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4 years ago

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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 magnitudeDepth Magnitude0.76 0.844.93 0.478.16 03533.58 1.3221.2 1.6135.03 4.5710.05 5.0247.91 1.99Depth: μ= ___km ; M=___ km; Range=___km ; σ=___ km ; Q1=___km ; Q3=___km
Magnitude: μ=___; M=___; R=____; σ=_____; Q1=____; Q3=_____

1 answer:

Sunny_sXe [5.5K]4 years ago

4 0

Answer:

Depth:

μ =20.2025 km

M = 15.625 km

Range = 47.15 km

σ ≈ 15.92 km

Q₁ = 5.7375 km

Q₃ = 34.6675 km

Magnitude:

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

Step-by-step explanation:

The given data are;

Depth ${}$ Magnitude

0.76 ${}$ 0.84

4.93 ${}$ 0.47

8.16 ${}$ 0.35

33.58 ${}$ 1.32

21.2 ${}$ 1.61

35.03 ${}$ 4.57

10.05 ${}$ 5.52

47.91 ${}$ 1.99

For the Depth, we have;

The mean, μ = (0.76+4.93+8.16+33.58+21.2+35.03+10.05+47.91)/8 =20.2025 km

The median, M = The (n + 1)/2th term after arranging the term in increasing order as follows;

0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 , the median is therefore;

(8 + 1)/2th term or the 4.5th term which is 10.05 + (21.2 - 10.05)/2 = 15.625 km

The Range = The highest - The lowest value = 47.91 - 0.76 = 47.15 km

The Standard deviation of, σ, is given as follows;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{N}}$

Where;

$x_i$ = The individual data point = (0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 )

N = The total number of data point = 8

Substituting, (using Microsoft Excel) we get;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-20.2025 \right )^{2} }{8}} \approx 15.92 \ km$

Q₁ = The first quartile = The (n + 1)/4th = term arranged in increasing order

Q₁ = The (8 + 1)/4th term = The 2.25th term = 4.93 + (8.16 - 4.93)×0.25) = 5.7375 km

Q₃ = The first quartile = The 3×(n + 1)/4th = term arranged in increasing order

Q₃ = The 3×(8 + 1)/4th term = The 6.75th term = 33.58 + 3×(35.03 - 33.58)×0.25) = 34.6675 km

For the magnitude, we have, using the same formulas and procedures as above;

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

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