Question

PLEASE ANSWER FAST

Thirteen earthquakes were measured using the Richter scale. Their magnitudes are listed below. What is the range for this data set?

8.2, 3.1, 5.9, 2.5, 6.2, 5.1, 7.6, 9.3, 8.1, 7.4, 7.8, 6.5, 8.7
A. 6.8
B. 2.6
C. 4.1
D. 5.6

Answer 1

The range is found by subtracting the smallest data value from the largest data value. Here, the smallest data value is 2.5 and the largest is 9.3. Therefore, the range is:

`9.3 - 2.5 = 6.8`

Therefore, the answer is Option A.

Just for extra.

The variance:

1. The steps that follow are also needed for finding the standard deviation. Start by writing the computational formula for the variance of a sample:

`{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1}`

2. Create a table of 2 columns and 14 rows. There will be a header row and a row for each data value. The header row should be labeled with x and x^2. Enter the data values in the x column, with each data value in its own row. In the second column, put the square of each of the data values, x^2.

x y

8.2 67.24

3.1 9.61

5.9 34.81

2.5 6.25

6.2 38.44

5.1 26.01

7.6 57.76

9.3 86.49

8.1 65.61

7.4 54.76

7.8 60.84

6.5 42.25

8.7 75.69

3. Find the sum of all the values in the first column,
`{\sum}{x}`.

`\sum{x} = 86.4`

4. Square the answer from step 3, then divide that number by the size of the sample.

`\frac{({\sum}{x})^2}{n} = (7464.96)/(13) = 574.22769230769`

5. Find the sum of all the values in the second column,
`{\sum}{x^2}`.

`{\sum}{x^2} = 625.76`

6. Subtract the answer in step 4 from the answer in step 5.

`{\sum}{x^2} - \frac{({\sum}{x})^2}{n} = 625.76 - 574.22769230769 = 51.532307692308`

7. Divide the answer in step 6 by n - 1, one less than the size of the sample. This answer is the variance of the sample.

`{s^2}= \frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n-1} = ( 51.532307692308 )/(12) = 4.294358974359`

Standard Deviation

To find the standard deviation, first write the computational formula for the standard deviation of the sample.

`{s}= \sqrt{\frac{{\sum}{x^2} - \frac{({\sum}{x})^2}{n}}{n - 1}}`

Take the square root of the answer found in step 7 above. This number is the standard deviation of the sample. It is symbolized by
`s`. Here, we round the standard deviation to at most 4 decimal places.

`{s} = √(4023.0714285714) = 63.4277`