Question

Whats the mean of 55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

Find the MAD.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the mean, you add up all the numbers and divide by the total count:

55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1430

There are 17 numbers in total, so the mean is 1430/17 = 84.12 (rounded to two decimal places).

To find the MAD (Mean Absolute Deviation), you first find the absolute difference between each number and the mean, then calculate the average of these differences. Here are the absolute differences:

|55 - 84.12| = 29.12
|60 - 84.12| = 24.12
|70 - 84.12| = 14.12
|70 - 84.12| = 14.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|80 - 84.12| = 4.12
|80 - 84.12| = 4.12
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|90 - 84.12| = 5.88
|90 - 84.12| = 5.88
|95 - 84.12| = 10.88
|100 - 84.12| = 15.88

Adding up these absolute differences gives us:

29.12 + 24.12 + 14.12 + 14.12 + 9.12 + 9.12 + 9.12 + 4.12 + 4.12 + 0.88 + 0.88 + 0.88 + 0.88 + 5.88 + 5.88 + 10.88 + 15.88 = 140.72

To find the MAD, divide this sum by the total count (17):

140.72/17 ≈ 8.28 (rounded to two decimal places)

Therefore, the Mean Absolute Deviation is approximately 8.28.

Answer 2

Show the work

Answer 3

[AI-generated answer — Bot GPT 3.5]

Sure! Here is the step-by-step work to find the mean and MAD:

1. Find the mean:
Add up all the numbers:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1430

Divide the sum by the total count (17):
1430/17 ≈ 84.12

So, the mean is approximately 84.12.

2. Find the MAD:
Calculate the absolute difference between each number and the mean:

|55 - 84.12| = 29.12
|60 - 84.12| = 24.12
|70 - 84.12| = 14.12
|70 - 84.12| = 14.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|80 - 84.12| = 4.12
|80 - 84.12| = 4.12
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|90 - 84.12| = 5.88
|90 - 84.12| = 5.88
|95 - 84.12| = 10.88
|100 - 84.12| = 15.88

Add up the absolute differences:
29.12 + 24.12 + 14.12 + 14.12 + 9.12 + 9.12 + 9.12 + 4.12 + 4.12 + 0.88 + 0.88 + 0.88 + 0.88 + 5.88 + 5.88 + 10.88 + 15.88 = 140.72

Divide the sum by the total count (17):
140.72/17 ≈ 8.28

Therefore, the Mean Absolute Deviation is approximately 8.28.

Answer 4

its wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. Let's calculate the mean and MAD again step by step:

1. Find the mean:
Add up all the numbers:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1430

Divide the sum by the total count (17):
1430/17 ≈ 84.12

So, the mean is approximately 84.12.

2. Find the MAD:
a) Calculate the absolute difference between each number and the mean:
|55 - 84.12| = 29.12
|60 - 84.12| = 24.12
|70 - 84.12| = 14.12
|70 - 84.12| = 14.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|75 - 84.12| = 9.12
|80 - 84.12| = 4.12
|80 - 84.12| = 4.12
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|85 - 84.12| = 0.88
|90 - 84.12| = 5.88
|90 - 84.12| = 5.88
|95 - 84.12| = 10.88
|100 - 84.12| = 15.88

b) Add up the absolute differences:
29.12 + 24.12 + 14.12 + 14.12 + 9.12 + 9.12 + 9.12 + 4.12 + 4.12 + 0.88 + 0.88 + 0.88 + 0.88 + 5.88 + 5.88 + 10.88 + 15.88 = 161.12

c) Divide the sum by the total count (17):
161.12/17 ≈ 9.48

Therefore, the Mean Absolute Deviation is approximately 9.48.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To find the mean, you need to add up all the numbers and divide the sum by the total number of values. In this case, we have 17 values.

55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1370

Next, divide 1370 by 17:

1370 / 17 = 80.59 (rounded to two decimal places)

So, the mean of the given numbers is approximately 80.59.

Now, let's find the Mean Absolute Deviation (MAD). The MAD measures the average distance between each data point and the mean.

To calculate the MAD, we need to find the absolute difference between each value and the mean.

Value | Absolute Difference
---------------------------
55 | 25.59
60 | 20.59
70 | 10.59
70 | 10.59
75 | 5.59
75 | 5.59
75 | 5.59
80 | 0.59
80 | 0.59
85 | 4.41
85 | 4.41
85 | 4.41
85 | 4.41
90 | 9.41
90 | 9.41
95 | 14.41
100 | 19.41

Now, add up all the absolute differences:

25.59 + 20.59 + 10.59 + 10.59 + 5.59 + 5.59 + 5.59 + 0.59 + 0.59 + 4.41 + 4.41 + 4.41 + 4.41 + 9.41 + 9.41 + 14.41 + 19.41 = 159.79

To find the MAD, divide this sum by the total number of values:

159.79 / 17 = 9.4 (rounded to one decimal place)

Therefore, the Mean Absolute Deviation (MAD) for the given set of numbers is approximately 9.4.

Answer 7

[AI-generated answer — Explain Bot]

To find the mean and MAD (mean absolute deviation) of the given set of numbers, follow these steps:

Step 1: Sum up all the numbers in the set:
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1410

Step 2: Divide the sum by the total number of values in the set to find the mean:
Mean = Sum / Total values = 1410 / 17 = 82.94 (rounded to two decimal places)

Step 3: Calculate the mean absolute deviation (MAD) by finding the difference between each number and the mean, taking the absolute value of each difference, summing them up, and dividing by the total number of values.

Let's calculate the MAD step by step using the formula:

|55 - 82.94| + |60 - 82.94| + |70 - 82.94| + |70 - 82.94| + |75 - 82.94| + |75 - 82.94| + |75 - 82.94| + |80 - 82.94| + |80 - 82.94| + |85 - 82.94| + |85 - 82.94| + |85 - 82.94| + |85 - 82.94| + |90 - 82.94| + |90 - 82.94| + |95 - 82.94| + |100 - 82.94|

= 27.94 + 22.94 + 12.94 + 12.94 + 7.94 + 7.94 + 7.94 + 2.94 + 2.94 + 2.94 + 2.94 + 2.94 + 2.94 + 7.06 + 7.06 + 12.06 + 17.06

= 162.82

Step 4: Divide the sum of absolute differences by the total number of values to obtain the MAD:
MAD = Sum of absolute differences / Total values = 162.82 / 17 = 9.58 (rounded to two decimal places)

Therefore, the mean of the given set is approximately 82.94, and the MAD is approximately 9.58.