Question

identify the maximum, minimum, range, mode, mean, and median for each data set. show your work in the empty space within each box.

(10, 5, 10, 3)
put the data set in order from least to greatest
(__, , , __)

maximum: ____
minimum: ____
range: ____
mode: ____
mean: ____
median: ____

(7, 5, 11, 1)
put the data set in order from least to greatest
(__, , , __)

maximum: ____
minimum: ____
range: ____
mode: ____
mean: ____
median: ____

(13, 5, 13, 3)
put the data set in order from least to greatest
(__, , , __)

maximum: ____
minimum: ____
range: ____
mode: ____
mean: ____
median: ____

(20, 15, 15, 4)
put the data set in order from least to greatest
(__, , , __)

maximum: ____
minimum: ____
range: ____
mode: ____
mean: ____
median: ____

Explanation:

Data Set (10, 5, 10, 3)

Step1: Order from least to greatest

Sort the numbers: \(3, 5, 10, 10\)

Step2: Find Maximum

The largest number is \(10\)

Step3: Find Minimum

The smallest number is \(3\)

Step4: Calculate Range

Range = Maximum - Minimum = \(10 - 3 = 7\)

Step5: Find Mode

The number that appears most often is \(10\) (appears twice)

Step6: Calculate Mean

Mean = \(\frac{10 + 5 + 10 + 3}{4}=\frac{28}{4}=7\)

Step7: Find Median

For even number of values, median is average of middle two: \(\frac{5 + 10}{2}=\frac{15}{2}=7.5\)

Data Set (7, 5, 11, 1)

Step1: Order from least to greatest

Sort the numbers: \(1, 5, 7, 11\)

Step2: Find Maximum

The largest number is \(11\)

Step3: Find Minimum

The smallest number is \(1\)

Step4: Calculate Range

Range = Maximum - Minimum = \(11 - 1 = 10\)

Step5: Find Mode

All numbers appear once, so no mode (or all are modes, but typically we say no unique mode; however, since the problem might expect, we can note none, but if we consider, all appear once. But maybe the problem expects, but let's check: \(1,5,7,11\) each once. So mode: none (or state all, but maybe the problem expects, but let's proceed)

Step6: Calculate Mean

Mean = \(\frac{7 + 5 + 11 + 1}{4}=\frac{24}{4}=6\)

Step7: Find Median

For even number of values, median is average of middle two: \(\frac{5 + 7}{2}=6\)

Data Set (13, 5, 13, 3)

Step1: Order from least to greatest

Sort the numbers: \(3, 5, 13, 13\)

Step2: Find Maximum

The largest number is \(13\)

Step3: Find Minimum

The smallest number is \(3\)

Step4: Calculate Range

Range = Maximum - Minimum = \(13 - 3 = 10\)

Step5: Find Mode

The number that appears most often is \(13\) (appears twice)

Step6: Calculate Mean

Mean = \(\frac{13 + 5 + 13 + 3}{4}=\frac{34}{4}=8.5\)

Step7: Find Median

For even number of values, median is average of middle two: \(\frac{5 + 13}{2}=\frac{18}{2}=9\)

Data Set (20, 15, 15, 4)

Step1: Order from least to greatest

Sort the numbers: \(4, 15, 15, 20\)

Step2: Find Maximum

The largest number is \(20\)

Step3: Find Minimum

The smallest number is \(4\)

Step4: Calculate Range

Range = Maximum - Minimum = \(20 - 4 = 16\)

Step5: Find Mode

The number that appears most often is \(15\) (appears twice)

Step6: Calculate Mean

Mean = \(\frac{20 + 15 + 15 + 4}{4}=\frac{54}{4}=13.5\)

Step7: Find Median

For even number of values, median is average of middle two: \(\frac{15 + 15}{2}=15\)

Answer:

Data Set (10, 5, 10, 3)

• Ordered: \((3, 5, 10, 10)\)
• Maximum: \(10\)
• Minimum: \(3\)
• Range: \(7\)
• Mode: \(10\)
• Mean: \(7\)
• Median: \(7.5\)

Data Set (7, 5, 11, 1)

• Ordered: \((1, 5, 7, 11)\)
• Maximum: \(11\)
• Minimum: \(1\)
• Range: \(10\)
• Mode: None (or all, but each once)
• Mean: \(6\)
• Median: \(6\)

Data Set (13, 5, 13, 3)

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

Data Set (20, 15, 15, 4)

• Ordered: \((4, 15, 15, 20)\)
• Maximum: \(20\)
• Minimum: \(4\)
• Range: \(16\)
• Mode: \(15\)
• Mean: \(13.5\)
• Median: \(15\)