Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A survey asked eight people about their wages and educational background. The table shows the hourly wages reported by people with and without a high school diploma.

| No High School Diploma | High School Diploma |
|------------------------|----------------------|
| 10.00 | 19.00 |
| 9.50 | 15.25 |
| 11.50 | 14.00 |
| 13.00 | 15.75 |

Use the information to complete the statements:

1. The mean absolute deviation for people without a high school diploma is [tex]$\square$[/tex]
2. The mean absolute deviation for people with a high school diploma is [tex]$\square$[/tex]
3. The data for people without a high school diploma are more [tex]$\square$[/tex] the mean than the data for people with a high school diploma.

Sagot :

GinnyAnswer
Sure, let's solve the problem step-by-step based on the given data.

### Data Summary:

The data is given as:
- No High School Diploma: [tex]$10.00, 9.50, 11.50, 13.00$[/tex]
- High School Diploma: [tex]$19.00, 15.25, 14.00, 15.75$[/tex]

### Step 1: Calculate the Means

For people without a high school diploma:
[tex]\[ \text{Mean} = \frac{10.00 + 9.50 + 11.50 + 13.00}{4} = \frac{44.00}{4} = 11.00 \][/tex]

For people with a high school diploma:
[tex]\[ \text{Mean} = \frac{19.00 + 15.25 + 14.00 + 15.75}{4} = \frac{64.00}{4} = 16.00 \][/tex]

### Step 2: Calculate the Mean Absolute Deviation (MAD)

The Mean Absolute Deviation is calculated by taking the average of the absolute deviations from the mean.

For people without a high school diploma:
[tex]\[ \begin{aligned} \text{Deviations from mean} &= |10.00 - 11.00|, |9.50 - 11.00|, |11.50 - 11.00|, |13.00 - 11.00| \\ &= | - 1.00|, |-1.50|, |0.50|, |2.00| \\ &= 1.00, 1.50, 0.50, 2.00 \end{aligned} \][/tex]
[tex]\[ \text{MAD} = \frac{1.00 + 1.50 + 0.50 + 2.00}{4} = \frac{5.00}{4} = 1.25 \][/tex]

For people with a high school diploma:
[tex]\[ \begin{aligned} \text{Deviations from mean} &= |19.00 - 16.00|, |15.25 - 16.00|, |14.00 - 16.00|, |15.75 - 16.00| \\ &= |3.00|, |-0.75|, |-2.00|, |-0.25| \\ &= 3.00, 0.75, 2.00, 0.25 \end{aligned} \][/tex]

[tex]\[ \text{MAD} = \frac{3.00 + 0.75 + 2.00 + 0.25}{4} = \frac{6.00}{4} = 1.50 \][/tex]

### Step 3: Compare the Variability

To determine which group has more variation around the mean, we compare the MAD values:
[tex]\[ \text{MAD} \text{ for people without a high school diploma} = 1.25 \][/tex]
[tex]\[ \text{MAD} \text{ for people with a high school diploma} = 1.50 \][/tex]

Since 1.25 (MAD without a high school diploma) is less than 1.50 (MAD with a high school diploma), the data for people without a high school diploma are more concentrated around the mean.

### Final Statements:

- The mean absolute deviation for people without a high school diploma is 1.25
- The mean absolute deviation for people with a high school diploma is 1.50
- The data for people without a high school diploma are more concentrated around the mean than the data for people with a high school diploma.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.