Summarized Video Lesson: Mean, Median, and Mode

In statistics, the three measures of central tendency are mean, median, and mode. While describing a set of data, we identify the core position of any data set. This is referred to as the main tendency measure. Every day, we encounter data. They can be found in newspapers, publications, financial records, cell phone bills, and utility bills. The list is endless, and they are all around us. The challenge now is if we can determine some key aspects of the data by considering only a subset of the data. This is accomplished by using measures of central tendency or averages, like mean, median, and mode.

Mean

The summation of all data divided by the total number of data is the arithmetic mean of a sample of information. For example, a cricketer’s four ODI scores are as follows: 32,45,7,39.  To get his average score in a game, we use the mean formula to compute the arithmetic mean of the data:

Mean = Summation of all observations divided by the total number of observations

Mean = 32+45+7+39/4

Mean = 30.75

Median

The median of the data is the value of the middlemost observation obtained after organizing the details in ascending or descending order.

Consider the following data: 5, 4, 7, 1, 9. Let’s put this information in ascending order: 1, 4, 5, 7, 9. There are 5 data points in this example. As a result, median = middle value of the data set, i.e. 5.

Mode

A mode of data is the value that appears the most frequently in the provided data, i.e. the data with the highest frequency. For example, with the following data: 6, 7, 8, 5, 3,8, 5, 4, 1, the value 8 appears the most times. Consequently, mode = 8.

Formula to calculate Mean, Median & Mode

Mean formula for ungrouped data: Sum of all observations/total Number of observations

Mean formula for grouped data: x̄ = (x1f1 + x2f2 + … + xnfn)/(f1 + f2 + … + fn)

Median formula for ungrouped data: If n is odd, then use the formula: Median = (n + 1)/2th observation. If n is even, then use the formula:

Median = [(n/2)th obs.+ ((n/2) + 1)th obs.]/2

where,

l = median class’s lower limit

c = the cumulative frequency of the previous class before the median class

f denotes the frequency of the median class.

h denotes the class size.

Mode formula for ungrouped data: Mode = Maximum Frequency Observation

where,

l = modal class lower limit,

f_m = modal class frequency,

f₁= frequency of class preceding modal class,

f₂ = frequency of class following modal class,

h = class width

Relationship Between Mean Median And Mode

The mean of a data set is calculated by adding all of the data values together and dividing the overall number of data sets by the total number of data sets.

The median is the value in the center of the observed set of data, and it is calculated by sorting the values in ascending or descending order and then picking the middle value.

A data set’s mode is the number with the highest frequency, which is calculated by counting the frequency with which each data value occurs.

The mean is the average of the data values shown, and it is calculated by dividing the sum of all data values by the number of data values. The median is the value in the center of a data collection when the values are sorted in ascending or descending order. The most often occurring data value is the mode data value.

Conclusion

We studied what is the mean, mode formula, mean median mode, and other topics related to Mean Median and Mode.

Mean, median, and mode are measures of central tendency or distinct types of averages in statistics. The mean is the “average,” which is calculated by adding all of the values and then dividing by the number of figures, whereas the median is the “middle” value in the list of numbers. The mode value is the value that appears the most frequently in the given collection of data.