The median of the following numbers arranged in ascending order is 2.5, if so find x? 0, 0, 1, 1, 2, 2, x, 3, 3, 4, 5, 7
Solving for x using Median
The question provides a list of numbers in ascending order: 0, 0, 1, 1, 2, 2, x, 3, 3, 4, 5, 7. It states that the median of these numbers is 2.5 and asks to find the value of x.
Understanding Median Calculation
The median is the middle value in a dataset that is ordered. Since there are 12 numbers in the list (an even count), the median is calculated as the average of the two middle terms.
- Total number of observations (N) = 12.
- The middle terms are the N/2-th and (N/2 + 1)-th terms.
- N/2 = 12/2 = 6. So, the 6th term.
- N/2 + 1 = 6 + 1 = 7. So, the 7th term.
- Median = (6th term + 7th term) / 2
Applying the Median Formula
From the ordered list, we can identify the terms:
- The 6th term is 2.
- The 7th term is x.
We are given that the median is 2.5. Using the formula:
$ 2.5 = \frac{2 + x}{2} $
Calculating the Value of x
To find x, we solve the equation:
- Multiply both sides by 2:
$ 2.5 \times 2 = 2 + x $
$ 5 = 2 + x $
- Subtract 2 from both sides:
$ 5 - 2 = x $
$ x = 3 $
Therefore, the value of x is 3.
Similar Questions
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Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
