Statistics

The word “statistics” is derived
from the Latin word “status” meaning condition. The simplest way to understand
statistics is to understand it by means of collection, presentation of data and
then draw inferences or figures according to the gathered data. Most of the
time, information about an object is revealed in terms of data. However, it is
not at all possible to draw conclusions from a large amount of data, so the
data is pictorially represented with the help of bar graphs, pie charts or pictograph.
Some of the basic terms related to statistics are:

Numerical Data: Numerical
data is the information given with the help of numbers.

Pictorial Representation or
Graph of the Data: The representation of numerical data through pictures or
graphs is known as pictorial or graphical representation of data.

Pictograph: Pictograph is
a pictorial representation of the gathered data.Â

Bar Graph: When data is
represented in a figure form that resembles a bar, then it is called bar graph.

Bar Graphs in Details

When numerical data is represented in the form of a number of bars, then it is called bar graph or
chart. The bars are of uniform width and erected horizontally or vertically.
The bars are placed in equal distances from each other. As there are numerous
bars to represent a large number of data, each bar represents only a particular
value of the numerical data. If two bars represent data of different value,
they are of different sizes. The horizontal bars are drawn on x-axis and the
vertical lines which show the scale of height of the bars is the y-axis.

Example

Bar graphs or charts provide
various advantages, like:

Bar graphs help a lot in easy
representation of the data. A bar graph or a chart also helps in drawing a
quick conclusion by having just a glance. For instance as in the following
figure, a graphical figure would reflect the easy way to show government
expenditures in different sectors. The y-axis represents the amount of money
spent in million and the x-axis represents the different sectors. By looking at
the bar graph, you can easily tell that government has spent the most in the
Defense sector.

Test

Represent the number of government companies in different
years by means of a bar graph.

Pie chart in details

In a particular area, the amount of wheat production for
three consecutive years are 20 million in 2001, 25 million in 2002 and 55 million
in 2003. When we represent the following figures in the form of a pie, chart,
the degree of the angle to represent each of the quantity needs to be
calculated.

For instance, the production of wheat:

2001 = 20 million tonnes

2002 = 25 million tonnes

2003 = 55 million tonnes

Therefore, the total amount of wheat produced in these three
years are, 20 + 25 + 55 = 100 million tonnes.

Let’s take 100 million tonnes = 360 degree

Therefore, 1 million tonne will be = 360/100

20 million tonne will be = 360/100 x 20 = 3.6 x 20 = 72
degree. (Applying Unitary method)

Similarly, 25 million tonne will be = 360/100 x 25 = 3.6 x
25 = 90 degrees. (by unitary method)

Similarly, 55 million tonne will be = 360/100 x 55 = 3.6 x
55 = 198 degrees.(by unitary method)

The best way to check the result,
whether it is correct or not can be done by adding up the three quantities, 72
degree + 90 degree + 192 degree = 360 degree.

If the result of the sum is 360
degree, then most of the time your calculations are fine but in any case if the
sum does not result to 360 degree then it is definitely wrong.

A pie chart also known as circle
graph is a representation of a circle chart divided into sectors. The circle is
divided into various parts and each part or each arc represents a value. The
arc length is directly proportional to the quantity it represents. The total
value of the data should be represented within 360 degrees because the pie
chart is always a circle.

Pie charts are especially
effective in places where there is a need to compare between various
quantities. Pie charts are a very good analysis tool in case of journalism or
business but it is not so effective in case of scientific literature. However,
the particular form of pictorial representation of data is widely used and
attractive too.

Example

In a survey which represents the
percentage of intelligence in a class it is seen that 20% of the students are highly
intelligent, 70% of the students are average and 10% are below standard. While
analyzing the data, if it is represented in the form of a pie chart then it
will be much easier to get a conclusion. The pie chart representing the above
data will look like the following:

Test

Represent the following data in a pie chart which gives the
number of staffs in different ages in a particular office, which has a total
number of 60 staffs. 20 people are below 25 years of age, 30 people are between
25 to 50 age group and there are only 10 people above 50 years of age.

Answer:

By unitary method, we have to take total number of staffs as
360 degrees.

Therefore, 60 staffs represent = 360 degree

1 staff will represent =  360/60

20 staffs (below 25 years) will represent = 360/60 x 20 =
120 degrees

30 staffs (between 25-50 years) will represent = 360/60 x 30
= 180 degrees

10 staffs (above 50 years) will represent = 360/60 x 10 = 60
degrees

Therefore, number of staffs below 24 years of age will
represent 120 degree.

Number of staffs between 25-50 years of age will represent
180 degree and number of staffs above 50 years of age will be 60 degree.

Checking:

Three quantities in degree calculated are 120 degree, 180
degree and 60 degree.

Sum of the quantities are 120 degree + 180 degree + 60
degree = 360 degree.

Therefore, the calculation is right.

Mean, Median, Mode

Mean

Mean or arithmetic mean refers to calculating the sum of all
numbers in the set and then dividing the numbers by the number of quantities or
members. It is very much helpful when you need to draw a summary out of a large
collection of numbers. However, don’t confuse mean with average as mean is only
one of the several kinds of average.

The Median

Getting the median is as easy as getting the ‘middle value’
in a list of numbers. When you are given with a set of odd quantities, then you
need to sort out those numbers into increasing order and find out the middle
number. That middle number is the median. However, when you are given an even
number of quantity, again you need to sort them out in increasing order. Then
you need to find out the sum of the two middle numbers and divide it by two.
The result is the median.

Mode

Finding the mode is very easy as all you need to do is to
find out the number which occurs most in a given list of numbers. However, if a
list contains no number, occurring more than once then that list has no mode.
Range of a set of numbers is also easy as it needs you to calculate the
difference between largest number and the smallest number of the list.

Example

1) Find the mean of the set {3,7,8}.

The first step is to add the three numbers that is, 3 + 7 +
8 = 18.

The value of the addition is 18.

No. of quantities in the set = 3.

Therefore, the mean is 18/3 = 6.

2) Find the median of the set {4, 2, 6, 12, 5}

The first step would be to sort them in increasing order
that is, 2, 4, 5, 6, 12.

The middle number is 5.

With odd rule, the median is 5.

3) Find the median of the set {3, 5, 10, 6, 15, 11}

Sorting the set in increasing order, we get, 2, 4, 7, 5, 9, 11

The two middle numbers are 7 and 5.

Sum of those two numbers = 7 + 5= 12.

Dividing the value by 2, we get, 12/2 = 6.

Therefore the median is 6.

4) Get the mode from the set {2, 9, 3, 9, 2, 6, 12, 9}

Sorting the numbers we get, 2, 2, 3, 6, 9, 9, 9,12…

9 is the mode as it has appeared the most number of times.

5) Calculate the range of the set {3, 5, 29, 14, 9, 11}

The largest number in the set is 29 and the smallest number
is 3.

Therefore, the difference is 29 – 3 = 26.

The range is 26.
Think you’re ready? – Try our Statistics Test.