One Variable Statistics

Introduction :

The statistics includes the variables as mean, median, mode, range, variance and standard deviation. Statistics is that one of the important branch of applied mathematics which deals with the scientific analysis of data. In this article we shall discuss the concept of mean, median, mode, range and standard deviations as well as example and find the one variable value in statistics.

Examples – One Variable Statistics:

In this example we will declare the variable as x and find that value with help of example.

Now we will solve the example problems for one variable in statistics.

14, 12, 16,18,52,20.

Now locate the mean, median, mode and range for solve variables in statistics.

Mean:

Here we will declare the mean as `stackrel(-)(x)` variable.

Mean is the sum of values divided by the number of given data in the given numbers.

`stackrel(-)(x)` = Mean = `("Sum of given values")/("Total number of given values")`

The given numbers are,

14, 12, 16,18,52,20.

Mean = `stackrel(-)(x)` = `132/6` .

`stackrel(-)(x)`= 22.

Median:

In this example we will declare median as x.

Median means center values.

The given values are 80, 74,96,32,65.

Now sort the numbers in ascending orders.

32, 65,74,80,96.

So, the x = median = 74.

Mode:

In this example we will declare mode as x.

The given values are

88, 22, 36, 50, 40, 88.

In the given values most repeated value is known as mode.

In the given values 88 is repeated.

x = 88.

Range:

In this example we will declare the variable as x.

The range is defined as difference among smallest value and maximum value.

88, 22, 36, 50, 40, 88.

In this given numbers highest value is 88.

Then smallest value is 22.

So the range is,

= 88 - 22

x = 66.

These are mode, mean, range and median examples in one variable statistics.

Standard Deviation – One Variable Statistics:

Let us we will solve standard deviation example problems for one variable in statistics.

In this example the standard deviation declared as `sigma`

Example 1:

The given values are 100, 58,96,84,60.

Solution:

The given numbers are 100, 58,96,84,60.

Find the approximating mean value for the given data.

Mean (M) = 100 + 58 + 96 + 84 + 60.

= `398/5`

= 79.6.

Find

`sigma`   = `(1555.2)/(5-1)`

`sigma` = 388.8

Formula of the standard deviation =`sqrt((sum_(i=1)^n (x-m)^2) / (n-1))`

The answer for standard deviation is 19.72

That’s all about one variable statistics.