Question

The median and mode of the data 8, 7, x, 5, 4, 4, y, z, 5, 5, 6, 7, 8 are x and y respectively. If both z, y > x, then the value of (x + y + z) cannot be equal to

• A. 20
• B. 21
• C. 22
• D. 23

Answer 1

The correct option is B 21

Given: Median = x
Mode = y
Also both z, y > x
Here, the total number of observations are 13.
∴ Median = $(\frac{n+1}{2}{)}^{th}$ term ($\therefore$ n = 13, odd)
$\Rightarrow$ Median = 7th term = x
Arranging the observations in ascending order,
4, 4, 5, 5, 5, 6, x, 7, 7, 8, 8
Now, x is either equal to 6 or 7 and y and z can be 7 or 8, but they have to be equal as y is the mode.
So, when x = 6, y = 7, z = 7:
x + y + z = 6 + 7 + 7
= 20
When x = 6, y = 8, z = 8:
x + y + z = 6 + 8 + 8
= 22
When x = 7, y = 8, z = 8:
x + y + z = 7 + 8 + 8
= 23
Therefore, (x + y + z) can have the values 20, 22 or 23.
Hence, the correct answer is option (b).