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

Question

34, 41, 28, 35, 27, 44, 29, 33, 41, 39

Watch THE MODE TOADS video to review about measures of center.

*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.***

(8 points)
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 the 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 4: 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.

Answer 1

Let's solve this step by step.

Part 1: RANGE

1. Ordered List: First, we need to arrange the ages in order from least to greatest.

   Sorted List: 27, 28, 29, 33, 34, 35, 39, 41, 41, 44

2. Oldest Employee: The oldest employee is 44 years old.

3. Youngest Employee: The youngest employee is 27 years old.

4. Range Calculation: The range is calculated as:

   \[ \text{Range} = \text{Oldest} - \text{Youngest} = 44 - 27 = 17 \]

Part 2: MEDIAN

1. Finding the Median: Since there are 10 employees (an even number), the median will be the average of the 5th and 6th numbers in the ordered list.

   The 5th and 6th values are:

   • 5th: 34
   • 6th: 35

2. Median Calculation:

   \[ \text{Median} = \frac{34 + 35}{2} = \frac{69}{2} = 34.5 \]

Part 3: MODE

1. Finding the Mode: The mode is the number that appears most frequently in the list.

   In the sorted list: 27, 28, 29, 33, 34, 35, 39, 41, 41, 44. The number 41 appears twice, while all other numbers appear only once.

2. Mode: Hence, the mode is 41.

Part 4: MEAN

1. Sum of the Ages: We calculate the sum of all ages:

   \[ 27 + 28 + 29 + 33 + 34 + 35 + 39 + 41 + 41 + 44 = 380 \]

2. Number of Employees: There are 10 employees.

3. Mean Calculation: The mean is calculated as:

   \[ \text{Mean} = \frac{\text{Sum of Ages}}{\text{Number of Employees}} = \frac{380}{10} = 38 \]

Summary of Results

• Part 1: RANGE

  • Oldest Employee: 44 years
  • Youngest Employee: 27 years
  • Range: 17

• Part 2: MEDIAN

  • Median: 34.5

• Part 3: MODE

  • Mode: 41

• Part 4: MEAN

  • Sum of Ages: 380
  • Number of Employees: 10
  • Mean: 38