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• ## Definition of Statistics in Mathematics

Introduction to definition of statistics:

Statistics is the most significant and useful part of mathematics. Statistics deals with the group, organization, examination, and interpretation of numerical value. A word statistics defined from the Latin word -Statis’. More simply the statistics is defined as the study of data value and how to gather, summarize and present that data. Statistics is especially useful in drawing common result about a collection of data value from a sample of the data. In mathematics statistics is divided into different number of types. They are called as mean, mode, median, range, quartile, standard deviation and so on. In this article we are going to discuss about the definition of different types of statistics and its related example problems with its solution of each type of statistics.

Definition of statistics:

Statistics is defined as the science of the gathering, maintenance and interpretation of value. It contract with every aspects that is it together with the planning of data gathering in terms of the design of surveys and researches. Statistics is linked with probability theory, with which it is frequently grouped. Statistics can be used as a singular or plural. The Statistics is called singular when it denotes the discipline which is act in -Statistics is an art-. The Statistics is called plural when it denotes the quantities that is mean and median which is act in -Statistics are misleading-.

Definition of mean: In mathematics statistics the mean defined as the average of the values. You can calculate the mean by adding the given values together and then divide the obtained addition result by given number of values in the given set.

Example:

In preparation for a move across town, Ronald packed 8 boxes weighing:

7.1 pounds, 9.9 pounds, 7.1 pounds, 7.5 pounds, 9.9 pounds, 9.9 pounds, 9.9 pounds, 8.3 pounds.

What was the mean weight of the boxes?

Solution:

Given data set: 7.1 pounds, 9.9 pounds, 7.1 pounds, 7.5 pounds, 9.9 pounds, 9.9 pounds, 9.9 pounds, 8.3 pounds.

First, count how many numbers are in the group; There are 8 numbers.

Now add all the numbers together:

9.9 + 7.1 + 9.9 + 7.1 + 7.5 + 8.3 + 9.9 + 9.9 = 69.6

Now divide the sum by the number of numbers:

`69.6/8 = 8.7`

The mean weight of the boxes was 8.7 pounds.

Definition of median: In mathematics statistics median is defined as a middle value of the given data set. It is done by first arranging the given setoff values from least to greatest.

Example:

What is the median?

-6, 10, 8, -6, 10.

Solution:

Given data set: -6, 10, 8, -6, 10

Now, arrange the given numbers from least to greatest.

That is: -6, -6, 8, 10, 10

Now find the number in the middle.

-6, -6, 8, 10, 10

The number in the middle is 8; Therefore, the median value is 8.

Definition of mode: In mathematics statistics mode is described as the value that appears most often.

Example:

What is the mode?

0, -3, -4, -4, -3, 0, -4.

Solution:

Given data set: 0, -3, -4, -4, -3, 0, -4

First, sort the given values as ascending order.

-4, -4, -4, -3, -3, 0, 0

Now count how many number of times each value appears.

-4 presents 3 times. -3 presents 2 times. 0 presents 2 times.

The value that appears most often is -4.

Therefore the mode value is -4.

Definition of range: In mathematics statistics the range defined as the difference among the greatest value and the least value.

Example:

Jesse volunteers at the local skating rink. On his last 8 shifts, there were:

5 skaters, 5 skaters, 6 skaters, 9 skaters, 7 skaters, 7 skaters, 9 skaters, 7 skaters.

What was the range of the numbers of skaters?

Solution:

Given data set: 5 skaters, 5 skaters, 6 skaters, 9 skaters, 7 skaters, 7 skaters, 9 skaters, 7 skaters.

First, calculate the greatest number: The greatest number is 9.

Next, calculate the least number: The least number is 5.

Subtract the least number from the greatest number:

9 – 5 = 4

The range of the numbers of skaters was 4.

More definition of statistics:

Definition of quartile: In mathematics statistics quartiles are values that split a group of data into four equal divisions. There are three types of quartiles available in data set.

Median Lower quartile Upper quartile Median: In mathematics statistics median is defined as a middle value of the given data set. It is done by first arranging the given setoff values from least to greatest.

Lower quartile: The lower quartile is defined as the median of the lower half of the data.

Upper quartile: The upper quartile is defined as the median of the higher half of the data.

Example:

In the data set below, what are the lower quartile, the median, and the upper quartile?

31, 33, 35, 37, 39, 40, 42.

Median:

Find the median in the middle of the set.

31, 33, 35, 37, 39, 40, 42

The median is 37.

Divide the numbers into a lower half and an upper half.

31, 33, 35, 37, 39, 40, 42.

Lower quartile:

Find the lower quartile in the middle of the lower half.

31, 33, 35

The lower quartile is 33.

Upper quartile:

Find the upper quartile in the middle of the upper half.

39, 40, 42

The upper quartile is 40.