Mean Mode Median Standard Deviation

By Author: Pierce Brosnan
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Introduction to mean mode median standard deviation:

Mean:

The mean is the standard of the integers.

It is simple to calculate: Just attach up all the integers, then divide by how many integers there are.

Formula for mean is, `barx`= `sum x` / n

Median:

The middle number in the sorted list of numbers is median. Half the numerals in the directory are a lesser amount, and half the numbers are greater are called as the median.

To get the Median, place the given set of integers arrange and find the middle number.

Mode:

The mode of a set of data is the value which happens frequently.

In other words, the mode is the value of a variable that occurs most frequently with in a sample or population of data values.

Concept of Mean, Median, Mode and Standard Deviation: Standard Deviation

Standard Deviation is the purpose of illustrating the variability of the spread of the Data set in the given total values in data set. It is used to take quantify for the average of integers in the given Data set. Standard Deviation given by the ...
... sum of the total squared mean difference and it is divided by the total number of values minus one.

Formula for standard deviation,

S = `sum (x - barx)` / (n - 1)

Where, S = the statistical variable is called as standard deviation.

Example for Mean Mode Median Standard Deviation:

Problem of find median:

Median example:

The points scored by a Tennis team in a series of matches are as follows:

22, 5, 10, 30, 18, 8, 16, 11, 14, 29, 53, 13, 9, 10, 25, 33

Find the median of the points scored by the team.

Sol:

To arrange the given points in ascending order, we get

5, 8, 9, 10, 10, 11, 13, 14, 16, 18, 22, 25, 29, 30, 33, 53

There are 16 terms. Therefore, there are two middle terms.

That is, (16/2) Th term and ((16/2) +1) Th term. Therefore, these are the 8th and 9th terms.

Hence, the median is the average values of the 8th and 9th terms.

Median (14+16)/2=15

Therefore, the medial point scored by the Tennis team is 15.

Problems of find mode:

Mode example:

Find the mode of the following numbers (out of 10) obtained by 20 peoples:

4, 6, 5, 8, 3, 2, 9, 9, 6, 5, 4, 8, 10, 10, 3, 5, 9, 6, 8, 8

Sol:

We organize this data given above in the following form:

2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 9, 9, 9, 8, 8, 8, 8, 10, 10

Here 8 happen most repeatedly, i.e., four times. Consequently, the mode is 8.

Finding mean, median, mode:

Find the mean, median and mode of the above set of data values.

17, 17, 9, 10, 15, 2, 18, 18, 17, 5, 4, 17 and 5

Sol:

Mean:

Mean = `barx`= `sum x` / n

=11.846

Median: the middle most value is 15.

Mode

In the data set the most frequently occurring number is 17. Thus, it is the mode of the data set.

Problem 2:

Find out mean, median and mode for the following list of numbers:

18, 2, 5, 8,9,12,18,16,18,9,18

Sol:

Mean = (18, 2, 5, 8,9,12,18,16,18,9,18)/(11)

Mean = `barx`= `sum x` / n

=11.636

Median: the middle most value is 12.

Mode

In the statistics set the most repeatedly taking place number is 18. Thus, it is the mode of the statistics set.

Problem for standard deviation:

Compute the standard deviation for the given data.

9, 10, 9, 14, 18

Sol:

Calculate the mean.

`barx`= `sum x` / n

= 60/5

= 12

Determine standard deviation.

S = `sum (x - barx)` / (n - 1)

S = 5/4

S = 1.25

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