9709 · 5.1
Representation of data — FAQ
Frequently asked questions for 9709 Representation of data. Direct answers first, then deeper explanation — then practise with marking.
What is the main difference between a histogram and a bar chart?
A histogram is used for continuous data grouped into intervals, and the bars must touch. The area of each bar represents frequency. A bar chart is for discrete or categorical data, and the bars have gaps between them. The height of each bar represents frequency.
Why do we use midpoints to estimate the mean of grouped data?
When data is grouped, we lose the original individual values. The midpoint of a class is our best estimate for the average value of all the data points within that class. By using it, we can calculate a weighted average that provides a good approximation of the true mean.
When should I use the median/IQR versus the mean/standard deviation to compare data?
Use the median and IQR when the data is skewed or contains significant outliers. The median is a 'resistant' measure, meaning it's not heavily influenced by extreme values. Use the mean and standard deviation when the data is roughly symmetrical and free from major outliers, as they use all data points in their calculation and are often more powerful.
On a cumulative frequency graph, why do we plot points at the upper class boundary?
The cumulative frequency for a given class represents the total count of all data points up to and including that class. Therefore, this total is reached at the very end of the class interval, which is the upper class boundary. The graph starts at the lower boundary of the first class with a cumulative frequency of zero.