Mean Median Mode

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Mean median and mode is a very important topic of statistics. Learn this concept and gain quality statistics help. Geometry, Median is defined as the line segment joining a vertex of a triangle and the midpoint of the side opposite to the vertex.

In Statistics, The center or the middle most value of the given data which are arranged in ascending or descending order is known as Median.

What is Mean median and mode?

Mean median and mode are more common terms in statistics.

The average or mean is calculated by arranging the values from the set in a particular way and computing a single number as being the average of the set.

The median of a list of number can be arranging all the values from lowest value to highest value and select the middle one.

Mode is also a compute of central tendency. In a set of individual observations, the value occurs most time is called as mode.

Below are the brief discussion about the Mean,median and mode

Mean

In general Arithmetic mean (A.M) or average of n number of data x1, x2, …, xn is defined to be the number x such that the sum of ...
... the deviations of the observations from x is 0. That is, the arithmetic mean x of n observations x1, x2, …, xn is given by the equation

(x1 - x) +(x2 - x) + ... +(xn - x) = 0

Hence `barx` = x1+x2+x3+…….xn / n

Mean or average= sum of elements / total number of elements

The given sets of data are arranging in ascending or descending order, find a value centrally positioned in the arranged order. This central value or the middle value is called the statistics median of the data.

The total number of elements in the distribution is odd; the middle location of data can be computed by using the statistics median formula `(n+1)/(2)` .

The total number of elements in the distribution is even, the middle location of data can be computed by using the statistics median formula `(n)/(2)` and `(n)/(2)` +1.

First, outline the cumulative frequency column and then find the value of `(2)/(N)` here N is the total number of frequency. Then we locate the class interval or the value of the variate in the table for which the cumulative frequency is either equal to `(N)/(2)` or just greater than `(N)/(2)` . This is the median class of this distribution.

Ex : To find the mean or average of 7, 5, 6

Step 1: Find the sum of numbers

7+5+6= 18

Step 2: Calculate the total value. Therefore 3 values

Step 3: Calculate mean use formula 18/3=6

Ans : 6

Median

For the definition, Consider the data 14, 28, 20, 29, 18, 25, 26, 17, 36. Arranging them in the ascending order, we get 14,17,18,20,25,26,28,29,36. We observe that 25 is centrally located in the series. Hence, it is the median of the data.

We note that there are odd number of observations and so we are able to locate the median as an observed value in the series.For the definition, Consider the data 85, 79, 57, 59, 66, 26, 40, 33, 48, 53. Arranging them in the ascending order, we get 26, 33, 40, 48, 53, 57, 59, 66, 79, 85. Since there are even number of observations, we get 53 and 57 centrally located in the series. Hence, we take their average, namely (53 + 57 )/2 = 110 / 2 = 55 as the middle most value for the series. This is the median of the given data.

To get the median for a raw data, we proceed as follows:

First we arrange the entire data in the ascending order. Let N be the number of observations. If N is an odd integer, then there is only one middle term and it is the [(N + 1 )/2 ]th term of the given set of observations. This is the median . If N is an even integer, there are two middle terms. They are the (N/2) th and [(N/2) + 1] th term. Hence the median is the average of these two terms.

When the data are arranged in the form of a frequency table, we proceed to find the median as follows:

Form the cumulative frequency column and then find the value of 2N where N is the total frequency.
Locate the class interval or the value of the variate in the table for which the cumulative frequency is either equal to2N or just greater than 2N. This is the median class of this distribution.
The value of the variable in the table corresponding to the median class is the median of the given data.
Median in Geometry:

As there are three vertices, there are three medians of a triangle. The medians of a triangle are concurrent. The point of concurrency is called the centroid of the triangle and is usually denoted by the letter G. The point G divides each median in the ratio 2 : 1. G is more near to the side than to the vertex. Based upon the properties of the centroid G, we give below the procedure to locate the point G.

Mode

Mode is also used to compute a central tendency. In a set of individual observations, the value occurs most time is called as mode.

Ex : Find the mode of 7, 1, 3, 1, 7, 3, 2, 6,7.

Sol : Arranging the data in the ascending order 1, 1, 3, 3, 4, 6, 7, 7, 7.

In the above data 7 occurs maximum number of times. Hence mode = 7.

Comprehend more on about natural numbers and its Circumstances. Between, if you have problem on these topics math tutor, Please talk about your thinking.