Suggested languages for you:

Americas

Europe

Problem 1

# The ages of the 6 people taking a water aerobics class are $$34,66,22,55,23$$, and 77. a. Find the mean. Round to the nearest hundredth. b. Find the median. c. Find the mode. $$\mathrm{d}$$. Find the range. e. Find the mean absolute deviation (MAD). Round your answer to the nearest tenth.

Expert verified
a. The mean age of people taking the water aerobics class is approximately 46.17. b. The median age of people taking the class is 44.5. c. There is no mode in the given ages of people taking the class as all ages appear only once. d. The range of the ages of people taking the water aerobics class is 55. e. The Mean Absolute Deviation (MAD) of the ages is approximately 19.8.
See the step by step solution

## Step 1: a. Finding the Mean

To find the mean, we need to add up all the ages and then divide the sum by the number of people. So, the mean can be calculated as follows: $$Mean = \dfrac{(34 + 66 + 22 + 55 + 23 + 77)}{6}$$ $$Mean = \dfrac{277}{6}$$ Mean ≈ 46.17 (rounded to the nearest hundredth)

## Step 2: b. Finding the Median

To find the median, we need to arrange the ages in order and then find the middle value. If there are two middle values, we take the mean of those two values. First, let's arrange the ages in ascending order: 22, 23, 34, 55, 66, 77 Since the number of ages is even (6), we will find the mean of the two middle numbers (34 and 55). $$Median = \dfrac{(34 + 55)}{2}$$ Median = 44.5

## Step 3: c. Finding the Mode

The mode is the value that appears most frequently in the dataset. In this case, all ages appear only once, which means there is no mode.

## Step 4: d. Finding the Range

The range is the difference between the highest and the lowest values in the dataset. In our dataset, the highest age is 77, and the lowest age is 22. So, the range can be calculated as follows: Range = 77 - 22 Range = 55

## Step 5: e. Finding the Mean Absolute Deviation (MAD)

To find the Mean Absolute Deviation, we first need to find the deviation of each age from the mean. Then, we will find the mean of these absolute deviations. Mean ≈ 46.17 (from part a) Deviations from mean: |34 - 46.17| ≈ 12.17 |66 - 46.17| ≈ 19.83 |22 - 46.17| ≈ 24.17 |55 - 46.17| ≈ 8.83 |23 - 46.17| ≈ 23.17 |77 - 46.17| ≈ 30.83 Now let's find the mean of these absolute deviations: MAD = $$\dfrac{(12.17 + 19.83 + 24.17 + 8.83 + 23.17 + 30.83)}{6}$$ MAD ≈ $$\dfrac{119}{6}$$ MAD ≈ 19.8 (rounded to the nearest tenth) So, the answers for this exercise are: a. Mean ≈ 46.17 b. Median = 44.5 c. Mode = None d. Range = 55 e. Mean Absolute Deviation (MAD) ≈ 19.8

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner