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alexandr1967 [171]
3 years ago
9

Use the data to answer the Question below. Size of shoe:8,7,8.5,6.5,5,11,15,8,8,7.5,6.5,8,14,12

Mathematics
1 answer:
madam [21]3 years ago
4 0

Answer:

Step-by-step explanation:

Mean: 8 + 7 + 8.5 + 6.5 + 5 + 11 + 15 + 8 + 8 + 7 + 7.5 + 6.5 + 8 + 14 + 12 = 132 / 15 = 8.8

Median: You have to arrange the numbers first in ascending order.

5, 6.5, 6.5, 7, 7, 7.5, 8, 8, 8, 8, 8.5, 11, 12, 14, 15

The median is 8 because that is the middle value/number.

Mean Absolute Deviation:

Get the average/mean (1), find the deviation (2) to get MAD (3).

Step #1 Mean = 8.8

Step #2 To get the deviation, you subtract the mean from the values given.

8 - 8.8 = -0.8

7 - 8.8 = -1.8

8.5 - 8.8 = -0.3

6.5 - 8.8 = -2.3

5 - 8.8 = -3.8

11 - 8.8 = 2.2

15 - 8.8 = 6.2

8 - 8.8 = -0.8

8 - 8.8 = -0.8

7 - 8.8 = -1.8

7.5 - 8.8 = -1.3

6.5 - 8.8 = -2.3

8 - 8.8 = -0.8

14 - 8.8 = 5.2

12 - 8.8 = 3.2

Step #3 Get the summation from step #2, and get its average. Disregard the negative signs.

0.8 + 1.8 + 0.3 + 2.3 + 3.8 + 2.2 + 6.2 + 0.8 + 0.8 + 1.8 + 1.3 + 2.3 + 0.8 + 5.2 + 3.2 = 33.6 / 15 = 2.24 is the Mean Asolute Deviation

Median Absolute Deviation:

Get the median (1) and subtract it from the values (2). Get the median of the new values (3)

Step #1 Median = 8

Step #2

8 - 8 = 0

7 - 8 = -1

8.5 - 8 = 0.5

6.5 - 8 = -1.5

5 - 8 = -3

11 - 8 = 3

15 - 8 = 7

8 - 8 = 0

8 - 8 = 0

7 - 8 = -1

7.5 - 8 = -0.5

6.5 - 8 = -1.5

8 - 8 = 0

14 - 8 = 6

12 - 8 = 4

Step #3 Arrange the numbers in ascending order.

-3, -1.5, -1.5, -1, -1, -0.5, 0, 0, 0, 0, 0.5, 3, 4, 6, 7

The Median Absolute Deviation is 0 since it is the middle value/number.

It is important that you calculate this by yourself in case I did some careless mistakes.

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Which expression represents the ratio of the difference of the two means to Sidney's mean absolute deviation
prohojiy [21]

Answer:

The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

Step-by-step explanation:

P.S - The exact question is -

Given - The means and mean absolute deviations of Sidney’s and Phil’s grades are shown in the table below.

                                       Sidney’s Grades           Phil’s Grades

Mean                                     82                                    78

Mean Absolute Deviation      3.28                                 3.96

To find - Which expression represents the ratio of the difference of the two means to Sidney’s mean absolute deviation?

Proof -

Given that Mean of Sidney Grades = 82

                 Mean of Phil's   Grades = 78

So,

The difference of two means = 82 - 78 = 4

Also,

Given, Mean Absolute Deviation of Sydney = 3.28

Now,

The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

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