How do we construct a histogram for continuous data using unequal class widths?

Note 1

Do not use frequencies or relative frequencies on vertical scale, (y-axis of the histogram) when drawing histogram.

Note 2

Use density scale instead.

Note 3

Density is defined as:

\[ density= \frac{relative frequency}{class width} \]

Here is histogram correctly drawn with unequal class intervals and density scale

How do we sketch a histogram for continuous data using unequal class widths?

Example 1

Use the frequency table below to determine:

##   Length.cut Freq
## 1     [0,40)    5
## 2    [40,50)    6
## 3    [50,60)    8
## 4    [60,70)    4
## 5   [70,100)    2

1. relative frequency for each interval

2. density frequency for each interval

3. appearance of the histogram with labeld axis and title assigned

Example 1 - Extension A

Use calculations from Example 1 to:

1. determine the area for each bar of the histogram sketched

2. calculate the sum of all areas

3. interpret the areas of the rectangles in your graph

Example 1 - Extension B, (What if … ?)

Use relevant information from Example 1 to:

1. sketch frequency distribution histogram

2. sketch relative frequency distribution histogram

3. compare appearaces of all three histograms and write one/two - sentence conclusion.