Brian recorded the number of commercials played during two types of television shows: an educational documentary and a primetime drama. Both types of shows lasted 1 hour, including commercials. He recorded the number of commercials for 10 episodes of each type of show.
Answers
Answer:
[tex]m(x)_A = 5.2[/tex] --- Mean absolute deviation of educational documentary
[tex]m(x)_B = 4.7[/tex] --- Mean absolute deviation of prime time drama
Step-by-step explanation:
Given
[tex]n = 10[/tex]
See attachment for table
Required
Determine the mean absolute deviation of each
Mean absolute deviation m(x) is calculated as:
[tex]m(x) = \frac{1}{n}\sum |x - \mu|[/tex]
For Educational Documentary
First, calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
So:
[tex]\mu_A = \frac{26 + 28 + 30 + 18+27 + 18 + 20 +31+17+17}{10}[/tex]
[tex]\mu_A = \frac{232}{10}[/tex]
[tex]\mu_A = 23.2[/tex]
The mean absolute deviation is then calculated as:
[tex]m(x)_A = \frac{1}{n}\sum |x - \mu_A|[/tex]
[tex]m(x)_A = \frac{1}{10}(|26 -23.2| +|28 -23.2| +|30 -23.2| +|18 -23.2| +|27 -23.2| +|18 -23.2| +|20 -23.2| +|31 -23.2| +|17 -23.2| +|17 -23.2|)[/tex]
[tex]m(x)_A = \frac{1}{10}(|2.8| +|4.8| +|6.8| +|-5.2| +|3.8| +|-5.2| +|-3.2| +|7.8| +|-6.2| +|-6.2|)[/tex]
[tex]m(x)_A = \frac{1}{10}(2.8 +4.8 +6.8 +5.2 +3.8 +5.2 +3.2 +7.8 +6.2 +6.2)[/tex]
[tex]m(x)_A = \frac{1}{10}*52[/tex]
[tex]m(x)_A = 5.2[/tex]
For Prime time Drama
First, calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
So:
[tex]\mu_B = \frac{39+39+35+29+40+27+41+29+32+30}{10}[/tex]
[tex]\mu_B = \frac{341}{10}[/tex]
[tex]\mu_B = 34.1[/tex]
The mean absolute deviation is then calculated as:
[tex]m(x)_B = \frac{1}{n}\sum |x - \mu_B|[/tex]
[tex]m(x)_B = \frac{1}{10}(|39-34.1|+|39-34.1|+|35-34.1|+|29-34.1|+|40-34.1|+|27-34.1|+|41-34.1|+|29-34.1|+|32-34.1|+|30-34.1|)[/tex]
[tex]m(x)_B = \frac{1}{10}(|4.9|+|4.9|+|0.9|+|-5.1|+|5.9|+|-7.1|+|6.9|+|-5.1|+|-2.1|+|-4.1|)[/tex]
[tex]m(x)_B = \frac{1}{10}(4.9+4.9+0.9+5.1+5.9+7.1+6.9+5.1+2.1+4.1)[/tex]
[tex]m(x)_B = \frac{1}{10}*47[/tex]
[tex]m(x)_B = 4.7[/tex]
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Answers
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A rectangular room measures 15 feet by 18 feet. It is going to be carpeted with carpeting that sells for $38 per square foot.
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Width = 18 feet
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From the above question:
1/4 inch = 1 foot
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x = 3.75 inches
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Cross Multiply
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x = 4.5 inches
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From the above question, we know that: A square foot of carpet is sold for $38
The area of the room is 270 square feet
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Cross Multiply
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