Frequency Tables- Finding Averages

A frequency table is a statistical tool that displays the frequency of various outcomes in a dataset.
Each entry in the table contains the count or the frequency of occurrence of values within a particular group or interval.
Frequency tables provide a snapshot of the distribution of data, making it easier to analyze larger datasets.

Mean is calculated as the total of all values (by multiplying each value by its frequency and adding them together) divided by the total number of values (sum of frequencies).
The median is the middle value when the values are arranged in increasing or decreasing order. If the data set count is even, the median is the mean of the two middle values.
Mode refers to the value(s) that occur most frequently in your data set. In a frequency table, it will be the value corresponding to the highest frequency.

Frequency tables enable you to visualize the spread and tendency of data, making it easier to compute averages.
The mean offers a measure of central tendency, giving an overall ‘average’ value.
The median offers another measure of central tendency, particularly useful in skewed distributions as it is not affected by extreme values.
The mode can give you a sense of the most popular or common values in your data set.

To create a frequency table, start by defining your intervals or categories.
Under each category, count the number of occurrences (frequency) of each value or data item.
To calculate the mean, multiply each value by its frequency, then add these totals together and divide by the total frequency.
To find the median, multiply the cumulative frequency of each group by its corresponding value. The value that takes you closest to half the cumulative frequency is the median group. If the total frequency is even, take the average of the two middle values.
The mode is simply the value(s) with the highest frequency.

The precise calculation of mean and median from a grouped frequency table requires assumptions about the distribution of data within each group.
The mean is sensitive to outliers, while the median is not, hence in a skewed dataset the median is a more accurate reflection of central tendency.
The mode is not necessarily indicative of central tendency or typical behaviour, and data may have one mode (unimodal), more than one mode (multimodal), or no mode at all.
A more sophisticated understanding of averages and frequency tables allows you to interpret data more critically and make more informed decisions.