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Question
Explain histogram with an example.
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Solution
First of all, remember that histogram is different from bar chart. In bar chart, the heights of bar represent the value of the element, whereas in histogram, it is the area of bar which denotes the value!!
Hence, in histograms, if the breadths (which represents the frequencies) are different, then we must ensure that area of the rectangles are proportional to the frequencies.
See the following example:
Example
The following frequency distribution gives the masses of 48 objects measured to the nearest gram. Draw a histogram to illustrate the data.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188
Solution :
Evaluate each class widths.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188Class width10510155
Since the class widths are not equal, we choose a convenient width as a standard and adjust the heights of the rectangles accordingly.
We notice that the smallest width size is 5. We can choose 5 to be the standard width. The other widths are then multiples of the standard width.
The table below shows the calculations of the heights of the rectangle.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188Class width105101552×standardstandard2×standard3×standardstandardRectanlgle′s height in histogram6÷2=3412÷2=618÷3=68
Hence, in histograms, if the breadths (which represents the frequencies) are different, then we must ensure that area of the rectangles are proportional to the frequencies.
See the following example:
Example
The following frequency distribution gives the masses of 48 objects measured to the nearest gram. Draw a histogram to illustrate the data.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188
Solution :
Evaluate each class widths.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188Class width10510155
Since the class widths are not equal, we choose a convenient width as a standard and adjust the heights of the rectangles accordingly.
We notice that the smallest width size is 5. We can choose 5 to be the standard width. The other widths are then multiples of the standard width.
The table below shows the calculations of the heights of the rectangle.
Mass(g)10−1920−2425−3435−5051−55Frequency6412188Class width105101552×standardstandard2×standard3×standardstandardRectanlgle′s height in histogram6÷2=3412÷2=618÷3=68
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