- Which of the following is not a measure of location?
(a) mean
(b) median
(c) variance
(d) percentile
(e) quartile
The Correct Answer and Explanation is :
The correct answer is (c) variance.
Explanation:
In statistics, measures of location (or central tendency) describe the central point or “location” of a distribution of data. These measures help summarize a set of values with a single representative number. The common measures of location are:
- Mean: The arithmetic average of all data points, calculated by summing all values and dividing by the total number of values.
- Median: The middle value of a dataset when the values are ordered from least to greatest. If the number of data points is even, the median is the average of the two middle values.
- Percentile: A value below which a given percentage of data falls. For example, the 90th percentile means that 90% of the data is below that value.
- Quartile: Specific percentiles that divide data into four equal parts. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the 50th percentile (which is the median), and the third quartile (Q3) is the 75th percentile.
On the other hand, variance is not a measure of location. Instead, variance is a measure of spread or dispersion, indicating how much the data points differ from the mean. It quantifies the degree of variation in a dataset. The variance is calculated as the average of the squared differences between each data point and the mean. A higher variance indicates that the data points are more spread out, while a lower variance indicates that they are more closely clustered around the mean.
Thus, while measures like the mean, median, percentiles, and quartiles describe the center or specific points within a dataset, variance is concerned with the distribution of values around that center.
I’ll also generate an image that visually contrasts the different measures of location and variance.
Here is the infographic that compares the different statistical measures of location and variance. As shown, variance is distinctly represented as a measure of spread, not location, and this visual should help clarify the differences. Let me know if you need further details!
