Class-IX Unit-15 Statistics
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Data
A systematic record of facts or different values of a quantity is called data.
Data recorded can be two types1) Measurement data( Quatitative data): Data which has some numeric values like marks in the examination,age of the student in the class, Weight of the students in the class
2) Qualitative data: Data which can be group according to common properties like Gender of students in the class,Blood group of the students
Data can be of two types as per there source type- Primary data and Secondary data.
Primary Data: The data collected by a researcher with a specific purpose in mind is called primary data.
Secondary Data: The data gathered from a source where it already exists is called secondary data
Data variable can be many types
1) Discrete: If the data is present in certain values only like Blood group ,gender
3) Continous:If the data can be present in any values from lower point to height points on the measurement scale like weight of the student,height of the student
1) Discrete: If the data is present in certain values only like Blood group ,gender
3) Continous:If the data can be present in any values from lower point to height points on the measurement scale like weight of the student,height of the student
Statistics
Statistics deals with collection, presentation, analysis and interpretation of numerical data.
Statistics Defination from Wikipedia Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data or as a branch of mathematics. Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty
Collection of data: The first step in any investigation is collection of data. The data may be collected for the whole population or for a sample only. Some real life example1. Weights of students of our class
2. Production of wheat in the last 10 years in our country
3. Number of 1 BHK, 2BHK and 3BHK flats in our locality
4. Rainfall in our city in the last 10 years
5. Blood group of the students in the class
Presentation :It means
1)Arranging data in a order to study their salient features is called presentation of data
2) Data arranged in ascending or descending order is called arrayed data or an array
3) organize numerical information in the form of tables, graphs, and charts.
Analysis and interpretation
1) understand statistical techniques underlying decisions that affect our lives and well-being and
make informed decisions.
2) The process by which sense and meaning are made of the data gathered and applied to clients problem
More on Presentation of Data
We can divide data into two Forms in terms of Presentation
1) Ungrouped data
The data obtained in original form is called raw data or ungrouped dataExample. The marks obtained obtained by 30 students in a class in a physics examination are given below;
20, 8, 31, 17, 40, 41, 28, 11, 41, 22, 13 ,16, 15, 19, 10, 32, 33, 22, 26, 31, 12, 31, 45, 49,54,52,53,57,56,58
This is ungrouped data.
Data arranged in ascending or descending order is called arrayed data or an array.
Arranging the marks out of 60 of 30 students in ascending order, we get the following array.
8, 10, 11,12, 13, 15, 16, 17, 19,20,22, 24, 26,28, 31,31,32, 33, 35, 40, 41,41, 45, 49,52,53,54,56,57,58
Range of the data is the difference between the maximum and the minimum values of the observations
So in this example range =57-8=51
We can put this in tabular format which is called a frequency distribution tableSo in this example range =57-8=51
frequency distribution table is a Table that shows the frequency of different values in the given data
| Marks | No of Students |
| 8 | 1 |
| 10 | 1 |
| 11 | 1 |
| 12 | 1 |
| 13 | 1 |
| 15 | 1 |
| 16 | 1 |
| 17 | 1 |
| 19 | 1 |
| 20 | 1 |
| 24 | 1 |
| 26 | 1 |
| 28 | 1 |
| 31 | 2 |
2) Grouped data
The ungrouped data approach becomes very hard with large values of number.So we make groups of suitable size to put the data in a more condensed form and mention the frequency of each group. Such a table is called a grouped frequency distribution table.A table that shows the frequency of groups of values in the given data is called a grouped frequency distribution table
The groupings used to group the values in given data are called classes or class-intervals. The number of values that each class contains is called the class size or class width. The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit.
Class mark of a class is the mid value of the two limits of that class.
A frequency distribution in which the upper limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.
A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution
Lets us take previous example only
Example. The marks obtained obtained by 30 students in a class in a physics examination are given below;
20, 8, 31, 17, 40, 41, 28, 11, 41, 22, 13 ,16, 15, 19, 10, 32, 33, 22, 26, 31, 12, 31, 45, 49,54,52,53,57,56,58
Inclusive or discontinuous Frequency Distribution.
| 0-9 | 1 |
| 10-19 | 8 |
| 20-29 | 5 |
| 30-39 | 5 |
| 40-49 | 5 |
| 50 -59 | 6 |
Exclusive or continuous Frequency Distribution
| 0-10 | 1 |
| 10-20 | 8 |
| 20-30 | 5 |
| 30-40 | 5 |
| 40-50 | 5 |
| 50 -60 | 6 |
Graph’s
Bar Graph
A bar graph is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them on one axis, usually the x axis. The value of the variable is shown on the other axis that is the y axis.
Histogram
A histogram is a set of adjacent rectangles whose areas are proportional to the frequencies of a given continuous frequency distribution
Measures of Central Tendency
Mean
The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.
The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.
Median
The median of a set of data values is the middle value of the data set when it has been arranged in ascending order. That is, from the smallest value to the highest value
Median is calculated as
Where n is the number of values in the data
If the number of values in the data set is even, then the median is the average of the two middle values.
Mode
Mode of a statistical data is the value of that variable which has the maximum frequency.
If the number of values in the data set is even, then the median is the average of the two middle values.
Mode
Mode of a statistical data is the value of that variable which has the maximum frequency.
How to Solve Mean,Median and Mode problem's
1) Arrange the data in ascending order from low value to high value2) Create the frequency distribution table of the data
3) Calculate Mean,medain and mode using it
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