Histograms - SS2 Mathematics Lesson Note

A histogram is a graphical representation of a frequency distribution. Histograms are useful for handling data that deal with continuous values such as the measurement of physical mechanical components in a manufacturing plant.

The table below shows the thickness of 20 samples of steel plates in millimeters to two significant figures:

\[Thickness\ (mm)\ \ x\]	\[Frequency\ f\]
\[6.2 - 6.4\]	\[1\]
\[6.5 - 6.7\]	\[4\]
\[6.8 - 7.0\]	\[6\]
\[7.1 - 7.3\]	\[5\]
\[7.4 - 7.6\]	\[3\]
\[7.7 - 7.9\]	\[1\]

\[Total\ number\ of\ samples,\]

\[n = \sum_{}^{}f = 20\]

 

In this example, the values of the thickness of each steel plate is 2 significant figures. Considering the usual rounding procedure in math, each class (\(6.2 - 6.4,\ 6.5 - 6.7,\ldots\)) in effect extends from \(0.05\) below the first stated value of the class to just under \(0.05\) above the second stated value of the class. So, the class, \(7.1 - 7.3\) includes all values between \(7.05\) and \(7.35^{-}\). From this, we can observe that:

1. The class values stated in the table are the lower and upper limits of the class and their difference gives the class width.

2. The class boundaries are \(0.05\) below the lower-class limit and \(0.05\) above the upper-class limit.

3. The class interval is the difference between the lower and upper-class boundaries.

4. The central value is the average of the lower and upper-class boundaries.

The data is the table is represented in the histogram: