In the previous section we completed the discussion on Proportions. In this section we will see some topics in Statistics.
In our day to day life, we come across different types of information. For example:
• Temperatures recorded at major cities
• Profits obtained by a company in the last five years
• Performance of various parties in an election etc.,
We find such variety of information in news papers, televisions, online services etc.,
■ These information may be numerical. That is., in the form of numbers. For example:
• Profit of 2.5 crores in 2014
• Profit of 2.7 crores in 2015 etc.,
■ These information can also be in the form of graphs showing the profits in various years.
Whether numerical or not, such information is collected for a specific purpose. They are called data. We have seen different types of data, and have performed various calculations on them. See chapter 1.
• Many of those models are performing very well in the market
• A very few models are performing poorly
• Though the majority of the models are performing very well, the company is showing decreasing profits year after year. What could be the reason?
• The answer can be found out by carefully analysing the income and expense data. The poorly performing models may be using up large amounts of money for their making.
Statistics is the branch of mathematics which performs the following activities:
• Collection of data
• Analysis of that data
• Extraction of useful information from that data.
■ You are given the task of recording the heights of 20 students in your class.
The task can be performed by two methods:
• Method 1 is by personally meeting each of the 20 students, measuring the heights, and then recording them.
• Method 2 is by taking the values from the register book kept at the physical training department.
■ Consider another example:
You are given the task of recording the number of absent students on each day for the current month
This task can also be performed by two methods:
• Method 1 is to take the number by yourself, at the time of calling attendance at the beginning of every day
• Method 2 is to take the numbers later at the end of the month, from the attendance register
■ The final data obtained by method 1 or method 2, may or may not show the same values. But what is important is this:
• At the time of presenting the data, you must specify which method you used to collect the data.
■ In example 1,
• If you used the method 1,
♦ You were collecting the data yourself.
♦ And you were collecting it for a particular purpose. The purpose is to ‘record the height of 20 students’
• If you used the method 2,
♦ You were taking the values from a data collected by some one else. The purpose of that pre-existing data is not be the same as your present purpose. That pre-existing data was prepared for a general picture of the physical ability of students in the whole school.
■ In example 2,
• If you used method 1,
♦ You were collecting the data yourself.
♦ And you were collecting it for a particular purpose. The purpose is to ‘record the number of absentees’
• If you used the method 2, you were taking the values from a data collected by some one else. The purpose of that pre-existing data may not be the same as your present purpose.
■ So the data collected by the two methods are different, and must be specified in the presentation.
When using secondary data, the following points should be noted:
• The pre-existing data was collected by some one else
• That pre-existing data was collected for a different purpose
• So the reliability of that pre-existing data should be verified.
• To present the data in a meaningful and ‘easy to understand’ way.
• Also, the presentation should show the main features of the data at a glance.
Consider the following example:
1. The marks obtained by 12 students in a test are given below:
2. The data in this form is called raw data. We saw it earlier here.
3. From the raw data, we can see that:
Lowest score is 24, and the highest score is 90
4. Those lowest and highest scores can be found out easily if we arrange the raw data in ascending or descending order. The ascending order is shown below:
5. The difference of the highest and the lowest values in the data is called the range of the data. So, the range in this case is 90 – 24 = 66
2. We can see that some marks repeat. For example, 4 students have scored 58 marks. So the value 58 occurs 4 times. The number of times that a value occurs in the raw data is called frequency of that value. In our case, frequency of the value 58 is 4.
3. We find the frequencies of the different values, and make the frequency distribution table. For accuracy, we can use the method of tally marks as shown below. This also we have seen before.
• From the above table, we can note that, there is no need to write all the 35 values. Because, repeating values are shown by 'frequency'.
• The results in the above table can be presented in a more user friendly form, if we sort the scores in ascending order. This is shown below:
• The results in the above modified table can be still be made more user friendly, by using bar graph as shown below. We have seen bar graphs also earlier.
In the next section we will see a case which will require a grouped frequency distribution table.
In our day to day life, we come across different types of information. For example:
• Temperatures recorded at major cities
• Profits obtained by a company in the last five years
• Performance of various parties in an election etc.,
We find such variety of information in news papers, televisions, online services etc.,
■ These information may be numerical. That is., in the form of numbers. For example:
• Profit of 2.5 crores in 2014
• Profit of 2.7 crores in 2015 etc.,
■ These information can also be in the form of graphs showing the profits in various years.
Whether numerical or not, such information is collected for a specific purpose. They are called data. We have seen different types of data, and have performed various calculations on them. See chapter 1.
Large amounts of data are seen in various fields. Such fields include whether forecasting, business management, science and engineering, sport tournaments etc., Just having a lot of data is not good enough. We must be able to extract useful information from them. Consider an example:
• A car manufacturing company makes different models of cars. There are big cars, medium cars and small cars.• Many of those models are performing very well in the market
• A very few models are performing poorly
• Though the majority of the models are performing very well, the company is showing decreasing profits year after year. What could be the reason?
• The answer can be found out by carefully analysing the income and expense data. The poorly performing models may be using up large amounts of money for their making.
Statistics is the branch of mathematics which performs the following activities:
• Collection of data
• Analysis of that data
• Extraction of useful information from that data.
Primary data and Secondary data
Consider the following example:■ You are given the task of recording the heights of 20 students in your class.
The task can be performed by two methods:
• Method 1 is by personally meeting each of the 20 students, measuring the heights, and then recording them.
• Method 2 is by taking the values from the register book kept at the physical training department.
■ Consider another example:
You are given the task of recording the number of absent students on each day for the current month
This task can also be performed by two methods:
• Method 1 is to take the number by yourself, at the time of calling attendance at the beginning of every day
• Method 2 is to take the numbers later at the end of the month, from the attendance register
■ The final data obtained by method 1 or method 2, may or may not show the same values. But what is important is this:
• At the time of presenting the data, you must specify which method you used to collect the data.
■ In example 1,
• If you used the method 1,
♦ You were collecting the data yourself.
♦ And you were collecting it for a particular purpose. The purpose is to ‘record the height of 20 students’
• If you used the method 2,
♦ You were taking the values from a data collected by some one else. The purpose of that pre-existing data is not be the same as your present purpose. That pre-existing data was prepared for a general picture of the physical ability of students in the whole school.
■ In example 2,
• If you used method 1,
♦ You were collecting the data yourself.
♦ And you were collecting it for a particular purpose. The purpose is to ‘record the number of absentees’
• If you used the method 2, you were taking the values from a data collected by some one else. The purpose of that pre-existing data may not be the same as your present purpose.
■ So the data collected by the two methods are different, and must be specified in the presentation.
■ When the information is collected by the investigator herself/himself, with a definite objective in mind, the data obtained is called primary data.
■ When the information is collected from a source, which already had the information stored, the data obtained is called secondary data. When using secondary data, the following points should be noted:
• The pre-existing data was collected by some one else
• That pre-existing data was collected for a different purpose
• So the reliability of that pre-existing data should be verified.
Presentation of Data
When the task of ‘collecting data’ is over, the next task is:• To present the data in a meaningful and ‘easy to understand’ way.
• Also, the presentation should show the main features of the data at a glance.
Consider the following example:
1. The marks obtained by 12 students in a test are given below:
3. From the raw data, we can see that:
Lowest score is 24, and the highest score is 90
4. Those lowest and highest scores can be found out easily if we arrange the raw data in ascending or descending order. The ascending order is shown below:
Presentation of data in ascending or descending order can be quite time consuming, particularly when the number of observations is large, as in the case of the next example:
1. The marks obtained (out of 100) by 35 students of Class IX of a school are given below:
2. We can see that some marks repeat. For example, 4 students have scored 58 marks. So the value 58 occurs 4 times. The number of times that a value occurs in the raw data is called frequency of that value. In our case, frequency of the value 58 is 4.
3. We find the frequencies of the different values, and make the frequency distribution table. For accuracy, we can use the method of tally marks as shown below. This also we have seen before.
• The results in the above table can be presented in a more user friendly form, if we sort the scores in ascending order. This is shown below:
• The results in the above modified table can be still be made more user friendly, by using bar graph as shown below. We have seen bar graphs also earlier.
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