The median for the given numbers is 21, 22, 26, 27, 28, 26
Understanding Median Calculation
The question asks us to find the median for the given set of numbers: 21, 22, 26, 27, 28, 26.
The median is the middle value in a data set that is listed in order. If there is an even number of observations, the median is the average of the two middle values.
Step-by-Step Median Calculation
- Order the Numbers: First, arrange the given numbers in ascending order. The numbers are: 21, 22, 26, 27, 28, 26. Arranged in order: 21, 22, 26, 26, 27, 28.
- Identify the Middle Value(s): Count the total number of values in the set. There are 6 numbers, which is an even count. For an even number of values, the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th values in the ordered list. Middle Numbers: 26 (3rd) and 26 (4th).
- Calculate the Average (if needed): Since we have two middle numbers (26 and 26), we need to calculate their average. The formula for the average of two numbers $a$ and $b$ is $\\frac{a + b}{2}$. Average = $ \\frac{26 + 26}{2} $ Average = $ \\frac{52}{2} $ Average = 26
Conclusion on Median Value
The calculated median for the given data set (21, 22, 26, 27, 28, 26) is 26.
Important Questions from Measures of Central Tendency
If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of \(\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?\) ?
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?
Which one of the following measures of central tendency is used in construction of index numbers?
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at
