(A) mean ≤median ≤mode (B) median ≤mean ≤mode (C) median ≤mode ≤mean (D) mode ≤mean ≤median (E)

step 1 Hello everybody, this is Ricky, and today we're working on problem number 16 from the diagnostic

(A) mean ≤median ≤mode (B) median ≤mean ≤mode (C) median...

(A) mean $\leq$ median $\leq$ mode
(B) median $\leq$ mean $\leq$ mode
(C) median $\leq$ mode $\leq$ mean
(D) mode $\leq$ mean $\leq$ median
(E) The relationship cannot be determined because the median cannot
be calculated.

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Key Concepts

Mean

The mean is the arithmetic average of a data set, calculated by summing all the values and dividing by the number of values. It is sensitive to extreme values (outliers), which can skew the average, particularly in asymmetrical distributions.

Median

The median represents the middle value in an ordered data set, splitting the data into two equal halves. It is less affected by outliers and skewed data than the mean, making it a more robust measure of central tendency in non-symmetrical distributions.

Mode

The mode is the value that occurs most frequently in a data set. In cases where data are skewed or multi-modal, the mode provides insight into the peak or common occurrence, complementing the information gleaned from the mean and median.

Skewness

Skewness describes the asymmetry of a distribution. In positively skewed (right-skewed) distributions, the mean tends to be greater than the median, which is in turn greater than the mode, whereas in negatively skewed (left-skewed) distributions, the order is typically reversed. Understanding skewness is key to interpreting the relative positions of mean, median, and mode.

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