How do you interpret the shape of a cumulative frequency curve?

A cumulative frequency curve shows how the total frequency accumulates as you move through the data set.

When you look at a cumulative frequency curve, you're essentially seeing how the data builds up over time. The x-axis usually represents the data values, while the y-axis represents the cumulative frequency. As you move from left to right along the x-axis, the curve will either stay flat or rise, but it will never fall. This is because cumulative frequency can only increase or stay the same; it never decreases.

A steep section of the curve indicates that a lot of data points fall within a small range of values. This means there's a high frequency of data points in that interval. Conversely, a flatter section of the curve suggests that fewer data points fall within that range, indicating a lower frequency.

The shape of the curve can also tell you about the distribution of the data. For example, if the curve rises quickly at the beginning and then levels off, it suggests that many data points are clustered at the lower end of the range. If the curve rises slowly at first and then steeply towards the end, it indicates that many data points are clustered at the higher end.

By analysing the cumulative frequency curve, you can also find the median, lower quartile, and upper quartile. These are important for understanding the spread and central tendency of the data. The median is found where the curve reaches 50% of the total frequency, while the lower and upper quartiles are found at 25% and 75%, respectively.