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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The mode of the data is: - In the given data if 30 is replaced by 100 then find the difference of the two medians.
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Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
