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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsStatistics and ProbabilityStatistics : Analysis of Data

Representative Values of Data : Mean, Median, Mode

In this page, the mean, median, mode of a data is introduced with examples.



click on the content to continue..

We have studied about representation of data in

tally marks
tabular form
pictograph
bar-graph

All these representations help to visualize and understand the data.

Consider the data : The height values of five students from a class are given below in centimeters.

`90`, `97`, `91`, `92`, `90`.

All these students are of the same age.

Another student of the same age is joining the class. Using the above data, one can say that, the new student will be about the same height as the current students, little more or less.

The height values of five students from a class are given below in centimeters.

`90`, `97`, `91`, `92`, `90`.

This data is used to predict the height of student of the same age. Instead of giving the entire data, can the data be summarized?data representation To summarize the data, there are three possible solutions.

   1. Mean: The value when all data are evenly distributed among the given data values. This involves addition and division.

   2. Median: The value that is in the middle of the increasing or decreasing order of the given data values. This involves arranging in increasing or decreasing order.

   3. Mode: The data value that is repeating most number of times in the given data values. This involves counting.

Each of these three is explained with the given dataset.

finding mean The height values of `color(coral)(5)` students from a class are given below in centimeters.

`color(deepskyblue)(90)`, `color(deepskyblue)(97)`, `color(deepskyblue)(91)`, `color(deepskyblue)(92)`, `color(deepskyblue)(90)`.

The given values are added and divided by the number of values

mean
`=color(deepskyblue)((90+97+91+92+90))//color(coral)5`
`=color(deepskyblue)(460)//color(coral)(5)`
`=92`

This is understood as "evenly distributing the values". This is illustrated in the figure.

This value is represented as the "mean" of the given data.

The word "mean" has a meaning, value of each data point when all are grouped together and evenly distributed among them.

familiarize with the terminology
mean

Mean is also called arithmetic mean.
Mean is also called as average by some authors.

Generally, average includes all three measures mean, median, and mode. These three measures are also called as central tendencies.

finding median The height values of `color(coral)(5)` students from a class are given below in centimeters.

`color(deepskyblue)(90)`, `color(deepskyblue)(97)`, `color(deepskyblue)(91)`, `color(deepskyblue)(92)`, `color(deepskyblue)(90)`.

The given values are arranged in increasing order and middle one is found.

median
`=text( middle of increasing order )color(deepskyblue)((90, 97, 91, 92, 90))`
`=text( middle value of )color(deepskyblue)((90, 90, 91, 92, 97))`
`=91`

This is understood as "removing equal number of data values that are smaller and larger". This is illustrated in the figure.

This is represented as "median" of the data.

The word "median" means: the data value at the middle with equal number of smaller and larger data values.

familiarize with the terminology
median

finding mode The height values of `color(coral)(5)` students from a class are given below in centimeters.

`color(deepskyblue)(90)`, `color(deepskyblue)(97)`, `color(deepskyblue)(91)`, `color(deepskyblue)(92)`, `color(deepskyblue)(90)`.

The values that is repeating most number of times is found.

`90` is repeated twice, and other data points `91`, `92`, `97` are repeated only once. So,
mode
`=90`

This is understood as "the value that repeats most number of times". This is illustrated in the figure.

This value is represented as the "mode" of the data.

The word "mode" means: most repeating data value.

familiarize with the terminology
mode

Mean : The value when the data is evenly distributed to all the values.

Simplified Procedure to calculate Mean : Add all the data values and divide the sum by the number of data-points.

Median : The value that has equal number of smaller and larger data values in the given data.

Simplified Procedure to calculate Median : Arrange the data values in ascending order and find the value in the middle.

Mode : The value that is repeated most number of times in the data.

Simplified Procedure to calculate Mode : Count the number of times a data-point repeats and find the data value with most repetition.

                            
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