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The three types of “averages” are defined in Mathematical statistics ad these are mean, median, and mode. There are numerous “averages” in statistics, but these are the three the most prevalent, and most likely to encounter pre-statistics courses
Mean Median and Mode can be differentiated as follows:
The mean, median, and mode are all measures of central tendency in statistics. They inform us what value in a data set is typical or indicative of the data set in different ways.
- Mean
A calculation is used to find the mean, which is the same as the average value of a data set. Divide the total number of numbers in the data set by the total number of numbers in the data set.
- Median
The median can be defined as the middle number of a data set. Arrange the data points in ascending order and find the Centre number. This is the middle point. If two numbers lie in the Centre, the median is the average of the two.
- Mode
The mode will be the number that appears the most frequently in a data set. We have to count the number of times each number appears in the data. The number with the greatest frequency is the mode. It’s fine if there are multiple modes. There is no mode if all numbers appear the same amount of times.
How to calculate mean
- To get the total, add up all the data values.
- Count how many values your data set has.
- Divide the sum by the count.
In a data set, the mean corresponds to the average value.
Formula to Calculate the mean
The total of all the data divided by the count n is the mean x̄ of a data set.
How to Calculate the Median
The median x~ is the data value that separates the upper and bottom halves of a data set.
- firstly, we have to arrange the data values in ascending order from lowest to highest.
- The data value in the middle of the set is called the median.
- The median of two data values in the Centre is the mean of the two numbers.
Formula for the Median
The median x˜ is the data point that separates the upper half of the data values from the lower half when ordering a data collection X1≤ X2≤ X3≤ …….≤ Xn from lowest to highest value
The median is the value at location p where the size of the data set n is odd
How to calculate mode
A mode of data can be defined as the value that appears the most frequently in the provided data, i.e. the observation with the highest frequency.
- Case 1: Data that hasn’t been grouped
For ungrouped data, we just need to find the observation that occurs the most. A data with the highest frequency is referred to as mode.
For example, with the following data: 6, 8, 9, 3, 4, 6, 7, 6, 3, the number 6 appears the most. As a result, mode = 6. The following is a simple approach to remember mode: The most often entered data. Note that a datum can have no mode, one mode, or multiple modes. The data can be classified as unimodal, bimodal, trimodal, or multimodal depending on the number of modes it contains. The given example is unimodal since it only has one mode.
- Case 2: Data in Groups
When the data is continuous, the following steps can be used to determine the mode:
Step 1: Determine the modal class, or the class with the highest frequency.
Step 2: To find mode we have to use the following formula :
were,
- l = lower limit of a modal class of the given set,
- fm is frequency of modal class of the given set,
- f1 is frequency of class preceding modal class of the given set,
- f2 is frequency of class succeeding modal class of the given set,
- h is the class width of the given set.
All the three measures of central values, namely mean, median and mode are related (called an empirical relationship).
3Median = 2Mean + Mode
For example, if we are requested to discover the mean, median, and mode of continuous grouped data, we can use the formulas mentioned in the preceding sections to obtain the mean and median, and then use the empirical relation to find the mode.
If we have data with a mode of 45 and a median of 35.2
Then, utilizing the aforementioned mean, median, and mode relations, we can find the mean.
2mean + mode = 3 median
Or, 2mean = 3 x 35.2 – 45
Or, 2mean = 60.6
Or, mean = 60.6 / 2 = 20.3
Conclusion:
Here we come to know that the measures of central tendency mean, median, and mode is used to investigate the various properties of a set of data. A measure of central tendency identifies the centre position in a data collection as a single value and uses it to characterize a set of data.
