Q. 4 - The Practice of Statistics for AP

Question

Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between 4.0 and 9.0 the Richter scale. Measurements of nine earthquakes gave the following readings: 

where L indicates that the earthquake had an intensity below 4.0 and an H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is (a) 5.75. (c) 6.47. (e) Cannot be determined. (b) 6.00. (d) 8.70. 

Step-by-Step Solution

Answer

b. The sample of median earthquake intensity is 6.00

Step 1: Given information

Given: 

Earthquake intensities are measured using device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between $4.0$ and $9.0$ on the Richter scale. Measurements of nine earthquakes gave the following readings:

Where $\mathrm{L}$ indicates that the earthquake had an intensity below$4.0$ and an $\mathrm{H}$ indicates that the earthquake had an intensity above 9.0.

Step 2: Explanation for correct option

The median earthquake intensity of the sample is$(\mathrm{L},4.5,5.2,5.5,6,8.7,8.9,\mathrm{H},\mathrm{H})$

Here $L$indicates that the earthquake had intensity below$4.0$ and h indicates that the earthquake had intensity above 9.0.

Therefore, (b) 6.00 is the correct option.

Step 3. Explanation for incorrect option

(a) The median earthquake intensity of the sample will not be$5.75$.

(c) The median earthquake intensity of the sample will not be $6.47$.

(d) The median earthquake intensity of the sample will not be $8.70$.

(e) The median earthquake intensity of the sample is Cannot be determined.