Question

Tommy calculated the distances between 5 pairs of stars in an observatory image. They were:

94 light-years92 light-years94 light-years19 light-years43 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

Answer 1

To find the mean absolute deviation (MAD) of Tommy's observed distances between pairs of stars, calculate the mean of the distances, determine the absolute deviations from the mean, and then find the average of these deviations. The MAD is 29.9 light-years after rounding to the nearest tenth.

Step-by-step explanation:

To calculate the mean absolute deviation (MAD) of the distances, first, we need to find the mean (average) of these distances:

• 94 light-years
• 92 light-years
• 94 light-years
• 19 light-years
• 43 light-years

The mean is calculated by adding all the distances together and then dividing by the number of distances:

(94 + 92 + 94 + 19 + 43) / 5 = 342 / 5

= 68.4 light-years

Next, calculate the absolute deviation of each distance from the mean:

• |94 - 68.4| = 25.6 light-years
• |92 - 68.4| = 23.6 light-years
• |94 - 68.4| = 25.6 light-years
• |19 - 68.4| = 49.4 light-years
• |43 - 68.4| = 25.4 light-years

Now find the mean of these absolute deviations:

(25.6 + 23.6 + 25.6 + 49.4 + 25.4) / 5 = 149.6 / 5

= 29.92 light-years

Round this to the nearest tenth:

The mean absolute deviation (MAD) is 29.9 light-years.