Frequency Tables and Dot Plots

What you will learn

• Build a frequency table from raw data.
• Draw and read a dot plot.
• Find the total, the most common value and the middle value.

Before you start: you should be able to use tally marks and bar charts. See Bar Charts.

The idea

Raw data is a messy list. A frequency table tidies it by listing each value and how many times it occurs, which is its frequency. A dot plot draws the same information: one dot for each item, stacked above its value on a number line.

Making a frequency table

1. List every possible value in order.
2. Go through the data and make a tally mark for each.
3. Count the tallies to get the frequencies.
4. Add the frequencies. The total must equal the number of items. If not, you missed one or counted one twice.

Reading it

• The mode is the value with the biggest frequency.
• The total number of items is the sum of the frequencies.
• For the middle value, count along the ordered data to the half-way item.

Worked examples

Example 1: Building the table

Shoe sizes: $3, 4, 4, 5, 3, 4, 5, 4, 3, 5$. Make a frequency table.

1. Size $3$ appears $3$ times, size $4$ appears $4$ times and size $5$ appears $3$ times.
2. Check: $3 + 4 + 3 = 10$ items. ✓

Answer: $3$: $3$, $4$: $4$, $5$: $3$

Example 2: The middle value

Use the pets table. Find the middle value of the $20$ pupils.

1. The middle falls between the $10$th and $11$th pupils.
2. Running totals: $3$, $9$, $16$, so the $10$th and $11$th are both in the group with $2$ pets.

Answer: $2$ pets

Example 3: Total pets

Find the total pets owned.

1. Multiply each value by its frequency: $0$, $6$, $14$, $9$, $4$.
2. Add: $33$.

Answer: $33$ pets, so the mean is $33 \div 20 = 1.65$.

Tip: always add the frequencies as a check. The total is the number of people asked.

Why it matters

Frequency tables are how scientists, shops and sports analysts summarise large amounts of data. They are also the first step to finding the mean, median and mode.