Question

1. the ages of 22 students in a karate class are given below.

11, 5, 9, 13, 8, 9, 9, 11, 10, 8, 6, 7,
12, 11, 13, 12, 7, 6, 11, 12, 10, 8
a) make a line plot using the number line below.

what is the spread (range) of the data?
what is the mode of the data?
how many students are at least 10 years old?

Explanation:

Step1: Find the range

The range is calculated by subtracting the minimum value from the maximum value.
The minimum value in the data set is \(5\), and the maximum value is \(13\).

$$ \text{Range}=13 - 5 $$

$$ \text{Range}=8 $$

Step2: Find the mode

The mode is the value that appears most frequently.
Count the frequency of each value:

• \(5\) appears \(1\) time.
• \(6\) appears \(2\) times.
• \(7\) appears \(2\) times.
• \(8\) appears \(3\) times.
• \(9\) appears \(3\) times.
• \(10\) appears \(2\) times.
• \(11\) appears \(4\) times.
• \(12\) appears \(3\) times.
• \(13\) appears \(2\) times.

The value \(11\) appears most frequently.

Step3: Find the number of students at least 10 years old

Count the number of values that are \(10\) or greater.
Values of \(10\): \(2\) times.
Values of \(11\): \(4\) times.
Values of \(12\): \(3\) times.
Values of \(13\): \(2\) times.

$$ \text{Number of students}=2 + 4+3 + 2 $$

$$ \text{Number of students}=11 $$

Answer:

• The range of the data is \(8\).
• The mode of the data is \(11\).
• The number of students at least \(10\) years old is \(11\).