Frequency tables and estimating the mean

A frequency table shows how many times each value appears.

• The mode is the value with the highest frequency.
• The median is the (n + 1) ÷ 2th value, where n is the total frequency. Add up the frequencies until you reach it.

Example: find the mode and median number of goals.

1. Highest frequency is 7, so the mode = 1 goal
2. n = 4 + 7 + 5 + 3 + 1 = 20, so the median is the 10.5th value
3. Running totals: 4, then 4 + 7 = 11, so the 10th and 11th values are both 1
4. Median = 1 goal

1. Add a column for f × x: the frequency times the value.
2. Add up the fx column (Σfx) and the frequencies (Σf).
3. Mean = Σfx ÷ Σf (learn this)

Σ means "the sum of".

Example: find the mean number of goals.

1. Σfx = 30 and Σf = 20
2. Mean = 30 ÷ 20 = 1.5 goals

When data is grouped into classes, you can't find exact averages, but you can find:

• the modal class: the class with the highest frequency
• the class that contains the median.

Example: find the modal class and the class containing the median.

1. Modal class: 10 < t ≤ 20
2. n = 30, so the median is the 15.5th value
3. Running totals: 5, then 17, so the 15.5th value is in 10 < t ≤ 20

For grouped data, assume every value is at the midpoint of its class.

1. Find each class's midpoint.
2. Multiply each midpoint by its frequency.
3. Mean ≈ total of (midpoint × frequency) ÷ total frequency.

Example: estimate the mean time from the grouped table.

1. Total = 25 + 180 + 225 + 140 = 570
2. Mean ≈ 570 ÷ 30 = 19 minutes

It's an estimate because you don't know the exact values, only their classes.