Question

Lightning Deaths Refer to the sample data in Cumulative Review Exercise 1.

a. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?

b. Are the values discrete or continuous?

c. Are the data categorical or quantitative?

d. Is the sample a simple random sample?

Short answer

a. Ratio

b. Discrete

c. Quantitative

d. No, this sample is not a simple random sample

Step-by-step solution

Given information

Data are given on the number of deaths that have occurred due to lightning strikes for 14 consecutive years.

Level of measurement

a.

The following four levels of measurement are defined:

Nominal: All categorical variables that cannot be arranged in any order are measured under a nominal scale.

Ordinal: All categorical variables that can be arranged in an order but the distances between values are unknown are measured under the ordinal scale.

Interval: All numerical variables that can be arranged in an order, and the distances between each value are known are measured under an ordinal scale. The natural zero starting point is undefined.

Ratio: All numerical variables whose ratios can be computed and whose natural zero starting point exists

Here, the number of deaths due to lightning strikes is quantitative, their ratios can be computed, and a value of 0 death means no death. Thus, the level of measurement is the ratio.

Discrete data vs. continuous data

b.

Discrete data refers to numerical data that can only be counted and not measured on a scale. The values cannot contain decimals.

Continuous data refers to numerical data that can be measured and exists in a range of values. It can contain decimal values.

Here, the number of deaths due to lightning strikes can only be counted and cannot assume decimal values. Thus, the data are discrete.

Categorical data vs. quantitative data

c.

Data that contains numerical values is called quantitative or numerical data.

Data that contains names or labels is called qualitative or categorical data.

Here, since the variable under consideration (number of deaths) contains values, the data is quantitative.

Simple random sample

d.

A simple random sample is a sample that consists of randomly selected units from the entire population, and each unit or item has an equal probability of getting chosen.

Here, the population consists of the number of deaths due to lightning strikes in all the years (a large number of years).

Since 14 consecutive years are selected for the sample which is not randomly selected, the given sample is not a simple random sample.