Question

The accompanying data contains the depth​ (in kilometers) and​ magnitude, measured using the Richter​ Scale, of all earthquakes in a particular region over the course of a week. Depth is the distance below the surface at which the earthquake originates. A one unit increase in magnitude represents ground shaking ten times as strong​ (an earthquake with magnitude 4 is ten times as strong as an earthquake with magnitude​ 3). Complete parts​ (a) through​ (d) below.

depth   magnitude
2.24   0.57
1.78   0.98
1.1   1.52
7.39   2.49
2.33   1.38
9.35   0.35
8.12   1.34
2.38   0.76
8.79   0.81
5.07   2.38
8.46   0.56
3.04   2.69
0   1.89
5.84   1.71
128.04   3.29
2.19   1.33
15.94   1.99
1.58   1.1
12.18   1.27
115.12   4.42
23.45   4.3
9.58   0.05
6.43   0.62
14.68   1.29
3.77   1.65
2.5   0.82
2.57   0.94
20.14   6.62
18.38   1.61
10.86   1.56
17.37   1.12
19.88   0.67
15.75   0.62
8.55   1.59
16.48   0.66
512.01   4.28
131.62   2.41
7.36   1.99
2.5   0.43
6.99   0.99
2.91   2.4
2.09   1.04
211.91   2.92
10.8   1.9
34.65   1.71
0.03   1.42
8.58   1.08
17.28   1.11
3.39   0.61
6.97   1.36
1.84   0.59
44.9   3.39
6.12   0.9
2.25   0.52
2.07   2.7
1.16   1.63
3   0.88
75.74   1.49
1.92   1.15
2.24   1.13
0.19   0.39
0.75   0.85
4.95   0.47
8.27   0.35
33.85   1.33
21.44   1.59
34.87   4.57
10.06   5.54
47.83   1.99
10.7   1.27
14.85   1.4
6.25   0.94
6.41   0.89
97.92   3.4
4.14   0.67
9.45   1.57
9.57   0.98
0.01   1.17
6.47   5.08
14.15   1.39
6.31   0.75
348.35   5.01
1.81   1.81
6.41   1.05
137.74   4.32
5.95   1.4
6.79   0.1
13.27   0
10.8   0.9
18.27   0.88
7.28   1.63
0   1.06
0   1.03
22.56   1.2
6.86   1.31
16.32   1.16
2.27   1.27
4.75   2.61
4.55   1.54
2.6   0.78

(a) Find the​ mean, median,​ range, standard​ deviation, and quartiles for both the depth and magnitude of the earthquakes. Based on the values of the​ mean, median, and quartiles conjecture the shape of the distribution for depth and magnitude.

​Depth: and Magnitude:

μ=

​km;M=

​km;Range=

​km σ=

​km; Q1=

​km;Q3=

km

​

Answer 1

I have used excel function to calculate mean, median,​ range, standard​ deviation, and quartiles for both the depth and magnitude of the earthquakes.

DEPTH OF EARTHQUAKES (IN KILOMETERS):

To calculate Mean: "=AVERAGE(select array of data values of depth of earthquakes)"

To calculate Median: "=MEDIAN(select array of data values of depth of earthquakes)"

To calculate Range: "=MAX(select array of data values of depth of earthquakes)-MIN(select array of data values of depth of earthquakes)"

To calculate Standard deviation: "=STDEV(select array of data values of depth of earthquakes)"

To calculate First Quartile: "=QUARTILE(select array of data values of depth of earthquakes,1)"

{Here 1 represents first quartile}

To calculate Third Quartile: "=QUARTILE(select array of data values of depth of earthquakes,3)"

{Here 3 represents third quartile}

Mean of depth of earthquakes km

Median of depth of earthquakes km

Range of depth of earthquakes km

Standard deviation of depth of earthquakes

First quartile of depth of earthquakes km

Third quartile of depth of earthquakes

From the above measures, we could see that the mean is larger than the median. Thus the distribution of depth of earthquakes is positively skewed (right skewed).

A distribution is said to be positively or right skewed when the tail on the right side of the distribution is longer than the left side. In a positively skewed distribution it is common for the mean to be pulled toward the right tail of the distribution where the median value tend to be less than the mean value.

MAGNITUDE OF EARTHQUAKES:

To calculate Mean: "=AVERAGE(select array of data values of magnitude of earthquakes)"

To calculate Median: "=MEDIAN(select array of data values of magnitude of earthquakes)"

To calculate Range: "=MAX(select array of data values of magnitude of earthquakes)-MIN(select array of data values of magnitude of earthquakes)"

To calculate Standard deviation: "=STDEV(select array of data values of magnitude of earthquakes)"

To calculate First Quartile: "=QUARTILE(select array of data values of magnitude of earthquakes,1)"

{Here 1 represents first quartile}

To calculate Third Quartile: "=QUARTILE(select array of data values of magnitude of earthquakes,3)"

{Here 3 represents third quartile}

Mean of magnitude of earthquakes

Median of magnitude of earthquakes

Range of magnitude of earthquakes

Standard deviation of magnitude of earthquakes

First quartile of magnitude of earthquakes

Third quartile of magnitude of earthquakes

From the above measures, we could see that the mean is larger than the median. Thus the distribution of magnitude of earthquakes is positively skewed (right skewed).

A distribution is said to be positively or right skewed when the tail on the right side of the distribution is longer than the left side. In a positively skewed distribution it is common for the mean to be pulled toward the right tail of the distribution where the median value tend to be less than the mean value.