A data set is given to be $[1, 2, 0, -1, -3, 1, 2, 0, 1]$. The median of the data set is ____. (rounded off to the nearest integer)
Median Calculation for Data Set
To find the median of the given data set, we first need to arrange the numbers in ascending order.
The data set is: $[1, 2, 0, -1, -3, 1, 2, 0, 1]$
Ordering the Data Set
Arranging the data set in ascending order:
$[-3, -1, 0, 0, 1, 1, 1, 2, 2]$
Determining the Median
The number of observations in the data set is $n = 9$. Since $n$ is an odd number, the median is the middle value.
The position of the median is calculated using the formula:
Position = $\frac{n+1}{2}$
Substituting $n=9$: Position = $\frac{9+1}{2} = \frac{10}{2} = 5$
The median is the 5th value in the ordered data set.
Looking at the ordered data set $[-3, -1, 0, 0, 1, 1, 1, 2, 2]$, the 5th value is $1$.
Rounding the Median
The median value is $1$. The question asks for the median rounded off to the nearest integer. Since $1$ is already an integer, no rounding is needed.
The median of the data set is $1$.
Important Questions from Mean Median Mode
- Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.
Ignoring permutations, the number of ways to pick these five integers is _____ - The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is
- The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is ________.
The mean absolute deviation about the median for the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21 (rounded off to two decimal places) is ________________.
- In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000, 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is
