If the mean deviation about the median of the numbers a, 2 a …50 a is 50 , then |a| equals (A) 3

step 1 In problem 52 we have the mean deviation about the median of the following numbers a to a until

If the mean deviation about the median of the numbers a, 2 a...

Key Concepts

Arithmetic Progression

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. This regularity allows for easy determination of any term in the sequence as well as aggregate measures such as sums and means. In statistical problems, arithmetic progressions often enable simplification when calculating spreads and central tendencies.

Median

The median is the value that divides an ordered data set into two equal halves. In cases where the data set has an even number of elements, the median is calculated as the average of the two central values. In the context of deviations, the median is particularly significant because the sum of absolute deviations from the median is minimized.

Mean Absolute Deviation

The mean absolute deviation is the average of the absolute differences between each data point and a central measure, usually the median. This statistic quantifies the spread of the data and is useful for understanding variability relative to a central value. It is especially relevant in problems where dispersion must be linked to known parameters or conditions.

Symmetry of Deviations in Evenly Spaced Data

In evenly spaced or arithmetic sequences, the deviations from the median exhibit symmetry. This means that the absolute differences of values below the median mirror those above it. This symmetric property greatly simplifies the process of summing absolute deviations and computing the mean absolute deviation.

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