Question

mode=27
mean: 22.5
median 22
(16,15,15,14)
the data set in order from least to greatest
(__, , , __)
maximum: ____
minimum: ____
range: ____
mode: ____
mean: ____
median: ____

Explanation:

Step1: Order the data set

Arrange the numbers \(16, 15, 15, 14\) from least to greatest. We compare the values: \(14 < 15 = 15 < 16\). So the ordered set is \((14, 15, 15, 16)\).

Step2: Find the Maximum

The maximum value in the ordered set \((14, 15, 15, 16)\) is the largest number, which is \(16\).

Step3: Find the Minimum

The minimum value in the ordered set \((14, 15, 15, 16)\) is the smallest number, which is \(14\).

Step4: Calculate the Range

The range is calculated as maximum - minimum. So \(16 - 14 = 2\).

Step5: Find the Mode

The mode is the number that appears most frequently. In the set \((14, 15, 15, 16)\), \(15\) appears twice and the others once, so the mode is \(15\).

Step6: Calculate the Mean

The mean is the sum of all values divided by the number of values. The sum is \(14 + 15 + 15 + 16 = 60\). There are \(4\) values, so the mean is \(\frac{60}{4}=15\).

Step7: Find the Median

For a set with an even number of values, the median is the average of the two middle numbers. The two middle numbers are \(15\) and \(15\). The average of \(15\) and \(15\) is \(\frac{15 + 15}{2}=15\).

Answer:

Ordered set: \((14, 15, 15, 16)\)
Maximum: \(16\)
Minimum: \(14\)
Range: \(2\)
Mode: \(15\)
Mean: \(15\)
Median: \(15\)