Statistics 2

Section 1Grouped data

Grouped data are organised into class intervals, such as 10-19, 20-29, and 30-39. This helps summarise large data sets, but it hides exact values. Watch out: with grouped data, calculations like mean are estimates because you usually use class midpoints.

Section 2Class boundaries and midpoints

Class boundaries show the real limits between continuous groups. For example, scores 20-29 have boundaries 19.5 and 29.5 when measured to the nearest whole number. The midpoint is the middle of the interval, found by adding the lower and upper class limits and dividing by 2.

Section 3Mean from grouped data

To estimate the mean from grouped data, multiply each class midpoint by its frequency, add those products, then divide by the total frequency. In plain words, pretend all values in a group sit at the midpoint. The estimate improves when intervals are narrow and data are spread fairly evenly.

Section 4Cumulative frequency

Cumulative frequency is a running total of frequencies. It tells how many values are less than or equal to an upper boundary. A cumulative frequency curve can be used to estimate the median, quartiles, and percentiles.

Section 5Quartiles and interquartile range

Quartiles split ordered data into four parts. Q1 is the lower quartile, Q2 is the median, and Q3 is the upper quartile. The interquartile range, IQR, is Q3 - Q1 and shows the spread of the middle half of the data.

Section 6Box-and-whisker plots

A box-and-whisker plot shows the minimum, Q1, median, Q3, and maximum. The box shows the IQR, while the whiskers show the overall spread. Easy to mix up - a longer box or whisker means more spread in that part of the data, not more people automatically.

Section 7Interpreting displays

Advanced data questions often test reading, not just calculating. Check the graph title, axis labels, scales, class intervals, and units before answering. This is one of the most common exam slip-ups: students read the height of a bar but ignore what the scale means.