Math Concepts

Representing Data

27th Oct '204 views7 mins read

27 October  2020

Reading Time: 7 Minutes

Introduction

When you collect and record information, you will be able to represent it in a graphical diagram to indicate the results. You can use a chart, pie chart, line graph, pictogram, frequency diagram, or scatter diagram.   


Types of graphs and charts 

The type of graph you employ depends on the sort of information you would like to represent. 

  • Discrete information is a best-portrayed using a bar chart. 
  • Temperature graphs would sometimes be represented using line graphs as a result of the data being continuous. 
  • When you are graphing percentages of distributing, a pie chart would be appropriate. 
  • When you have two variables, like marks in Maths and marks in Science, then a scatter diagram would be the one to use. 

 The other thing you should consider is that each graph needs SALT, ensure you bear in mind the information: 
S = Scale 
A = Axes 
L = Labels 
T = Title  

Bar charts 

A chart is employed to match two or additional values with the least set of results. 
In the bar chart, the peak of the bar shows the frequency of the result. 
As the height of the bar represents frequency, the x-axis would be called frequency. The labeling of the y-axis depends on what's being portrayed by the chart. To confirm an applicable scale, vary the axes uniformly and provide the acceptable label on the axes. Finally bear in mind to convey the graph an acceptable title. 

Example 

 

 

Leon surveys to search out the number of individuals in each of the cars incoming at the college gate between 8.30 am and 9.00 am. His results square measure shown within the chart below: 

Image 1

Questions: 
a) What percentage of cars contained one person? 
b) What percentage of cars contained quite three people? 
c) Why are there solely a tiny low variety of cars containing one person? 
d) What percentage of cars found out the college gate between 8.30 am and 9.00 am? 

Line graphs 

A line graph is commonly accustomed to show a trend over a variety of days or hours. It is therefore thought as a series of points that are then joined with straight lines. The ends of the road graph don't need to be a part of the axes. 

This line graph shows the noontide temperature over an amount of seven days: 

Image 2

 You can tell at a look that the temperature was at its highest on Monday which began to fall within the middle of the week before rising once more at the tip of the week. 
 Questions: 
a) What was the all-time low temperature, and on what day did it occur? 
b) On what day was the noontide temperature 26 °C? 
 

Pictograms 

Pictograms use the footage to represent information. to form a sense, a pictogram should always have a key. 

In a pictogram, it's necessary to form a certain image that is the same size, equally spaced out and lined up one at a lower place the opposite. 

Example

 

 

This pictogram shows the number of pizzas eaten by four friends within the past month: 

Image 3

The key tells you that one pizza on the pictogram represents four pizzas eaten, therefore Alan eats 4+2=6 pizzas. 
 
Questions: 
a) Who ate the foremost pizzas? 
b) What percentage of pizzas did Bob eat? 
c) What was the whole variety of pizzas eaten by the four friends? 
  

Pie charts 

Pie charts use different-sized sectors of a circle to represent information. 

In a chart, it's necessary to grasp that the angle of every sector represents the fraction, out of 360, allotted thereto information price. Pie charts must always be labeled, either directly on the chart or by suggesting that of a color-coded key. 

Example

 

 

This chart shows the results of a survey to search out however students travel to school: 

Example 1 image

a) What's the most common technique of travel? 
b) What fraction of the scholar's travel faculty by car? 
c) If half a dozen students travel by car, what percentage of folks took half within the survey? 
  

Frequency diagrams and frequency polygons 

This frequency diagram shows the heights of 100 people: 

Frequency diagrams and frequency polygons  Image

You can construct a frequency plane figure by connecting the midpoints of the super of the bars. 

The frequency polygons are significantly helpful for scrutinizing completely different sets of information on an identical diagram. 


 Image 3

Scatter diagrams - Plotting and Reading 

Scatter diagrams show the link between 2 variables. By looking at the diagram you will see whether or not there is a link between variables. If there is a link it is referred to as correlation. 

Example

 

 

The English and Maths results of 10 classmate's area unit shown within the table below: 

  Ria  Kim  Bill  Tom  Gita  Alex  Ben  Ken  Alan  Jo 
Maths mark  20  71  60  52  80  32  47  90  49  80 
English mark  30  80  65  50  81  38  40  87  55  70 


To see whether or not there is a correlation between the Maths marks and also the English marks, you will plot a scatter diagram. 

The Maths mark is on the x-axis. The corresponding English mark is on the y-axis. 
 
Bill's Maths mark was 60. His mark in English was 65, Therefore results from the area unit pictured by the purple purpose at coordinates (60, 65). 

Image 3

 
Notice that each one of the points representing Maths marks and English marks lie about on a line. It shows that there is a correlation between these two variables. 

The diagrams below show the correlations that you will deduct from different patterns of scattering. 

Positive correlation: 

Image 4

The points lie getting ready to a line that contains a positive gradient. 

It shows that one variable will increase the other will also increase. 
  
Negative correlation: 

Image 5


 
 

  • The points lie getting ready to a line that contains a negative gradient. 
  • It shows that the united variable will increase the opposite decreases. 

 No correlation: 


 Image 5

 The points do not form any straight line.   
It shows that there is no affiliation between these two variables. 
 
Scatter diagrams - the line of the best match 

The line of best fit goes roughly through the center of all the scatter points on a graph. The nearer the points area unit to the road of best match, the stronger the correlation is. 

Example

 

 

Ten pupils in a school study French and German. Their marks in recent tests area unit recorded within the table below: 

  Ben  Sara  Sun  Tom  Pari  Henry  Sia  Andy  Jo  Gita 
Mark in French  42 62 32 78 70 18 68 52 84 38
Mark in German  48 56 24 68 ? 22 76 54 89 39


Draw a scatter diagram to represent these marks, as Pari was absent on the day of the German test. You are doing not have enough data to mark his score. 


 Image 3

 Looking at this scatter diagram, 

There are robust correlational statistics between the marks in French and also the marks in German. Therefore, you will draw a line of best suitable shows that trend. 


 Image 4


 Pete scored seventy in French, therefore victimizing the road of best match, you will estimate that his mark in German would are about 72. 


 Image 6


 

  • A line of the best match will solely draw if there is a robust positive neither indirect correlation. 
  • The line of the best match does not have to undergo the origin. 
  • The line of the best match shows the trend. It is solely approximate. Any readings taken from it will be estimations. 

 Synopsis

Once an inquiry arises, we tend to collect information. The subsequent step is to classify and organize the collected information. It is often then followed by summarizing the information using the measures of central tendency. A piece of information that is collected, classified, organized, and summarised must be pictured and understood diagrammatically. The different kinds of graphical representations explained during this section are: pie charts, histograms, single-bar graphs, line graphs, and broken line graphs.  


Comprehend me (Practice Questions)

  1. What is data? 
  2. How do you differentiate between data and information? 
  3. What are the ways to represent data? 
  4. What are the different types of graphs? 
  5. What is the frequency? 

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