Which one of the options can be inferred about the mean, median, and mode for…

GATE · 2023 · CE · Set 1 · General AptitudeGATE · 2023 · ST · General Aptitude

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), P(x), of a variable x?

Cyan-filled probability mass bar chart with vertical axis P(x) and horizontal axis x. Printed horizontal labels, in order: −17, −13, −9, −5, −1, 1, 5, 9, 13, 17. Intermediate tick positions and the outer bars are unnumbered; vertical ticks carry no numbers. There are 20 bars, ten on each side of the vertical axis, with matching heights at corresponding positions on the left and right. Moving outward from the vertical axis on either side, the first bar (at −1 or 1) is followed by three successively shorter bars; the fifth bar rises, the sixth rises further, and the seventh (at −13 or 13) is the tallest. The eighth drops to the height of the first, the ninth drops to the height of the fourth, and the tenth, outermost bar is the shortest. The fifth matches the second in height; the sixth is taller than the first but shorter than the seventh. No numeric probabilities are printed.

A.
mean = median ≠ mode
B.
mean = median = mode
C.
mean ≠ median = mode
D.
mean ≠ mode = median

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