Question

In case of Principal Component Analysis (PCA), the variance of a single variable expresses the spread of its values about the

• A. Mode
• B. Median
• C. Mean
• D. Standard Deviation

Hint:

In PCA, variance is a measure of how much data points deviate from the mean. Understanding variance helps in identifying the most significant directions of variation in the data.

Answer 1

The Correct Option is C

Principal Component Analysis (PCA) is a statistical technique used to simplify a dataset by reducing its dimensions while retaining as much variance as possible. In PCA, the variance of a variable expresses the spread of its values around the mean. Variance measures how much the values of a variable deviate from the mean of that variable. Variance in PCA:
Variance is a measure of the spread of data points around the mean. It is calculated as the average squared deviation of each data point from the mean of the variable. The higher the variance, the more spread out the values are around the mean, indicating more diversity or dispersion in the dataset. - Option (A): Mode is the value that appears most frequently in a dataset. It is not related to the spread of the data, and variance does not measure how values are spread around the mode.
- Option (B): Median is the middle value of a dataset when the values are arranged in order. While the median provides a measure of central tendency, variance is specifically related to the mean, not the median.
- Option (C): The mean is the arithmetic average of the values in the dataset. Variance measures how much the values deviate from the mean. This is the correct answer, as PCA relies on the variance of data values around the mean to identify principal components.
- Option (D): Standard deviation is the square root of variance. While it is related to variance, the question specifically asks about variance, not standard deviation. Thus, the correct answer is (C) Mean, because variance in PCA is the spread of values around the mean of the variable.