ORGANISING THE DATA

What is data ?  Data is a collection of facts, such as values or Measurements.  It can be numbers, words, measurements, observations or even just description of things.

why do we organize data? The advantages of organizing data is that, we get an overall view of the result of our data and through this, one can easily interpret the data and can make decisions or policies. “ a picture is worth a thousand words”

We collected the data of – (a) the percentage of marks in class 12 th by the students our class (b) the height of the students of the students (c) weight of the students of our class Aman weighs 78 kg, is 172cm tall and has scored 91% marks, Rupal has scored 92%, is 153 cm tall and weighs 54 kg ; Yashika- height 146cm, scored 86 %, weight 43kg,……….

If one has to continue writing for 20 students, it would be extremely cumbersome and no one would have the patience to read the whole data. It would be difficult to interpret. Instead, we could neatly write down all the observations in the form of table.

Student Aman Rupal YashikaShubham Pratik PriyankaAbhishekParulAshish Mayank Marks (%) Height (cm) Weight (kg) Student Neetu Prerna Richi Shweta Manoj Arun VivekBushra Rahul Upasna Marks (%) Height (cm) Weight (kg)

Weight in kgNumber of student Total20  Here, we analyzed only the weight of the students. The least weight is 42 kg whereas the maximum weight is 87 kg.  The range in which the weight of the class lies is 42 kg- 87 kg.  Organizing the data in such a form is as discrete frequency distribution.  The data that consists of numbers (marks, height, weight, etc.). Such data is called Quantitative data.

Weight in kgNumber of student 40≤ weight < ≤ weight < ≤ weight < ≤ weight < ≤ weight < 902 Total20  Such a frequency distribution is called a continuous frequency distribution.  If we consider each quantity separately, we have a Discrete data and if we club them in intervals, we have a Continuous data.

Example : We have a frequency distribution which consists of the blood groups of 50 people, which is given below: Blood groupNumber of people A+7 A-6 B+12 B-7 AB+5 AB-8 O+3 O-2  A data that consists of observations which can be observed but not measured in units, is called a Qualitative data.

What happens, if the data is quite large ?  If the data is very large, it becomes difficult to handle it manually. We then take help of the available technology to manage huge data  There are a number of software available that can help us in organizing the data. Two of these are Microsoft Excel that comes with Microsoft office and the other openofficeorg-cal which is an open software.

Basic terms used in continuous frequency distribution  Class intervals : The data is divided into several groups and each group is called a class interval. ( Example 40-50, and so on).  Class limits : Lower and upper end of the class interval are called class limits. The lower limit of the class interval is 40 whereas the upper limit is 50.  Class size : Class size is the difference between the upper limit and the lower limit.

 Class mark : Class mark is the middle value of the class interval and is calculated as, Upper Limit + Lower Limit 2  Relative Frequency of a Class : Relative Frequency of a Class is given by, Relative Frequency of a Class = Frequency of that Class Sum of all Frequencies

How to make class intervals Step 1 : Find the minimum and the maximum values in the data. Step 2 : Find the range = Maximum value – Minimum value. Step 3 : Decide upon the class size h, of each class interval. Usually, class size is multiple of 5. Otherwise it can be any positive number. It depends on the nature and size of the data. Step 4: Find the number of class intervals by using the formula, Number of class intervals = least positive integer ≥ (range/h)

Step 5 : Decide upon the class limits of the class intervals by the following procedure : First class interval : Take The Lower Limit of the first class as the number ≤ min. value The Upper Limit of the first class as the number = L.L+U.P Second class interval : Take The Lower Limit of the second class as the number = upper of the class The Upper Limit of the second class as the number =Lower limit + Class size Continue the process of making class intervals till the last one. U.L. of the last class interval is the number ≥max. value

Different types of class intervals  Exclusive type class interval : In this, the Upper Limit of the current class = Lower Limit of the next class Frequency of such class interval is the number representing the count of all those numbers which are greater than or equal to the Lower Limit and strictly less than the Upper Limit. Weight in kgNumber of student

 Inclusive type class intervals : In this, the Upper Limit of the current class ≠ Lower Limit of the next class Frequency of such class interval is the number, representing the count of all those numbers which are greater than or equal to Lower Limit and also less than or equal to Upper Limit Weight in kgNumber of student

 Open End Classes : In this, both the first class has no lower limit and the last class has no Upper Limit Weight in kgNumber of student Below Above 801

CANDIDATES CONTESTING