Q. 13 - Elementary Statistics

Question

Explain the relative positioning of the bars in a histogram to the numbers that label the horizontal axis when each of the following quantities is used to label that axis.

a. Lower class limits

b. Lower class cut points

c. Class marks

d. Class midpoints

Step-by-Step Solution

Answer

Part$\left(a\right)$: Lower class limits: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower limit of the class to the lower limit of the next class.

Part$\left(b\right)$: Lower cut points: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower cut point of the class to the lower cut point of the next class. 

Part$\left(c\right)$: Class mark: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the mark of the class.

Part $\left(d\right)$: Class midpoints: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the midpoint of the class. 

Part a Step 1 . Given information

We need to explain the relative positioning of the bars in a histogram to the numbers that label the horizontal axis when each of the following quantities is used to label that axis. 

Part a Step 2 . Lower class limits:

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower limit of the class to the lower limit of the next class.

For example, let us the histogram which representing the frequency  distributions for the data on days to maturity for short-term investments.

From the diagram, let us consider $30-39$. Here, the lower class limit is, $30$.

Part b Step 1 . Lower cut points:

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower cut point of the class to the lower cut point of the next class. 

For example, let us consider the histogram which representing the frequency distribution for the data on weights of  males.

From the diagram, let us consider $120$-under $140$. Here, the lower class cut point is, $120$.

Part c Step 1 . Class mark:

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the mark of the class.

For example, let us consider the histogram which representing the frequency distributions for the data on days to maturity for short-term investments.

From the diagram, let us consider $30-39$.Here, the class mark is,$\frac{\left(30+39\right)}{2}=\frac{69}{2}=34.5$.

Part d Step 1 . Class midpoints:

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the midpoint of the class. 

For example, let us consider the histogram which representing the frequency distribution for the data on weights of  males.

From the diagram, let us consider $120$-under $140$.Here, the class midpoint is, $\frac{\left(120+140\right)}{2}=\frac{260}{2}=130$.