MAL-001 – BAR GRAPHS AND PIE CHARTS

Representing and interpreting data MAL-001 STATISTICS Representing and interpreting data 1 Bar charts 2 Pie charts

Bar Charts and Pie Charts A graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length of height of each bar represents the frequency or percentage of observations or some other measure associated with the category. The bars may be vertical or horizontal. The bars may all be the same color or they may be different colors depicting different categories. Additionally multiple variables can be graphed on the same bar chart.

Constructing Bar Charts Define the categories for the variable of interest. For each category, determine the appropriate measure or value. For a column bar chart, locate the categories on the horizontal axis. The vertical axis is set to a scale corresponding to the values in the categories. For a horizontal bar chart, place the categories on the vertical axis and set the scale of the horizontal axis in accordance with values in the categories. Then construct bars, either vertical or horizontal, for each category such that the length or height corresponds to the value for the category.

Bar charts for categorical data Bar charts can be used to display categorical or non-numerical data. For example, this bar graph shows how a group of children travel to school. What is the modal method of transport? How many of the pupils questioned travelled by train? How many children took part in this survey?

Bar charts for discrete data Bar charts can be used to display discrete numerical data. For example, this bar graph shows the number of CDs bought by a group of children in a given month. Discrete numerical data can only take certain values. For example, we couldn’t have 2.3 CDs.

Bar charts for two sets of data Two or more sets of data can be shown on a bar chart. For example, this bar chart shows favourite subjects for a group of boys and girls. What subject did most girls like the best? What subject did most boys like the best? Is it possible to tell if an equal number of boys and girls took part in the survey?

Department: GS -YUC Campus: Male and Female Combined Percent of Passing and Failing Rate By Course   Note: Result only shows courses that are being offered in both campuses

Drawing bar charts When drawing bar chart remember: Give the bar chart a title. Use equal intervals on the axes. Label both the axes. Leave a gap between each bar.

Bar graph Twenty four students of the class were asked the name of their favorite subject. The results are shown in the following table. Represent the given data on the bar graph Favorite subject Math Science Arabic English Islam Number of students 7 4 3

Drawing bar charts Q.1 Use the data in the frequency table to complete a bar chart showing the number of children absent from school from each year group on a particular day. Year Number of absences 7 74 8 53 9 32 10 11

Exercises Two hundred students of a school were asked to name their favorite color so as to decide upon what should be the color of their school building. The results are shown in the table. Represent the data on bar graph. From the bar graph answer the following questions. Which is the most preferred color and which is the least preferred? How many students have chosen white as their favorite color? Favorite color Pink Gray Blue White Off-white Number of Students 43 19 55 49 34

A test was conducted on water resistant watches made by different companies. Each of these companies claimed that their watches were water resistant . After the test the results were as shown in the graph. Write the data in tabular form. Which company has better watches?

Representing and interpreting data 2. Pie charts

Constructing Pie Charts: A graph in the shape of a circle. The circle is divided into “slices” corresponding to the categories or classes to the displayed. The size of each slice is proportional to the magnitude of the displayed variable associated with each category or class. Constructing Pie Charts: Define the categories for the variable of interest. For each category, determine the appropriate measure or value. The value assigned to each category is the proportion the category is to the total for all categories. Construct the pie chart by displaying one slice for each category that is proportional in size to the proportion the category value is to the total of all categories.

FURBLES PIE CHART

PIE CHART AND BAR GRAPH

Pie charts A pie chart is a circle divided up into sectors which are representative of the data. In a pie chart, each category is shown as a fraction of the circle. For example, in a survey half the people asked drove to work, a quarter walked and a quarter went by bus. In a bar chart, the size of each category is compared with each of the others. In a pie chart, each category is compared with the whole. Point out that if the sectors are not labelled we must include a key.

Pie charts This pie chart shows the distribution of drinks sold in a cafeteria on a particular day. Altogether 300 drinks were sold. Estimate the number of each type of drink sold. Coffee: 75 Soft drinks: 50 Tea: 175

Pie charts These two pie charts compare the proportions of boys and girls in two classes. The pie charts in the example show that 2/5 of the pupils in Mr Humphry’s class are girls and 3/5 of the pupils in Mrs Payne's class are girls. We can conclude from this that a higher proportion of the pupils in Mrs Payne’s class are girls. However, unless we are told otherwise we cannot assume that there are the same number of pupils in each class. Suppose, for example that there are 30 pupils in Mr Humphry’s class and 15 pupils in Mrs Payne’s class. 2/5 of 30 is 12, so that would give us 12 girls in Mr Humphry’s class. 3/5 of 15 is 9, so that would give us 9 girls in Mrs Payne’s class. Conclude that we cannot make statement about the actual amounts in a pie chart unless we are told how many the pie chart represents. Dawn says, “There are more girls in Mrs Payne’s class than in Mr Humphry’s class.” Is she right?

Drawing pie charts To draw a pie chart you need a compass and a protractor. The first step is to work out the angle needed to represent each category in the pie chart. This is done by working out what fraction of the total we want to represent and multiply it by 360 degrees.

Drawing pie charts Newspaper Number of people The Guardian 8 For example, 30 people were asked which newspapers they read regularly. The results were : Newspaper Number of people The Guardian 8 Daily Mirror 7 The Times 3 The Sun 6 Daily Express

Drawing pie charts Method: Write each category as a fraction of the whole and find this fraction of 360º. 8 out of the 30 people in the survey read The Guardian so to work out the size of the sector we calculate 8 30 × 360º = 96º 7 out of the 30 people in the survey read the Daily Mirror so to work out the size of the sector we calculate 7 30 × 360º = 84º

Drawing pie charts These calculations can be written into the table. Angle Working No of people Newspaper 6 Daily Express The Sun 3 The Times 7 Daily Mirror 8 The Guardian × 360º 8 30 96º × 360º 7 30 84º × 360º 3 30 36º × 360º 6 30 72º × 360º 6 30 72º Total 30 360º

Drawing pie charts Once the angles have been calculated you can draw the pie chart. Start by drawing a circle using a compass. The Daily Express The Guardian Draw a radius. Measure an angle of 96º from the radius using a protractor and label the sector. 72º 96º 72º The Sun 84º 36º The Daily Mirror Measure an angle of 84º from the the last line you drew and label the sector. The Times Repeat for each sector until the pie chart is complete.

Drawing pie charts Favourite colour No of people Red 10 Yellow 3 Blue Q.1 Use the data in the frequency table to complete the pie chart showing the favourite colours of a sample of people. Favourite colour No of people Red 10 Yellow 3 Blue 14 Green 5 Purple 4 Total 36

Drawing pie charts Holiday destination No of people UK 74 Europe 53 Q.2 Use the data in the frequency table to complete the pie chart showing the holiday destinations of a sample of people. Holiday destination No of people UK 74 Europe 53 America 32 Asia 11 Other 10 Total 180

Reading pie charts Q.3 The following pie chart shows the favourite crisp flavours of 72 children. 35º Smokey bacon 135º Ready salted 50º Cheese and onion 85º 55º Salt and vinegar Prawn cocktail How many children preferred ready salted crisps? The proportion of children who preferred ready salted is: 135 360 = 0.375 The number of children who preferred ready salted is: 0.375 × 72 = 27