Use the magnitudes (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set.
Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier (data value that is very far away from the others) when considered in the context of the sample data given in this data set? Explain.
Find the mean and median of the data set using a calculator or similar data analysis technology.
2.53 1.33 0.64 2.55 0.67 0.57 1.61 0.69 2.06 1.84
2.01 2.74 1.98 0.99 1.01 2.59 1.52 1.41 1.53 0.92
0.14 1.15 0.01 2.02 0.81 1.48 0.08 1.16 0.74 0.24
1.77 2.74 0.35 0.65 2.77 1.04 0.01 2.31 1.62 2.91
2.77 2.41 1.45 2.06 2.66 1.73 1.58 0.82 2.03 1.78
Find the mean and median of the data set using a calculator or similar data analysis technology.
2.53 1.33 0.64 2.55 0.67 0.57 1.61 0.69 2.06 1.84
2.01 2.74 1.98 0.99 1.01 2.59 1.52 1.41 1.53 0.92
0.14 1.15 0.01 2.02 0.81 1.48 0.08 1.16 0.74 0.24
1.77 2.74 0.35 0.65 2.77 1.04 0.01 2.31 1.62 2.91
2.77 2.41 1.45 2.06 2.66 1.73 1.58 0.82 2.03 1.78
2 answers:
Answer:
Step-by-step explanation:
When sorted, your data are:
0.01, 0.01, 0.08, 0.14, 0.24, 0.35, 0.57, 0.64, 0.65, 0.67, 0.69, 0.74, 0.81
0.82, 0.92, 0.99, 1.01, 1.04, 1.15, 1.16, 1.33, 1.41, 1.45, 1.48, 1.52
1.53, 1.58, 1.61, 1.62, 1.73, 1.77, 1.78, 1.84, 1.98, 2.01, 2.02, 2.03, 2.06
2.06, 2.31, 2.41, 2.53, 2.55, 2.59, 2.66, 2.74, 2.74, 2.77, 2.77, 2.91
I entered the data into a statistical and box plot generator.
The results were:
mean = 1.49
Median = 1.52
Q1 = 0.81
Q2 = 1.525
Q3 = 2.06
IQR = 1.25
One test for an outlier is if the value is greater than the upper fence: Q3 + 1.5IQR.
The box-and-whisker plot shows that a value of 7.0 is well above the upper fence (in red).
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Answer:
Step-by-step explanation:
We can break down this problem by first realizing different parts of the circle.
- The line which is 8 units long is a chord of the circle.
- The line that is 3.6 is <em>almost</em> the radius of the circle
- The line that x sits on is the radius.
With this, we can find out if we find the radius of the circle, we have our answer.
We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.
<em>What we need is a way to find the radius of the circle</em><em>. This will get us x</em>. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.
If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).
We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:
Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!
Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.
The line X does just that. Therefore, the value of x is also 5.4.
Hope this helped!
