Question

jenny calculated the distances between 5 pairs of stars in an observatory image. they were: 88 light - years, 40 light - years, 18 light - years, 76 light - years, 20 light - years. what was the mean absolute deviation of the distances? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): light - years

Explanation:

Step1: Find the mean (average)

First, we calculate the mean of the distances. The formula for the mean $\bar{x}$ is $\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n}$, where $x_{i}$ are the data points and $n$ is the number of data points.

The data points are 88, 40, 18, 76, 20. The sum of these values is $88 + 40 + 18 + 76 + 20 = 242$. There are $n = 5$ data points. So the mean is $\bar{x}=\frac{242}{5}=48.4$.

Step2: Find the absolute deviations

Next, we find the absolute deviation of each data point from the mean. The absolute deviation of a data point $x_{i}$ is $|x_{i}-\bar{x}|$.

• For 88: $|88 - 48.4| = 39.6$
• For 40: $|40 - 48.4| = 8.4$
• For 18: $|18 - 48.4| = 30.4$
• For 76: $|76 - 48.4| = 27.6$
• For 20: $|20 - 48.4| = 28.4$

Step3: Find the mean of the absolute deviations

Now, we calculate the mean of these absolute deviations. The formula for the mean absolute deviation (MAD) is $MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}$.

The sum of the absolute deviations is $39.6+8.4 + 30.4+27.6+28.4=134.4$. Since $n = 5$, the MAD is $\frac{134.4}{5}=26.88$. Rounding to the nearest tenth, we get $26.9$.

Answer:

26.9