Histograms
In this article we shall look at representing data in a histogram. Continuous data can be represented on a histogram. We use group frequency distribution tables to summarise the data before constructing histograms.
Histograms provide a clear view of how data is distributed. The generally shape of the data is visible and we get a graphical view of how the data is spread out.
Characteristics of a histogram
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- A histogram has the frequency lebal on the y-axis.
- A histogram is similar to a barchart except there are two major differences
- There are no gaps between the bars
- The are of the bar is proportional to the frequency
- The frequency density is the hieght of each bar;
Frequency density = frequency/class width
Drawing Histograms
The table below shows the time that a random sample of 200 students took to complete their homework.
| Time (minutes) | 25-30 | 30-35 | 35-40 | 40-45 | 50-80 |
|---|---|---|---|---|---|
| Frequency | 56 | 41 | 70 | 34 | 15 |
- Draw a histogram to represent the data
- Estimate how many students took between 36 and 45 minutes to complete their homework.
First we will need to draw a frequency distribution table by expanding the question table. We shall add two columns; a class width and frequency density column.
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Time (minutes) Frequency Class width Frequency density 25-30 56 5 11.2 30-35 41 5 8.2 35-40 70 5 14 40-50 34 10 3.4 50-80 15 30 0.5 To find the class width for instance the first rpw we find the difference between the boundaries
30 – 25 = 5Now we can draw the histogram using the frequency density. On the x-axis the bars use the class boundaries e.g. The first bar is from 25 to 30.
Remember to label the axis. The vertical axis is always the frequency density[IMAGE]
- We must find how many students took between 36 and 45 minutes to complete their homework. We can only estimate the number of students. To do that we find the area between 36 and 45 which has been shown on the histogram below.
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The histogram shows the time taken in seconds by a group of students to solve a puzzle. The shaded bar A represents a frequency of 80 children.
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- Why should a histogram be used to represent the data?
- Write down a feature associated with each of the bars in a histogram
- What area on the histogram represents one student?
- The total area under the histogram is 240 units²
Find the total number of students in the group.
- Time is continuous
- The area of the bar is proportional to the frequency
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Area of bar A = 2 × 28.3= 56.6 units²
Therefore 56.6 units represents 80 students.
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One child is = 56.6/80 = 0.7075 units240 ÷ 0.7075 = 339.22…⇒ 339 students
Remember it is just an estimation.
