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9.1 Graphical representation of data  (Page 19/2)

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Graphical representation of data

Once the data has been collected, it must be organised in a manner that allows for the information to be extracted most efficiently. One method of organisation is to display the data in the form of graphs. Functions and graphs have been studied in  Functions and Graphs , and similar techniques will be used here. However, instead of drawing graphs from equations as was done in Functions and graphs , bar graphs, histograms and pie charts will be drawn directly from the data.

Bar and compound bar graphs

A bar chart is used to present data where each observation falls into a specific category and where the categories, this is often for qualitative data. The frequencies (or percentages) are listed along the y -axis and the categories are listed along the x -axis. The heights of the bars correspond to the frequencies. The bars are of equal width and should not touch neighbouring bars.

A compound bar chart (also called component bar chart) is a variant: here the bars are cut into various components depending on what is being shown. If percentages are used for various components of a compound bar, then the total bar height must be 100%. The compound bar chart is a little more complex but if this method is used sensibly, a lot of information can be quickly shown in an attractive fashion.

Examples of a bar and a compound bar graph, for Data Set 1 , are shown in [link] . According to the frequency table for Data Set 1, the coin landed heads-up 44 times and tails-up 56 times.

Examples of a bar graph (left) and compound bar graph (right) for Data Set 1. The compound bar graph extends from 0% to 100%.

Histograms and frequency polygons

It is often useful to look at the frequency with which certain values fall in pre-set groups or classes of specified sizes. The choice of the groups should be such that they help highlight features in the data. If these grouped values are plotted in a manner similar to a bar graph, then the resulting graph is known as a histogram. Examples of histograms are shown in [link] for Data Set 2, with group sizes of 1 and 2.

Frequency table for Data Set 2, with a group size of 1.
Groups 0 < n ≤ 1 1 < n ≤ 2 2 < n ≤ 3 3 < n ≤ 4 4 < n ≤ 5 5 < n ≤ 6
Frequency 30 32 35 34 37 32
Frequency table for Data Set 2, with a group size of 2.
Groups 0 < n ≤ 2 2 < n ≤ 4 4 < n ≤ 6
Frequency 62 69 69
Examples of histograms for Data Set 2, with a group size = 1 (left) and a group size = 2 (right). The scales on the y -axis for each graph are the same, and the values in the graph on the right are higher than the values of the graph on the left.

The same data used to plot a histogram are used to plot a frequency polygon, except the pair of data values are plotted as a point and the points are joined with straight lines. The frequency polygons for the histograms in [link] are shown in [link] .

Examples of histograms for Data Set 2, with a group size = 1 (left) and a group size = 2 (right). The scales on the y -axis for each graph are the same, and the values in the graph on the right are higher than the values of the graph on the left.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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