Find the median of the following data. 7, 19, 88, 20, 19, 26, 90, 81, 44, 34.

Correct Option: 30

To find the median of a dataset, follow these step-by-step logical calculations:

Step 1: Count the total number of data points (n).
The given set of numbers is: 7, 19, 88, 20, 19, 26, 90, 81, 44, 34.
Counting these numbers gives $n=10$, which is an even number.

Step 2: Arrange the data in ascending order (from smallest to largest).
Sorting the numbers in ascending order gives:
7, 19, 19, 20, 26, 34, 44, 81, 88, 90

Step 3: Identify the middle terms.
Since $n=10$ is an even number, the median is the average of the two middle terms: the $\left(\frac{n}{2}\right)$^th term and the $(\frac{n}{2}+1)$^th term.

$\frac{n}{2}=\frac{10}{2}=5$

$\frac{n}{2}+1=5+1=6$

Looking at our sorted list:
1^st term: 7
2^nd term: 19
3^rd term: 19
4^th term: 20
5^th term: 26
6^th term: 34
7^th term: 44
8^th term: 81
9^th term: 88
10^th term: 90

The 5^th term is 26 and the 6^th term is 34.

Step 4: Calculate the median.
Take the mean (average) of the two middle terms (26 and 34):

$\text{Median}=\frac{26+34}{2}$

$\text{Median}=\frac{60}{2}=30$

Thus, the median of the given data is 30.