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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.
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