Median, Mean, Mode, Range from a Frequency Table

• Mean is found by dividing the sum of all values by the total number of values. $$ \text{Mean} = \frac{\sum \text{values}}{\text{Total number of values}} $$
• Median is the middle value when all numbers are arranged in order.
• Mode is the value that appears most frequently in the dataset.
• Range is the difference between the maximum and minimum values.

• Step 1: Multiply each value by its corresponding frequency and sum these products: $$(4 \times0) + (6 \times 1) + (3 \times 2) + (1 \times 3) + (1 \times 9) = 24$$
• Step 2: Calculate the total frequency: $$4 + 6 + 3 + 1 + 1 = 15$$
• Step 3: Divide the sum of products by the total frequency: $$24 \div 15 = 1.6$$

The mean of this frequency table is 1.6, meaning that, on average, the number of pets owned per person in this dataset is 1.6.

The formula to determine the position of the median in an ordered dataset is: $$\frac{n + 1}{2}$$

For example, if the total frequency $n$ is 15, then $$\frac{15 + 1}{2} = 8$$

This means the median is the 8th value in the ordered list. Based on the frequency table, the 8th value is 1, so the median is 1.

An outlier is a value that is much higher or lower than the rest of the data. 

The mean is affected by outliers because it includes all values in the calculation. A very high or low number can pull the mean up or down, making it less representative.

The median is more stable because it depends only on the middle value. Even if there is an outlier, the median stays close to the true center of the dataset.