Averages and quartiles - including frequency tables and box plots

mean

add all values, divide by number of values

how to find mean from a frequency table

multiply each item by its frequency, divide by total frequency of all items

how to find find (estimated) mean from a grouped frequency table

find midpoint between values in each class, multiply by frequency, divide by total frequency of all items

median (Q2)

middle number (in a list of numbers in order)

how to find median from a frequency table

1. find total frequency
2. add 1, divide by 2 to find the median frequency
3. find cumulative frequency
4. find result which contains the median frequency

how to find the class interval containing the median

1. find total frequency of all items
2. find median of total frequency (add 1, divide by 2)
3. find cumulative frequency
4. from cumulative frequency, find the class which the median is included in
5. write this class interval as the answer

mode

most common number

can there be multiple modes or no mode?

yes

how to find mode from a (grouped) frequency table

find the item/class interval with the highest frequency

range

difference between highest and lowest values

how to find range from a grouped frequency table

find midpoints of highest and lowest classes, find the difference from them

cumulative frequency table

table with a running frequency (adding up the frequencies as you go down the list)

lower quartile (Q1)

value 1/4 along list of data, median of lower half of data

upper quartile (Q3)

value 3/4 along list of data, median of upper half of data

interquartile range

range/difference between upper and lower quartiles

how to make a box plot

1. draw and label number line (if not given)
2. draw vertical lines to mark the minimum, maximum, lower and upper quartiles, and median
3. draw horizontal lines between min and Q1, Q3 and max
4. draw horizontal lines at the top and bottom of Q1 and Q3 lines to form a box