Question

The data set on Scottish schoolchildren discussed in Example 4.1.5 included the eye colors of the children also. The frequencies of their eye colors are \(\begin{array}{lccc}\text { Blue } & \text { Light } & \text { Medium } & \text { Dark } \\ 2978 & 6697 & 7511 & 5175\end{array}\) Use these frequencies to obtain a bar chart and an estimate of the associated pmf.

Short answer

First, calculate the total frequency and then the relative frequency for each eye color category by dividing its individual frequency by the total frequency. This gives the probability mass function. Plot a bar chart with eye color categories on x-axis and relative frequencies on y-axis.

Step-by-step solution

Sum up the total frequencies

First, calculate the total frequency by adding up all individual eye color frequencies. The total frequency equals 2978 (Blue) + 6697 (Light) + 7511 (Medium) + 5175 (Dark).

Calculate the relative frequency for each eye color

The relative frequency for each eye color category is obtained by dividing the individual frequency of each category by the total frequency. For example, the relative frequency of 'Blue' is calculated as \(\frac{2978}{2978+6697+7511+5175}\).

Create the Probability Mass Function (pmf)

The Probability Mass Function (pmf) can be obtained from these relative frequencies. For a given eye color e, the pmf is the relative frequency of eye color e.

Plot a bar chart

Plot a bar chart using the relative frequencies obtained. Place the eye color categories (Blue, Light, Medium, Dark) on the x-axis and the corresponding relative frequencies on the y-axis.