Question

The measures of central tendency of a data set (4, 2, 7, x, y, z) where, x < y < z; are as follows:

Choose the correct values of x, y, and z

• A. x = 2, y = 9, z = 6
• B. x = 2, y = 6, z = 9
• C. x = 3, y = 7, z = 10
• D. x = 4, y = 2, z = 9

Answer 1

The correct option is B x = 2, y = 6, z = 9

Arrange the data set in ascending order
2, 4, 7, x, y, z

$\to$ The mode of a given data set is 2
$\Rightarrow$ Either x or y or z has the value of 2

Let the x or y or z be []
Hence the new data set is 2, 2, 4, 7, [], []

$\to$ The median of a given data set is 5. To attain the mean value of 5, the unknown value should be placed next to 4

$\Rightarrow$ Hence the updated data set is as
2, 2, 4, [], 7, []
$\text{Median}=\frac{4+\left[\right]}{2}5=\frac{4+\left[\right]}{2}5\times 2=4+\left[\right]10=4+\left[\right]10-4=\left[\right]6=\left[\right]$

So, one of the unknown is 6
Hence the new data set is 2, 2, 4, 6, 7, []
Let's find the third unknown
$\to$ The mean of a given data set is 5
$\text{Mean}=\frac{2+2+4+6+7+\left[\right]}{6}5=\frac{21+\left[\right]}{6}5\times 6=21+\left[\right]30=21+\left[\right]30-21=\left[\right]9=\left[\right]$

$\therefore$ The unknowns are 2, 6, 9
Given: x < y < z or 2 < 6 < 9
Hence x = 2, y = 6, z = 9