Question

describing data with mean absolute deviation
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
9.50	15.25
11.50	14.00
13.00	15.75

use the information to complete the 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 dropdown with options 0, 1.25, 1.5, 6.
the data for people without a high school diploma are more clustered around the mean than the data for people with a high school diploma.

Explanation:

Step1: Find the mean of High School Diploma wages

First, calculate the mean (\(\bar{x}\)) of the wages for people with a high school diploma. The data points are \(19.00\), \(15.25\), \(14.00\), \(15.75\).
The sum of these values is \(19.00 + 15.25 + 14.00 + 15.75 = 64.00\).
The mean is \(\frac{64.00}{4}=16.00\).

Step2: Calculate absolute deviations

For each data point, find the absolute deviation from the mean (\(|x - \bar{x}|\)):

• For \(19.00\): \(|19.00 - 16.00| = 3.00\)
• For \(15.25\): \(|15.25 - 16.00| = 0.75\)
• For \(14.00\): \(|14.00 - 16.00| = 2.00\)
• For \(15.75\): \(|15.75 - 16.00| = 0.25\)

Step3: Find the mean of absolute deviations

Sum the absolute deviations: \(3.00 + 0.75 + 2.00 + 0.25 = 6.00\).
The mean absolute deviation (MAD) is \(\frac{6.00}{4}=1.5\). Wait, no, wait: Wait, the sum is 3 + 0.75 + 2 + 0.25 = 6? Wait, 3 + 0.75 is 3.75, plus 2 is 5.75, plus 0.25 is 6. Then divide by 4: 6/4 = 1.5? Wait, but let's check again. Wait, the data for High School Diploma is 19.00, 15.25, 14.00, 15.75. Mean is (19 + 15.25 +14 +15.75)/4. Let's calculate that: 19 +15.25 is 34.25, +14 is 48.25, +15.75 is 64. 64/4 is 16. Correct. Then absolute deviations: |19 -16|=3, |15.25 -16|=0.75, |14 -16|=2, |15.75 -16|=0.25. Sum: 3 + 0.75 + 2 + 0.25 = 6. Then MAD is 6/4 = 1.5? Wait, but the options include 1.5? Wait, the dropdown has 0, 1.25, 1.5, 6. Wait, 6 is the sum, not the mean. So the MAD is 1.5? Wait, but let's check the first MAD: for No High School Diploma, data is 10, 9.5, 11.5, 13. Mean is (10 +9.5 +11.5 +13)/4 = (44)/4 = 11. Absolute deviations: |10 -11|=1, |9.5 -11|=1.5, |11.5 -11|=0.5, |13 -11|=2. Sum: 1 +1.5 +0.5 +2 =5. MAD is 5/4=1.25. Which matches the given value. Then for High School, sum of absolute deviations is 6, MAD is 6/4=1.5. So the MAD for High School is 1.5. Then the third statement: The data for people without a high school diploma are more clustered around the mean than the data for people with a high school diploma. Since MAD for no diploma is 1.25, and for diploma is 1.5. Lower MAD means more clustered. So that part is correct. So the MAD for high school diploma is 1.5. Wait, but let's check the dropdown options. The dropdown has 0, 1.25, 1.5, 6. So the correct MAD for high school is 1.5? Wait, but wait, maybe I made a mistake. Wait, no, let's recalculate. Wait, 19, 15.25,14,15.75. Mean 16. Absolute deviations: 3, 0.75, 2, 0.25. Sum: 3 + 0.75 = 3.75; 3.75 + 2 = 5.75; 5.75 + 0.25 = 6. Then 6 divided by 4 is 1.5. Yes. So the MAD is 1.5.

Answer:

The mean absolute deviation for people with a high school diploma is 1.5. So the answer for the dropdown is 1.5.