Question

each box.
(7, 5, 11, 1)
put the data set in order from least to greatest
(____,__,__,____)
maximum: ______
minimum: ______
range: ______
mode: ______
mean: ______
median: ______

Explanation:

Step1: Order the data set

Arrange the numbers \(7, 5, 11, 1\) from least to greatest. We compare the values: \(1 < 5 < 7 < 11\). So the ordered set is \((1, 5, 7, 11)\).

Step2: Find the Maximum

The maximum value in the ordered set \((1, 5, 7, 11)\) is the largest number, which is \(11\).

Step3: Find the Minimum

The minimum value in the ordered set \((1, 5, 7, 11)\) is the smallest number, which is \(1\).

Step4: Calculate the Range

The range is calculated as maximum - minimum. So \(11 - 1 = 10\).

Step5: Find the Mode

The mode is the number that appears most frequently. In the set \(\{1, 5, 7, 11\}\), each number appears once, so there is no mode (or we can say all numbers are modes with frequency 1, but typically if no number repeats, we state there is no mode).

Step6: Calculate the Mean

The mean is the sum of the numbers divided by the count of numbers. The sum is \(1 + 5 + 7 + 11 = 24\), and the count is \(4\). So the mean is \(\frac{24}{4}=6\).

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 \((1, 5, 7, 11)\) are \(5\) and \(7\). The average is \(\frac{5 + 7}{2}=\frac{12}{2}=6\).

Answer:

Ordered set: \((1, 5, 7, 11)\)
Maximum: \(11\)
Minimum: \(1\)
Range: \(10\)
Mode: No mode (or all numbers with frequency 1)
Mean: \(6\)
Median: \(6\)