Question

For what value of 'a' 4 , 6 , a , 9 , 10 , 19 will 7.5 be the median​

Answer 1

Median is the middlemost observation in a given set of data.

Given: Observations and median.

To find: The value of a.

Answer:

Observations: 4 , 6 , a , 9 , 10 and 19.

Total number of observations: 6.

Median = $\sf\frac{n/2\ + n/2\ +\ 1}{2}$, where n = total number of observations.

NOTE: The above formula is used only if n = an even number.

$\sf7.5 = \frac{6/2\ +\ 6/2\ +\ 1}{2} \\\\7.5 = \frac{3rd\ term\ +\ 4th\ term}{2} \\\\7.5 = \frac{a\ +\ 9}{2} \\\\7.5 \times2 = a + 9\\\\15 = a + 9\\\\a = 15 - 9\\\\a = 6$

Therefore, a = 6.