tendencies. Which central tendency to choose to represent a specific data depends upon the type of data we are going to represent with the measure.
So let’s start our quest in this article for the mean and midpoint values and how can we calculate them?
Mean
The common average we are all aware of is the mean, in which we sum up all the vales and then divide it by the total number of values. However, there are four different types of means in central tendencies but here we will discuss the arithmetic mean.
Types of Mean
- Arithmetic Mean
- Weighted Mean
- Geometric Mean
- Harmonic Mean
Arithmetic Mean
In terms of Mathematics, arithmetic mean can be defined as a list of numbers to describe a central tendency. To calculate the arithmetic mean of the, add up all the variables in the data and then divide the sum by the number of items in the data collection.
The most well-known and popular measure of central tendency is the average or arithmetic mean. The mean could be used with discrete as well as continuous data. However, most commonly it is used with continuous data.
Mean Calculation
As mentioned above, the mean can be calculated simply by adding all the values and then by dividing with the total number of values. Mean can also calculate by using So if we want to calculate the mean of x number of values in a data collection and the values it contains are x1, x2, …………xn, then we can do this by:
M= sum of terms/no of term
In essence, the mean is a model of the data collection that we may calculate by using a mean solver. This is the most often used value. The mean, on the other hand, is rarely one of the real values in the data collection. One of its most valuable features, though, is that it reduces the amount of error in predicting any single value in the data collection.
That is, it is the value in the data set that causes the least amount of error when compared to all other values. The fact that every value in your data set is used in the equation is an essential property of the mean. The mean is therefore the only indicator of central tendency in which the sum of each value’s deviations from the mean is always zero.
Midpoint/Median
As the name implies the midpoint or median is the value that is present in the center or middle of a data collection. This quantity s could also be used to differentiate the given data set into two subgroups. These are higher half values of the sample and lower half values of the sample.
In order to find out the median in a given set of values. First, we have to arrange all of the values in ascending order of values, it is also known as ranking. Then we can find the midpoint by simply the center of the distribution. This method fits the situation when the data set has an odd number of values.
However, in the case of an even number of values, there can’t be a midpoint. Then we can find out our midpoint by forming a pair of two middle values. Then add both the values and divide the sum value by “2”. The resultant value then considered as the midpoint or median.
That means by taking the mean of two midpoint values we can calculate our midpoint. The median is such a central tendency that is least affected by skewed data and outliers.
