Q 61. - The Practice of Statistics for AP

Question

Birth months Imagine asking a random sample of $60$ students from your school about their birth months. Draw a plausible graph of the distribution of birth months. (Hint: Should you use a bar graph or a histogram?)

Step-by-Step Solution

Answer

Step 1: Given information

Randomly $60$ students are taken as a sample.

Step 2: Concept

A histogram is a widely used graphing tool. It's utilised to summarise discrete or continuous data that's measured on an interval scale. It's a common method of displaying key data distribution features in a user-friendly manner.

Step 3: Calculation

Because the months are categorical, a bar graph should be utilised (histogram requires that the variables are numerical).

The height of the bars must be equal to the number of pupils, and the width of the bars must be equal to the number of students. We expect the $60$ students in the sample to be evenly distributed over all months, resulting in around $\frac{60}{12}=5$ students per month.

Let's say the numbers of students born in each month are distributed as follows: 

Birth Month	Frequency
January	5
February	6
March	5
April	4
May	5
June	5
July	5
August	4
September	5
October	5
November	6
December	5

The corresponding bar graph is then: 

Thus, a required graph is drawn.