Question

The number of hours of TV watched each week by 8 seventh grade students is shown below.

11, 7, 9, 3, 3, 8, 10, 5











a. What is the mean number of hours of TV watching?


b. Mean absolute deviation =


c. Explain the meaning of the mean absolute deviation as it relates to the number of hours of TV watched.

Answer 1

a) 7 hours ; b) 2.5 hours; c) look at explanation
Explanation:
a)
The mean of a data set is what we usually refer
to as the average. To find the mean, you add
up all of the values and divide by the number of
values.
So, to find the mean, you need to add all of the
values (the "value" is the the number hours
each student watched)
11+7+9+3+3+8+10 + 5
= 56
You have 8 seventh-grade students, so your
number of values is 8.
Dividing the sum of the values by the number
of values would then be:
56 / 8
=7
So, your mean is 7.

Answer 2

a) 7 hours ; b) 2.5 hours ; c) look at explanation

Explanation:

a)

The mean of a data set is what we usually refer to as the average. To find the mean, you add up all of the values and divide by the number of values.

So, to find the mean, you need to add all of the values (the "value" is the the number hours each student watched)

11 + 7 + 9 + 3 + 3 + 8 + 10 + 5

= 56

You have 8 seventh-grade students, so your number of values is 8.

Dividing the sum of the values by the number of values would then be:

56 / 8

= 7

So, your mean is 7.

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b)

(A deviation is how much a value differs from a certain value. If a person was supposed to be 5 feet tall, and they were 6 feet tall, they would deviate 1 foot from the value of 5. If the person was 4 feet tall, they would also have a deviation of 1 foot.)

The mean absolute deviation is complicated. You probably want to set up two columns (or at least this is how I was taught to do it), the first column being the value (represented by x in the mean absolute deviation formula), the second column being the difference between the mean of the data set and the value (the mean is represented as x with a line over it).

∑ is the sum of the values of the second column.

To find the mean (remember, mean = average) of the deviations, you are going to add all of the deviations together, and divide by your number of values.

I'll write out the second column (the difference from mean) below:

| x -
`\frac{}{x}` |

4

0

2

4

4

1

3

2

if you add all of these values up, you will get 20; ∑ = 20

[ | | means absolute value--essentially the distance of the value from 0, so a negative number is written as a positive numbers; |-3| = 3 ; |3| = 3 ]

Now you will find the mean of your deviations. The sum of all deviations (∑) = 20. The number of deviations/the number of values is 8.

So, the equation of 20 / 8 will give us the absolute mean deviation.

20/8 = Mean Absolute Deviation

Mean Absolute Deviation = 2.5

Your Mean Absolute Deviation is 2.5 [hours] .

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c)

Now you are being asked to interpret what this 2.5 indicates. It means that each student has, on average, a difference of 2.5 hours of TV watched from the mean. The Mean Absolute Deviation gives us a sense of how spread out the values of a data set are. We know that a mean absolute deviation of 0 would indicate that all values of the set are exactly identical. A mean deviation of 100 would indicate that all of the values are drastically different. So, a mean deviation of 2.5 indicates that all of the values (each student's watch hours) are fairly similar.