Question

A researcher measures the heights of 200 randomly selected individuals of a tree species in a forest. Which one of the following is NOT a measure of variability in the sample?

• A. Inter-quartile range
• B. Range
• C. Standard deviation
• D. Standard error

Hint:

To differentiate between measures of variability:
1. Variability describes the spread of individual data points (e.g., IQR, range, SD).
2. Standard error reflects the accuracy of the sample mean as an estimate of the population mean.
3. Use the context of the question to identify the correct statistical measure.

Answer 1

The Correct Option is D

Step 1: Define measures of variability. Measures of variability are statistical tools used to describe the spread or dispersion of data in a sample. Common measures include: Inter-quartile range (IQR): The difference between the 75th percentile (Q3) and the 25th percentile (Q1), representing the spread of the middle 50\% of the data. Range: The difference between the maximum and minimum values in the data. Standard deviation (SD): A measure of the average deviation of data points from the mean. Step 2: Define standard error. The standard error (SE) measures the precision of the sample mean as an estimate of the population mean. It is calculated as: \[ \text{SE} = \frac{\text{SD}}{\sqrt{n}}, \] where \(n\) is the sample size. The standard error is not a measure of variability within the data but rather reflects the variability of the sample mean. Step 3: Evaluate the options. Option (A): The inter-quartile range measures the spread of the middle 50\% of the data, so it is a measure of variability.
Option (B): The range measures the difference between the maximum and minimum values, so it is a measure of variability.
Option (C): The standard deviation measures how data points deviate from the mean, so it is a measure of variability.
Option (D): The standard error measures the precision of the sample mean, not the variability of the data itself.