What are the definitions and uses of ogives, box plots, and waffle charts?

Here are the answers to your questions:

1. Another name for a cumulative frequency curve is an ogive.

2. In a box and whisker plot, the vertical line inside the box represents the median (or second quartile, $Q_2$).

3. A waffle chart typically consists of 100 squares (a 10x10 grid).

4. The main advantage of using a waffle chart over a pie chart is that it can more accurately represent proportions, especially when comparing multiple categories or when proportions are very similar, as it avoids the visual distortion that can occur with angles in a pie chart.

5. The type of ogive that shows cumulative frequency of data points less than or equal to a certain value is a less than ogive.

6. In a box plot, the whiskers extend from the edges of the box (the first quartile $Q_1$ and the third quartile $Q_3$) to the minimum and maximum data points within $1.5 \times IQR$ of the quartiles, respectively. Any points beyond the whiskers are considered outliers.

7. To calculate the cumulative frequency for a class interval, you sum the frequency of that class interval with the frequencies of all preceding class intervals.

8. The five numbers needed to construct a box and whisker plot are the minimum value, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum value.

9. The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range between the first quartile ($Q_1$) and the third quartile ($Q_3$), indicating the spread of the central portion of the dataset.

10. To find the cumulative frequency for the class 20-40: