Question

Measures of Center In what sense are the mean, median, mode, and midrange measures of “center”?

Short answer

• Mean is the central measure based on all observations.
• Median is the observation at the center as per the measurements.
• Mode is the value with the most frequency.
• Midrange is the central measure based on two extreme observations only.

Step-by-step solution

Mean

Mean is the measure for the central location of the data set. It is obtained using the measure of each observation along with the count of observations.

Thus, mean finds the center of all observations through the measures.

Median 

Median determines the observation that divides the entire data set into two halves. Thus, 50% of observations are, respectively, lesser or greater than the median value.

Thus, median finds the central observation of the data set by arranging the observations as per the measurement.

Mode

Mode forms the center of all observations as per the corresponding frequencies or number of repetitions in the entire dataset.

Thus, mode is/are the observation(s) with the highest frequency.

Midrange

Midrange is mathematically the average of two values; the highest and lowest measuring observations.

Thus, midrange provides a tentative measure of central observation based on two extreme values of the data.