When the elements are in an regular interval then mean = median
ans is C

we have 5 values. So we get 5x since we have -3 and 3 this cancels out and we are left with 4 + 11 = 15

(5x + 15)/5 = x + 3.

For an ordered set with odd number of values (such as 5 values)

The median will be 5+1 = 6/2 = 3

The median will be the third value in ascending order.

So it is x+3.

Hence both are equal.

Answer: C

*First, consider it is not told that x is negative or positive, but with a little try we can find out that in both cases we have the same sorted sequence:

A:
x-3, x, x+3, x+4, x+11

average: (x-3, x, x+3, x+4, x+11)/ 5 = (5x+ 15)/5 = x+3

B: x-3, x, x+3, x+4, x+11
Median separates the higher half from the lower half in an ordered sequence.
The median here is x+3

So both of these A and B are equal

But the values are not evenly spaced.

You're absolutely right.

Since the values are not equally spaced, we can't automatically conclude that mean = median (it just happens to be the case that, for this particular question, the mean and median are equal DESPITE the fact that the values aren't equally spaced).

Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ In case of even number of numbers in the set: Median is the mean of the two middle numbers (after the numbers are arranged in the increasing / decreasing order)
➡ In case of odd number of numbers in the set: Median is the middle number (after the numbers are arranged in increasing/ decreasing order )

Quantity A

The average (arithmetic mean) of x – 3, x, x +3, x + 4, and x + 11

Average = \(\frac{Sum}{5}\) = \(\frac{x -3 + x + x + 3 + x + 4 + x + 11}{5}\) = \(\frac{5x + 15}{5}\) = x + 3

Quantity B

The median of x – 3, x, x + 3, x + 4, and x + 11
Numbers are already arranged in ascending order and since there are 5 terms, so median = middle term = third term = x + 3

Clearly, Quantity A = Quantity B = x + 3

So, Answer will be C.
Hope it helps!

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