Question

(13, 5, 13, 3)
ata set in order from least to greatest
(____, __, __, ____)
maximum: ______
minimum: ______
range: ______
mode: ______
mean: ______
median: ______

Explanation:

Step1: Order the data set

Arrange the numbers \(13, 5, 13, 3\) from least to greatest. We compare each number: \(3 < 5 < 13 = 13\). So the ordered set is \((3, 5, 13, 13)\).

Step2: Find the maximum

The maximum value in the ordered set \((3, 5, 13, 13)\) is \(13\) (the largest number).

Step3: Find the minimum

The minimum value in the ordered set \((3, 5, 13, 13)\) is \(3\) (the smallest number).

Step4: Calculate the range

Range is calculated as \( \text{Maximum} - \text{Minimum} \). So \(13 - 3 = 10\).

Step5: Find the mode

The mode is the number that appears most frequently. In the set \((3, 5, 13, 13)\), \(13\) appears twice and the others appear once, so the mode is \(13\).

Step6: Calculate the mean

Mean is the sum of all numbers divided by the count of numbers. The sum is \(3 + 5 + 13 + 13 = 34\), and there are \(4\) numbers. So the mean is \( \frac{34}{4} = 8.5 \).

Step7: Calculate the median

For a set with an even number of elements, the median is the average of the two middle numbers. The two middle numbers in \((3, 5, 13, 13)\) are \(5\) and \(13\). So the median is \( \frac{5 + 13}{2} = \frac{18}{2} = 9 \).

Answer:

Ordered set: \((3, 5, 13, 13)\)
Maximum: \(13\)
Minimum: \(3\)
Range: \(10\)
Mode: \(13\)
Mean: \(8.5\)
Median: \(9\)