Which of the following is not a measure of central location?
a. mean
b. median
c. variance
d. mode
The correct answer and explanation is :
The correct answer is c. variance.
Explanation:
Measures of central location are statistical values that describe the center or typical value of a data set. They give us an idea of where most of the data points are located. The key measures of central location include:
- Mean: The arithmetic average of all the values in the data set. It is calculated by adding all the data points together and dividing by the number of data points. The mean is sensitive to outliers because extreme values can significantly affect the result.
- Median: The middle value when the data is arranged in ascending order. If there is an odd number of data points, the median is the value at the center. If there is an even number of data points, the median is the average of the two central values. The median is less sensitive to extreme values (outliers) compared to the mean.
- Mode: The value that appears most frequently in a data set. A data set can have one mode, more than one mode (bimodal, multimodal), or no mode if no number repeats. The mode is particularly useful for categorical data where the mean or median cannot be computed.
On the other hand, variance is a measure of variability or spread, not central location. Variance measures how much the data points deviate from the mean, indicating the extent of variation or dispersion in the data. It is calculated by finding the average of the squared differences between each data point and the mean. A high variance means that the data points are spread out widely around the mean, while a low variance indicates that the data points are close to the mean.
In summary, while the mean, median, and mode all describe central tendencies in data, variance provides information about the spread or dispersion of the data. Therefore, variance is not a measure of central location.