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
Demand for seats in a university is at its highest in the fall; demand also trends to grow and fall off in 25 year waves. In time service forecasting, the former demand characteristic would be called ______ and the latter would be called _______.
The system of combining two or more overlapping series of index numbers to obtain a single continuous series is called
The rise in the number of patients due to heatstroke is an example of:
According to government data, 24 percent of teenagers in India under the age of 18 years live in households with incomes that are classified at a particular income level. A simple random sample of 400 teenagers in India under the age of 18 years was selected for a study of learning. If the government data is correct, which of the following best approximates the probability that at least 27 per cent of the teenagers in the sample live in households that are classified at a particular income level?
Which index satisfies the factor reversal test?
