Representation of data

Need to know

What you need to know

• Shows the shape of the distribution (e.g., symmetry, skewness).
• Retains all original data values.
• Data is ordered, which makes finding the median and quartiles straightforward.
• Always include a key (e.g., 5 | 2 represents 52).

Explanation

Decoding Data Displays

1. First, group raw data into classes. For a histogram, calculate frequency density (frequency divided by class width) to determine the bar height, ensuring area represents frequency.
2. To estimate the mean from grouped data, use the midpoint of each class as a representative value. The formula is the sum of (midpoint × frequency) divided by the total frequency.
3. Plot a cumulative frequency curve (ogive) to find the median. Locate the position of the median at n/2 on the vertical axis, then read across to the curve and down to the horizontal axis.
4. Finally, measure the data's spread. Calculate the interquartile range (IQR) from the ogive or use your calculator for standard deviation to compare how consistent or varied different datasets are.