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.
(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. Use technology to obtain the summary statistics for magnitude, rounding to three decimal places.
Depth:
μ=____km
M=___km
Range=____km
σ=____km
Q1=___km
Q3= ___ km
(B) Draw a relative frequency histogram for both depth and magnitude. Label the mean and median on the histogram. Describe the shape of each histogram. Use technology to obtain the frequency histogram for depth.
(C) Draw a boxplot for both depth and magnitude. Are there outliers? Use technology to obtain the boxplot for depth.
(D) Determine the lower and upper fences for identifying outliers for both depth and magnitude.
DATA:
depth; magnitude
2.22; 0.57
1.77; 0.99
1.09; 1.53
7.44; 2.49
2.33; 1.37
9.42; 0.35
8.1; 1.33
2.4; 0.76
8.9; 0.79
5.13; 2.42
8.58; 0.56
3.05; 2.69
0; 1.91
5.77; 1.7
127.62; 3.31
2.19; 1.33
16.05; 1.97
1.59; 1.09
12.13; 1.27
115.39; 4.4
23.32; 4.31
9.65; 0.05
6.48; 0.62
14.7; 1.3
3.74; 1.64
2.47; 0.83
2.6; 0.94
20.15; 6.58
18.3; 1.6
10.85; 1.55
17.3; 1.12
19.91; 0.68
15.68; 0.62
8.65; 1.59
16.65; 0.66
515.25; 4.33
131.35; 2.41
7.41; 1.99
2.48; 0.43
7.03; 0.98
2.9; 2.39
2.08; 1.05
210.78; 2.91
10.75; 1.88
34.77; 1.69
0.03; 1.43
8.55; 1.07
17.42; 1.11
3.39; 0.61
7.03; 1.34
1.84; 0.59
45; 3.41
6.12; 0.91
2.23; 0.52
2.07; 2.72
1.18; 1.63
3.02; 0.87
76.01; 1.5
1.92; 1.14
2.25; 1.11
0.19; 0.39
0.75; 0.83
4.94; 0.47
8.21; 0.35
33.64; 1.34
21.14; 1.61
35.05; 4.64
10.03; 5.53
48.05; 1.98
10.59; 1.29
14.81; 1.41
6.3; 0.93
6.36; 0.89
98.94; 3.42
4.16; 0.68
9.4; 1.58
9.49; 0.98
0.01; 1.17
6.51; 5.14
14.01; 1.4
6.3; 0.77
348.59; 5.01
1.79; 1.81
6.45; 1.05
137.27; 4.3
5.9; 1.4
6.83; 0.1
13.25; 0
10.77; 0.91
18.51; 0.9
7.24; 1.63
0; 1.06
0; 1.03
22.77; 1.2
6.86; 1.29
16.23; 1.17
2.25; 1.27
4.72; 2.62
4.54; 1.54
2.61; 0.77
