**Frequency** the number of times an event occurs in an experiment

**Cumulative frequency** the sum of the frequency for a particular class and the frequencies for all the classes below it

Box and whisker plots neatly summarize the distribution of the data. It gives information about the range, the median and the quartiles of the data. The first and third quartiles are at the ends of the box, the median is indicated with a vertical line in the interior of the box, and the maximum and minimum points are at the ends of the whiskers.

**Outliers**will be any points lower than Q

_{1}− 1.5 × IQR and larger than Q

_{3}+ 1.5 × IQR (IQR =interquartile range)

_{1}, Q

_{2}and Q

_{3}, it is easiest to use the cumulative frequency graph. First, determine the percentage of the quartile in question. Second, divide the total cumulative frequency of the graph (i.e. the total sample size) by 100 and multiply by the corresponding percentage. Then, you will have found the frequency (y-value) at which 25% for Q

_{1}/ 50% for Q

_{2}/ 75% for Q

_{3}of the sample is represented. To find the x-value, find the corresponding x-value for the previously identified y-value.

Example: Using the histogram, create a cumulative frequency graph and use it to construct a box and whisker diagram.

Write out the table for frequency and cumulative frequency.

_{1}, Q

_{2}and Q

_{3}.

Plot box and whiskers.

### GDC

Find the descriptive statistics for the data used in the previous example, showing the ages of students.