### Calculating Weighted Mean for Number of Shoes OwnedThe data below represents the number of pairs of shoes owned per person by a group of classmates. Follow the steps to find the weighted mean of the number of shoes per person.#### Data Table| Number of Shoes per Person | Frequency ||----------------------------|-----------|| 4 | 6 || 8 | 1 || 12 | 2 || 16 | 3 |#### Explanation of Data- **Number of Shoes per Person**: This column lists the different quantities of shoe pairs owned by the individuals in the group.- **Frequency**: This column indicates how many people own that particular number of shoe pairs.#### Steps to Calculate the Weighted Mean1. **Multiply each number of pairs of shoes by its corresponding frequency** to find the weighted value for each category: - $ 4 \times 6 = 24 $ - $ 8 \times 1 = 8 $ - $ 12 \times 2 = 24 $ - $ 16 \times 3 = 48 $2. **Sum these weighted values** to find the total weighted value: - $ 24 + 8 + 24 + 48 = 104 $3. **Sum the frequencies** to find the total frequency: - $ 6 + 1 + 2 + 3 = 12 $4. **Calculate the weighted mean** using the formula: \[ \text{Weighted Mean} = \frac{\text{Total Weighted Value}}{\text{Total Frequency}} = \frac{104}{12} \approx 8.7 \]#### ResultThe weighted mean number of shoes per person is approximately $ 8.7 $ pairs.

The data below represents the number of pairs of shoes owned per person by a group of classmates. Find the weighted mean of the number of shoes per person. (Round your answer to the nearest tenth if necessary.) Number of Shoes per Person Frequency 4 6 8 1 12 2 16 3 Weighted mean

The data below represents the number of pairs of shoes owned per person by a group of classmates. Find the weighted mean of the number of shoes per person. (Round your answer to the nearest tenth if necessary.) Number of Shoes per Person Frequency 4 6 8 1 12 2 16 3 Weighted mean

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Calculating Weighted Mean for Number of Shoes Owned

The data below represents the number of pairs of shoes owned per person by a group of classmates. Follow the steps to find the weighted mean of the number of shoes per person.

#### Data Table

| Number of Shoes per Person | Frequency |
|----------------------------|-----------|
| 4 | 6 |
| 8 | 1 |
| 12 | 2 |
| 16 | 3 |

#### Explanation of Data

- **Number of Shoes per Person**: This column lists the different quantities of shoe pairs owned by the individuals in the group.
- **Frequency**: This column indicates how many people own that particular number of shoe pairs.

#### Steps to Calculate the Weighted Mean

1. **Multiply each number of pairs of shoes by its corresponding frequency** to find the weighted value for each category:
- $ 4 \times 6 = 24 $
- $ 8 \times 1 = 8 $
- $ 12 \times 2 = 24 $
- $ 16 \times 3 = 48 $

2. **Sum these weighted values** to find the total weighted value:
- $ 24 + 8 + 24 + 48 = 104 $

3. **Sum the frequencies** to find the total frequency:
- $ 6 + 1 + 2 + 3 = 12 $

4. **Calculate the weighted mean** using the formula:
\[
\text{Weighted Mean} = \frac{\text{Total Weighted Value}}{\text{Total Frequency}} = \frac{104}{12} \approx 8.7
\]

#### Result

The weighted mean number of shoes per person is approximately $ 8.7 $ pairs.

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