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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 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 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 go through each part of the problem step by step.

Given Ages:

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

Part 1: RANGE

  1. Order the ages from least to greatest:

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

  2. Youngest employee (minimum value):

    • 27 years old

  3. Oldest employee (maximum value):

    • 44 years old

  4. Calculate the range:

    • Range = Oldest age - Youngest age
    • Range = 44 - 27 = 17

Summary for Part 1:

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

Part 2: MEDIAN

  1. Find the position of the median:

    • There are 10 employees (even number), so the median will be the average of the 5th and 6th values.

  2. Locate the 5th and 6th values in the ordered list:

    • 5th: 34
    • 6th: 35

  3. Calculate the median:

    • Median = (34 + 35) / 2 = 69 / 2 = 34.5

Summary for Part 2:

  • Median: 34.5

Part 3: MODE

  1. Identify the most frequently occurring age:

    • In the ordered list: 27, 28, 29, 33, 34, 35, 39, 41, 41, 44
    • The age 41 appears twice, while all other ages appear once.

  2. Determine the mode:

    • Mode = 41

Summary for Part 3:

  • Mode: 41

Part 4: MEAN

  1. Calculate the sum of the ages:

    • Sum = 27 + 28 + 29 + 33 + 34 + 35 + 39 + 41 + 41 + 44
    • Sum = 27 + 28 + 29 + 33 + 34 + 35 + 39 + 41 + 41 + 44 = 380

  2. Count the number of employees:

    • Number of employees = 10

  3. Calculate the mean:

    • Mean = Sum of ages / Number of employees
    • Mean = 380 / 10 = 38

Summary for Part 4:

  • Mean: 38

Final Results:

  1. Range: 17
  2. Median: 34.5
  3. Mode: 41
  4. Mean: 38