Question

Given the four sample proportions 0.66, 0.4, 0.72, and 0.42, determine the MAD statistic. Round your answer to 3 decimal places, e.g. 0.583.

Answer 1

Answer 2

MAD (Mean Absolute Deviation) is a statistic used to measure the dispersion or variability in a set of data. To calculate the MAD, follow these steps:

Step 1: Calculate the mean of the sample proportions.

Mean (μ) = (0.66 + 0.4 + 0.72 + 0.42) / 4 Mean (μ) = 1.80 / 4 Mean (μ) = 0.45

Step 2: Calculate the absolute deviations from the mean for each sample proportion.

Absolute Deviations: |0.66 - 0.45| = 0.21 |0.4 - 0.45| = 0.05 |0.72 - 0.45| = 0.27 |0.42 - 0.45| = 0.03

Step 3: Calculate the MAD by taking the average of the absolute deviations.

MAD = (0.21 + 0.05 + 0.27 + 0.03) / 4 MAD = 0.56 / 4 MAD = 0.140

Rounded to three decimal places, the MAD statistic is 0.140.

Answer 3

To find the Mean Absolute Deviation (MAD) statistic for the four sample proportions, follow these steps:

Step 1: Calculate the mean of the sample proportions. Step 2: Find the absolute deviations of each sample proportion from the mean. Step 3: Calculate the mean of the absolute deviations to get the MAD.

Let's perform the calculations:

Step 1: Calculate the mean of the sample proportions. Mean = (0.66 + 0.4 + 0.72 + 0.42) / 4 Mean = 0.55

Step 2: Find the absolute deviations of each sample proportion from the mean. |0.66 - 0.55| = 0.11 |0.4 - 0.55| = 0.15 |0.72 - 0.55| = 0.17 |0.42 - 0.55| = 0.13

Step 3: Calculate the mean of the absolute deviations. MAD = (0.11 + 0.15 + 0.17 + 0.13) / 4 MAD = 0.14

Therefore, the Mean Absolute Deviation (MAD) statistic for the given sample proportions is 0.140 (rounded to three decimal places).