Key Concepts

Understand Fundamentals
Representation of data
For data to be useful, it is very important to collect complete, accurate & relevant data.
After collection of data, it is necessary to represent data in a precise manner so that it is easily understood. Representation of data in a visual manner is known as its Graphical Presentation or simply, Graphs. Data can also be presented in the form of a table; however a graphical form is easier to understand. Consider the family of Mr. Khanna. They are very fond of eating ice-creams. Some like butterscotch, some like vanilla flavor, some like strawberry and the rest of them likes chocolate. Some demand cones & some of them demand cups. A child of VIII class decides to construct the graphs according to their amount of icecreams consumed. There are 7 ways of representing the data.
Pictograph
Pictorial representation of numberical data, using picture symbol is known as a pictograph. Most business and industrial organizations use this method to represent their data.
         denotes cones and
         represents cups.
If we draw the pictograph, it will be in the above way where  represents cone &  represents cups.
FACTS THAT MATTER
•    The numerical information is called data.
•    Data can be arranged and presented by grouped frequency distribution.
•    Frequency is the number of times a particular entry occurs.
•    Histogram is a special type of bar graph in which the class intervals are shown on the horizontal axis and heights of the bars correspond to the frequency of the class.
•    In a histogram there is no gap between bars.
•    A circle graph or a pie chart shows the relation ship between a whole and its parts.
•    Outcomes of an event or experiment are equally likely if each has the same of occuring.
•    Probability of an event
        
•    Probability of an event can have a value from 0 to 1.
•    Probability of an impossible even is 0.
 Look at the below-given pictograph, answer the following questions:
  1. Find out the number of persons employed in private service?
  2. In which service, the maximum number of persons were employed?

Solution:

Given that, one symbol = 3000 persons.

(a) The number of persons employed in private service = 6 × 3000 = 18000 persons.

(b) The maximum number of persons were employed in government service.

I.e., 10 × 3000 = 30000 persons.

Draw the pie chart for the given observations, that shows the survey of different types of movies.

Action Comedy Romance Sci-Fi Drama
5 4 6 4 1

Solution:

From the given observation, total = 20.

Now, divide each value by 20 and multiply by 100 to get the percentage.

Action – (5/20)100 = 25%

Comedy – (4/20)100 = 20%

Romance = (6/20)100 = 30%

Sci-Fi = (4/20)100 = 20%

Drama = (1/20)100 = 5%

Now, we have to find the degree of each slice (sector).

Action – (5/20)360°= 90°

Comedy – (4/20)360°= 72°

Romance = (6/20)360°=108°

Sci-Fi = (4/20)360°= 72°

Drama = (1/20)360°= 18°

Hence, the pie chart for the obtained information is: