Q T1.4. - 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 $9.0$ on 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

The correct option is (b) $6.00$

Step 1: Given information

4.5

L

5.5

H

8.7

8.9

6.0

H

5.2

The letter $L$ denotes a magnitude of less than $4.0$ whereas the letter $H$ denotes a magnitude of greater than $9.0$

Step 2: Concept

The total of all observations divided by the number of observations is the observation means. The median of a distribution organized in ascending order is the midway.

Step 3: Explanation

The sample's median earthquake intensity was $(L, 4.5, 5.2, 5.5, 6, 8.7, 8.9, H, H)$ Here, $L$ denotes an earthquake with a magnitude less than $4.0$ and h denotes an earthquake with a magnitude greater than $9.0$ Therefore, (b) $6.00$ is the correct option.