Importance Of Statistics

10 Everyday Reasons Why Statistics Are Important

Statistics are sets of mathematical equations that are used to analyze what is happening in the world around us. You've heard that today we live in the Information Age where we understand a great deal about the world around us. Much of this information was determined mathematically by using statistics. When used correctly, statistics tell us any trends in what happened in the past and can be useful in predicting what may happen in the future. Let's look at some examples of how statistics shape your life when you don't even know it. 1. Weather Forecasts Do you watch the weather forecast sometime during the day? How do you use that information? Have you ever heard the forecaster talk about weather models? These computer models are built using statistics that compare prior weather conditions with current weather to predict future weather. 2. Emergency Preparedness What happens if the forecast indicates that a hurricane is imminent or that tornadoes are likely to occur? Emergency management agencies move into high gear to be ready to rescue people. Emergency teams rely on statistics to tell them when danger may occur. 3. Predicting Disease Lots of times on the news reports, statistics about a disease are reported. If the reporter simply reports the number of people who either have the disease or who have died from it, it's an interesting fact but it might not mean much to your life. But when statistics become involved, you have a better idea of how that disease may affect you. For example, studies have shown that 85 to 95 percent of lung cancers are smoking related. The statistic should tell you that almost all lung cancers are related to smoking and that if you want to have a good chance of avoiding lung cancer, you shouldn't smoke. 4. Medical Studies Scientists must show a statistically valid rate of effectiveness before any drug can be prescribed. Statistics are behind every medical study you hear about. 5. Genetics Many people are afflicted with diseases that come from their genetic make-up and these diseases can potentially be passed on to their children. Statistics are critical in determining the chances of a new baby being affected by the disease. 6. Political Campaigns Whenever there's an election, the news organizations consult their models when they try to predict who the winner is. Candidates consult voter polls to determine where and how they campaign. Statistics play a part in who your elected government officials will be 7. Insurance You know that in order to drive your car you are required by law to have car insurance. If you have a mortgage on your house, you must have it insured as well. The rate that an insurance company charges you is based upon statistics from all drivers or homeowners in your area. 8. Consumer Goods Wal-Mart, a worldwide leading retailer, keeps track of everything they sell and use statistics to calculate what to ship to each store and when. From analyzing their vast store of information, for example, Wal-Mart decided that people buy strawberry Pop Tarts when a hurricane is predicted in Florida! So they ship this product to Florida stores based upon the weather forecast. 9. Quality Testing Companies make thousands of products every day and each company must make sure that a good quality item is sold. But a company can't test each and every item that they ship to you, the consumer. So the company uses statistics to test just a few, called a sample, of what they make. If the sample passes quality tests, then the company assumes that all the items made in the group, called a batch, are good. 10. Stock Market Another topic that you hear a lot about in the news is the stock market. Stock analysts also use statistical computer models to forecast what is happening in the economy.

Bar Graphs

Construction of Bar Graphs

Now we will discuss about the construction of bar graphs or column graph. In brief let us recall about, what is bar graph?

Bar graph is the simplest way to represent a data.

● In consists of rectangular bars of equal width.

● The space between the two consecutive bars must be the same.

● Bars can be marked both vertically and horizontally but normally we use vertical bars.

● The height of bar represents the frequency of the corresponding observation.

For example, let us observe the following data of the bar graph.

The following data gives the information of the number of children involved in different activities.

Activities	Dance	Music	Art	Cricket	Football
No. of Children	30	40	25	20	53

How to Construct a Bar Graph?

Steps in construction of bar graphs/column graph:

● On a graph, draw two lines perpendicular to each other, intersecting at 0.

● The horizontal line is x-axis and vertical line is y-axis.

● Along the horizontal axis, choose the uniform width of bars and uniform gap between the bars and write the names of the data items whose values are to be marked.

● Along the vertical axis, choose a suitable scale in order to determine the heights of the bars for the given values. (Frequency is taken along y-axis).

● Calculate the heights of the bars according to the scale chosen and draw the bars.

Bar graph gives the information of the number of children involved in different activities.

Solved examples on construction of bar graphs:

1. The percentage of total income spent under various heads by a family is given below.

Different Heads	Food	Clothing	Health	Education	House Rent	Miscellaneous
% Age of Total Number	40%	10%	10%	15%	20%	5%

Represent the above data in the form of bar graph.

2. 150 students of class VI have popular school subjects as given below:

Subject	French	English	Maths	Geography	Science
Number of Students	30	20	26	38	34

Draw the column graph/bar graph representing the above data.

Solution:

Take the subjects along x-axis, and the number of students along y-axis

Bar graph gives the information of favourite subjects of 150 students.

3. The vehicular traffic at a busy road crossing in a particular place was recorded on a particular day from 6am to 2 pm and the data was rounded off to the nearest tens.

Time in Hours	6 - 7	7 - 8	8 - 9	9 - 10	10 - 11	11 - 12	12 - 1	1 - 2
Number of Vehicles	100	450	1250	1050	750	600	550	200

Bar graph gives the information of number of vehicles passing through the crossing during different intervals of time.

Frequency Distribution

Frequency Distribution of
Ungrouped and Grouped Data

Frequency distribution of ungrouped and grouped data is discussed below with examples.

Frequency distribution of ungrouped data:

Given below are marks obtained by 20 students in Math out of 25.

21, 23, 19, 17, 12, 15, 15, 17, 17, 19, 23, 23, 21, 23, 25, 25, 21, 19, 19, 19 

 

Frequency distribution of grouped data:

The presentation of the above data can be expressed into groups. These groups are called

classes or the class interval.

Each class interval is bounded by two figures called the class limits.

Marks 0 - 10 10 - 20 20 - 30

Number of Students (Frequency) 0 11 9

Note: The lower value of a class interval is called lower limit and upper value of that class interval is called the upper limit. Thus, each class interval has lower and upper limits.

For Example:

In the class interval 10 - 20, 10 is the lower limit and 20 is the upper limit.

Exclusive form of data:

This above table is expressed in the exclusive form.

In this, the class intervals are 0 - 10, 10 - 20, 20 - 30. In this, we include lower limit but exclude upper limit.

So, 10 - 20 means values from 10 and more but less than 20.

20 - 30 would mean values from 20 and more but less than 30.

Data in the inclusive form:

Marks obtained by 20 students of class VIII in Math text are given below.

23, 0, 14, 10, 15, 3, 8, 16, 18, 20, 1, 3, 20, 23, 24, 15, 24, 22, 14, 13

Let us represent this data in the inclusive form.

Marks 0 - 10 11 - 20 21 - 30

Number of Students (Frequency) 6 9 5

Here, also we arrange the data into different groups called class intervals, i.e., 0 - 10, 11 - 20, 21 - 30.

0 to 10 means between 0 and 10 including 0 and 10.

Here, 0 is the lower limit and 10 is the upper limit. 11 to 20 means between 11 and 20 including 11 and 20.

Here, 11 is the lower limit and 20 is the upper limit.

When the data is expressed in the inclusive form, it is converted to exclusive form by subtracting 0.5 from lower limit and adding it to upper limit of each class interval.

11 - 20 is expressed in the inclusive form which can be changed and taken as 10.5 - 20.5 which is the exclusive form of the data.

Similarly, 21 - 30 can be taken as 20.5 - 30.5.

Statistics is a branch of mathematics that deals with the interpretation of data. Statisticians work in a wide variety of fields in both the private and the public sectors.

In real life statistics, we come across numerical data in the newspapers, magazines and television regarding different aspects like increase or decrease in population, profit made by a company in different years, weather report, etc. These numerical facts are also represented by graphs which are easy to understand.

The term statistics is derived from a Latin word status meaning condition. The branch of mathematics which deals with the collection, presentation, analysis and interpretation of the numerical data is called statistics.

Terms Related to Statistics

Data:

The collection of information in the form of numerical figures, regarding different aspects of life is called data. The data can be about population, birth, death, temperature of place during a week, marks scored in the class, runs scored in different matches, etc. We need to analyze this data.

The following table gives the data regarding the number of students opting for different activities.

Activities	Dance	Music	Art	Sports
No. of students	15	25	10	40

Raw data:

When some information is collected randomly and presented, it is called a raw data.

For Example:

Given below are the marks (out of 25) obtained by 20 students of class VII A in mathematics in a test.

18, 16, 12, 10, 5, 5, 4, 19, 20, 10, 12, 12, 15, 15, 15, 8, 8, 8, 8, 16

Observation:

Each entry collected as a numerical fact in the given data is called an observation.

Array:

The raw data when put in ascending or descending order of magnitude is called an array or arrayed data.

For Example:

The above data is arranged in ascending order and represented as:

4, 5, 5, 8, 8, 8, 8, 10, 10, 12, 12, 12, 15, 15, 15, 16, 16, 18, 19, 20

Range:

The difference between the highest and the lowest value of the observation is called the range of the data.

In the above data,

Highest marks obtained = 20

Lowest marks obtained = 4

Therefore, range = 20 - 4 = 16

Mean:

It is calculated by dividing the sum of all the observation by the total number of observations. If x, x1, x3, ……… xn are n observations then

Arithmetic mean = (x1 + x2 + xn, ……………. xn)/n = (∑xi)/n

[∑ is the Greek letter sigma and is used to denote summation]

For Example:

The heights of 10 girls were measured in cm and results are as follows:

142, 149, 136, 148, 129, 140, 148, 145, 150, 133

(i) What is the height of the tallest girl?

Solution:

The height of the tallest girl is 150 cm.

(ii) What is the height of the shortest girl?

Solution:

The height of the shortest girl is 129 cm

(iii) What is the range of the data?

Solution:

Range = 150 cm – 129 cm = 21 cm

(iv) Find the mean height.

Solution:

The mean height = (142 + 149 + 136 + 148 + 129 + 140 + 148 + 145 + 150 + 133)/10

= 1420/10

= 142 cm

(v) How many girls are there whose height is less than the mean height?

Solution:

There are 4 girls whose height is less than the mean height, i.e., the girl having heights 136 cm, 129 cm, 133 cm, 140 cm.

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