Jake played a different game 20 times. The stem and leaf diagram shows information about his scores. 0 & 9 & & & & & 1 & 2 & 3 & 3 & 4 & 5 & 2 & 5 & 6 & 6 & 6 & 6 & 7 3 & 1 & 3 & 4 & 6 & 8 & 4 & 0 & 2 & 9 & & & Jake said his modal score was 6 points because 6 occurs most often in the diagram. (b) Is Jake correct? You must explain your answer.

## Step1:<br />Firstly, we need to understand the stem-and-leaf diagram. In this diagram, the 'stem' represents the tens digit of the number, and the 'leaf' represents the units digit. For example, in the key, \(1 \mid 2\) represents 12 points.<br /><br />## Step2:<br />Next, we need to find out the mode, which is the most frequently occurring number in a data set. Jake claims that his modal score was 6 points because 6 occurs most often in the diagram.<br /><br />## Step3:<br />To verify Jake's claim, we need to count the number of times each score appears in the diagram. We need to pay attention to the 'stem' and 'leaf' to correctly identify the scores.<br /><br />### The score of 6 points is represented as \(0 \mid 6\) in the diagram, but there is no such representation. <br />### The score of 16 points is represented as \(1 \mid 6\) in the diagram, but there is no such representation. <br />### The score of 26 points is represented as \(2 \mid 6\) in the diagram, and it appears four times. <br />### The score of 36 points is represented as \(3 \mid 6\) in the diagram, but there is no such representation. <br /><br />## Step4:<br />From the above analysis, we can see that the score of 26 points appears the most frequently in the diagram, not the score of 6 points as Jake claimed. Therefore, Jake is not correct.