Basic Concepts Of Mean, Median, And Mode

In statistics and mathematics, the set of observations is represented by a value that describes the entire collection. The value used to represent the data set is called a measure of central tendency. It is the value around which the given data is centered. Let’s know more about these central tendencies including a mean median mode to make our basic concepts clearer and stronger.

What is mean in mathematics?

Mean or Arithmetic Mean in mathematics represents the average of a given set of data. It is the most common tool used in measures of central tendency. The value of mean is equal to the sum of all values given in the set of data divided by the total number of values given in the same data set.

Calculation of mean:

The mean for the ungrouped data is calculated by dividing the sum of the observations given in the data set by the total number of observations. It can be represented mathematically as:

Mean = ∑x/n

where,

∑ = values that are to be added

x = all values in the given data set

n = total number of values in the given data set

When it comes to calculation of mean for grouped data then there are three methods:

• Direct method
• Assumed Mean Method
• Step Deviation Method

What is median in mathematics?

Median is that tool of measure of central tendency that represents the middlemost value of the given set of observations when the same are arranged in ascending or descending order. To calculate the value of median it is imperative to know if the total numbers given in the data set are odd or even.

Calculation of median:

To calculate the median of the ungrouped data first the numbers in the given data set are arranged in ascending or descending order. If the total number of observations (n) is odd then the following formula is used:

Median = n + 1/2th Observation

If the total number of observations (n) is even, then the following formula is used:

Median = [(n /2)th Observation + ((n/2) + 1) th Observations] / 2

When it comes to the calculation of median for ungrouped data, the following formula is used:

Median = l + [n2-cf] × h

where,

l = lower limit of the median class

c = cumulative frequency of the class preceding the median class

f = frequency of the median class

h = class size

What is the mode in mathematics?

The mode represents the most repetitive value in the set of data. It is possible to have more than one mode in the data set. When there are two modes for a given set of observations then it’s called bimodal and when there are more than two modes then it is called multimodal.

Calculation of mode:

The mode for ungrouped data can be found by visually observing the value with the highest frequency.

When it comes to the calculation of mode for grouped data, the following formula is used:

Mode = l+(f1-f02f1-f0-f2) × h

Where,

l = lower limit of the modal class

h = size of the class interval

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

Bottom Line

Mean, median, and mode are the important tools of measures of central tendency used in providing information about the center, or middle part, or frequently repeated number, of a given data, set. Cuemath is an online platform that helps students to learn all about the above-mentioned concepts. Teachers here will teach you using different approaches making the learning easy and fun.