Mode, Median, Mean & Range - (Stem and Leaf)

Sometimes in your exam the question will already have a completed Stem and Leaf diagram, and you will be asked questions about it.

Question
Below is a Stem and Leaf Diagram of the ages of music shop customers

Key: 1 | 7 = 17







a) What is the modal age of customer?

"Modal" means work out the mode from your data.

Mode = most common value

Solution: mode = 17    (17 is the value that appears the most often in the Sem and Leaf diagram)


b) What is the median age of customer?

Median = middle value

There are 12 values in the table, so the middle value will be half-way between the 6th and 7th values.
Cross off the data in the Stem and Leaf diagram until you get to the middle values (crossing off from each end as you go along):

You cannot have two medians, so the median will be half-way between 1 and 3.

Solution: median = 2


c) Work out the range

Range = difference between highest value and lowest value    (= highest value - lowest value)

The highest value is 31. The lowest value is 17.

Solution: range = 31 - 17 = 14


d) Find the mean

Mean = total of all pieces of data ÷ number of pieces of data

To work out the mean age of customer, you must add up all the ages (to get the total of all pieces of data) and divide by the number of customers (the number of pieces of data, 12).

Solution: 17 + 17 + 17 + 18 + 21 + 21 + 23 + 23 + 24 + 26 + 28 + 31 = 266
266 ÷ 12 = 22.1666... 
Mean = 22.2 (1 decimal place)

Remember:
- Learn the definitions of mode, median, mean and range


Top Tip: These questions will probably be the same if they come up in your exam, so practice them well as only the values will change.