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
- The median of the following set of numbers: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138 is:
- Let $X$ be a continuous random variable whose cumulative distribution function (CDF)
$F_X(x) = \begin{cases} 0 & x < t \\ \frac{x-t}{4-t} & t \le x \le 4 \\ 1 & x \ge 4 \end{cases}$
If the median of $X$ is $3$, then what is the value of $t$? - The elements of the dataset $\{-5,1, a, 5, b\}$ are in ascending order. If both mean and median of the dataset are equal to 3, what is the value of $b$?
- 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 above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?
