If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022

₹0.0

Question: If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)

Options:

Correct Answer: 8

Exam Year: 2022

Solution:

For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.

If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)

If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)

Step 1: Understand that the median is the middle value of a data set when it is ordered from smallest to largest.
Step 2: Write down the data set: 3, 7, 9, x, 15.
Step 3: Since we want the median to be 9, we need to arrange the numbers in order including x.
Step 4: If x is less than 9, the ordered set will be 3, 7, x, 9, 15. The median will be 9.
Step 5: If x is equal to 9, the ordered set will be 3, 7, 9, 9, 15. The median will still be 9.
Step 6: If x is greater than 9, the ordered set will be 3, 7, 9, 15, x. The median will be 9.
Step 7: The only value of x that keeps the median at 9 is when x is equal to 9.
Step 8: Therefore, the value of x is 9.

Median – The median is the middle value of a data set when it is ordered from least to greatest.
Data Set Ordering – Understanding how to order a data set is crucial for finding the median.
Variable Substitution – The problem involves substituting a variable (x) and determining its value based on the median.