Data Handling

Green House

(by Wasim Ahmed VIII-B9)

ALL ABOUT DATA In various fields, we need information in the of numerical figures.Each figure of this kind is called an observation.The collection of all the observation is called data.

Some important terms are defined below:-Data:- A collection of numerical facts regarding a particular type of information is called data.Raw data :- A collection of observation gathered initially is called raw data.

TYPES OF GRAPHICAL REPRESENTATION

Tally chart / frequency chart Pictograph Bar graph Double bar graph Histogram Pie chart

FREQUENCY DISTRIBUTION

Example :- Suppose we make survey of 20 families of a locality and find out the number of children in each family. Let the observation be.

2,2,3,1,1,2,3,2,2,1,2,2,3,1,2,1,1,3,2,2. State the frequency of each observation.Solution:- Arranging the data in ascending order, we get the

observation as 1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3. We find that 1 occurs 6 times; 2 occurs 10 times; and 3 occurs 4 times;We say that the frequency of families having 1 child is 6, the frequency of families having 2 children is 10, and the frequency of families having 3 children is 4. Thus, the frequency distribution table of the above data

may be presented as given in the next slide…………

FREQUENCY TABLE / TALLY CHAT

No. of children.

Tally Marks. No. of families (frequency)

1

2

3

llll l

llll llll

llllTOTAL

6

10

4

20

PICTOGRAPH A Pictograph represents data using

pictures or symbols.

= 2 FlowersMonth PictographJanuary

= 6 Flowers

February = 8 Flowers

March = 4 Flowers

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BAR GRAPHA bar graph is a graph that displays the frequency or numerical distribution of a categorical variable, showing values for each bar next to each other for easy comparison.

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BAR GRAPH EXAMPLEIn June 2005, the US Dept of Transportation

reported the following data by observing 1700 motorcyclists nationwide at randomly selected roadway location: Proper Helmet 731 Insufficient Helmet 153 No Helmet 816Total 1,700 Thus, the bar graph of the above data

may be presented as given in the next slide…………

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Helmets Used by Motorcyclists

731

153

816

0

100

200

300

400

500

600

700

800

900

Proper Helmet Insufficient Helmet No Helmet

Num

ber

of M

oto

rcyclis

ts

Source: US Dept of Transportation

Source: US Dept of Transportation

Helmet Type

The table shows the number of pets owned by students in two classes.

Pet Class A Class B

Dog 12 14

Cat 9 8

Bird 2 3

DOUBLE BAR GRAPH EXAMPLE

Represent the information in double bar graph

.

16

12

8

4

0

Pet Class A Class B

Dog 12 14

Cat 9 8

Bird 2 3

Dog Cat Bird

Nu

mb

er

of

pets

Pets Owned in Two Classes

Class A Class B

Thus, the double bar graph of the previous slide data may be presented as given below

HISTOGRAM

Example :The table below shows the number of hours students watch TV in one week. Make a histogram of the data.

A histogram is a bar graph that shows the frequency of data within equal intervals. There is no space between the bars in a histogram.

FrequencyNumber of Hours of TV

1–3 15

4–6 17

7–9 17

1–3

FrequencyNumber of Hours of TV

15

4–6 17

7–9 17

20

16

12

8

4

0

1–3 4–6 7–9

Hours of Television Watched

Frequency

Hours

HISTOGRAM EXAMPLE

Thus, the histogram of the previous slide data may be presented as given below

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CIRCLE GRAPH/ PIE CHARTA circle graph represents data in a circular form. A circle graph shows the relationship between a whole and its parts. It is divided into sectors.  Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.

HOW TO DRAW A PIE CHART

Step 1 : Calculate the angle of each sector, using the formula

Step 2 : Draw a circle using a pair of compasses

Step 3 : Use a protractor to draw the angle for each sector.

Step 4 : Label the pie chart and all its sectors.

HOW TO CALCULATE AN ANGLE OF A PIE CHART

Calculate the angle of each sector, using the formula

Total angles should add up to 360°

Example :In a school, there are 750 students in Year1, 420 students in Year 2 and 630 students in Year 3. Draw a circle graph to represent the numbers of students in these groups

Solution: Total number of students = 750 + 420 + 630 = 1,800. Year 1: size of angle = 750 x 360 =150 degrees 1800Year 2: size of angle = 420 x 360 = 84 degrees 1800Year 1: size of angle = 630 x 360 = 126 degrees 1800

PIE CHART EXAMPLE

PIE CHART EXAMPLE Thus, the pie graph of the previous slide data may be presented as given below

THE MEANING OF PROBABILITY

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Probability is used to describe RANDOM or CHANCES of events to occur.  Every day we are faced with probability statements involving the words:

1. What is the likelihood that X will occur?2. What is the chance that Brazil will win the 2014 World Cup?

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•An event is some specified result that may or may not occur when an experiment is performed.

•For example, in an experiment of tossing a coin once, the coin landing with heads facing up is an event, since it may or may not occur.

•The probability of an event is a measure of the likelihood of its occurrence.

EVENT & PROBABILITY

THE EQUAL-LIKELIHOOD MODEL

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•This model applies when the possible outcomes of an experiment are equally likely to occur.

•Suppose there are N equally likely possible outcomes from an experiment.

•Then the probability that a specified events equals the number of ways, f, that the event can occur, divided by the total number, N, of possible outcomes.

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The probability is

f = No. of ways event can occur N = Total number of possible outcomes.

In other words, in a situation where several different outcomes are possible, we define the probability for any particular outcome as a fraction of the proportion.

N

f

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Example A jar contains 1000 marbles, 800 are black and 200 are red. What is the probability of drawing a black marble out of the jar.

Solution: Here 800 is the number of possible outcomes, fThe total number of possible outcomes is 1000, N

Thus the probability is

and

8.010

8

marbles total1000

marblesblack 800)black( p

2.010

2

marbles total1000

marblesblack 200)red( p

The probability of drawing a black marble is much higher than the probability of you picking a red marble because there are more black marbles in the jar.

PROBABILITY EXAMPLE