Explain how to draw a histogram using the provided frequency distribution table.

The table provides the following information:

• Class Limits: The intervals for the data (e.g., $30-39$).
• Frequency: The count of data points in each class.
• Class Boundaries: The continuous intervals for plotting on the x-axis (e.g., $29.5-39.5$).
• Class Center: The midpoint of each class.

The frequencies are:

• $30-39$: 5
• $40-49$: 13
• $50-59$: 9
• $60-69$: 6
• $70-79$: 8
• $80-89$: 8
• $90-99$: 1

The sum of these frequencies is $5+13+9+6+8+8+1 = 50$. This matches the total frequency written in the table. (My previous check had a calculation error, apologies for that. The total is indeed 50.)

• Draw a horizontal axis (x-axis) and label it "Class Boundaries" or "Scores". Mark the class boundaries: $29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5, 99.5$.
• Draw a vertical axis (y-axis) and label it "Frequency". Scale this axis from 0 up to at least the maximum frequency, which is 13. A scale of 0 to 15 with increments of 1 or 2 would be appropriate.

For each class interval, draw a rectangular bar:

• The width of each bar will span from its lower class boundary to its upper class boundary on the x-axis.
• The height of each bar will correspond to its frequency on the y-axis. The bars should touch each other, as the class boundaries are continuous.

Here's how to draw each bar:

• For the class $30-39$ (boundaries $29.5-39.5$): Draw a bar from 29.5 to 39.5 on the x-axis, with a height of 5 on the y-axis.
• For the class $40-49$ (boundaries $39.5-49.5$): Draw a bar from 39.5 to 49.5 on the x-axis, with a height of 13 on the y-axis.
• For the class $50-59$ (boundaries $49.5-59.5$): Draw a bar from 49.5 to 59.5 on the x-axis, with a height of 9 on the y-axis.
• For the class $60-69$ (boundaries $59.5-69.5$): Draw a bar from 59.5 to 69.5 on the x-axis, with a height of 6 on the y-axis.
• For the class $70-79$ (boundaries $69.5-79.5$): Draw a bar from 69.5 to 79.5 on the x-axis, with a height of 8 on the y-axis.
• For the class $80-89$ (boundaries $79.5-89.5$): Draw a bar from 79.5 to 89.5 on the x-axis, with a height of 8 on the y-axis.
• For the class $90-99$ (boundaries $89.5-99.5$): Draw a bar from 89.5 to 99.5 on the x-axis, with a height of 1 on the y-axis.

This process will result in a complete histogram representing the given frequency distribution.