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The ages, in years, of randomly selected employees are listed below.

34, 41, 28, 35, 27, 44, 29, 33, 41, 39
To solve for measures of center, we first need to reorder the numbers on paper from LEAST to GREATEST.
Count the values in the problem to make sure you have the same number of values on your ordered list.
Do not round the answers.
Part 1: RANGE
What is the age of the oldest employee? ____
What is the age of the youngest employee? ____
Determine the range of the ages? _____
Part 2: MEDIAN
To find the MEDIAN, we will find the center value. If there are 2 center values, you must find the mean of 2 center values.
Determine the median of the ages. _____
Part 3: MODE
To find the MODE, we will find the value that repeats the most.
Determine the MODE of the ages.
Part 3: MEAN
What is the sum of the ages? ____
How many employees were selected? _____
To find the MEAN, divide the sum of the ages by the number of employees selected.
Determine the mean of the ages. _____

1 answer

Let's solve the problem step by step.

Step 1: Reorder the ages from least to greatest

Original ages: 34, 41, 28, 35, 27, 44, 29, 33, 41, 39

Ordered list: 27, 28, 29, 33, 34, 35, 39, 41, 41, 44

Counting the values

There are 10 values in the ordered list.

Part 1: RANGE

  • Age of the oldest employee: 44
  • Age of the youngest employee: 27
  • Range of the ages: \[ \text{Range} = \text{Oldest} - \text{Youngest} = 44 - 27 = 17 \]

Part 2: MEDIAN

Since there are 10 values (an even number), the median will be the average of the 5th and 6th values in the ordered list.

  • The 5th value is 34.
  • The 6th value is 35. \[\text{Median} = \frac{34 + 35}{2} = \frac{69}{2} = 34.5\]

Part 3: MODE

To find the mode, we look for the number that appears most frequently in the ordered list.

  • The value 41 appears twice, while all other values appear once.
  • Mode: 41

Part 4: MEAN

  • Sum of the ages: \[ 27 + 28 + 29 + 33 + 34 + 35 + 39 + 41 + 41 + 44 = 380 \]
  • Number of employees selected: 10
  • Mean: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of employees}} = \frac{380}{10} = 38 \]

Summary of Answers

  • Part 1:

    • Oldest age: 44
    • Youngest age: 27
    • Range: 17

  • Part 2:

    • Median: 34.5

  • Part 3:

    • Mode: 41

  • Part 4:

    • Sum of ages: 380
    • Number of employees: 10
    • Mean: 38