The mean of the following series is ______. (rounded off to three decimal places) $0.01, 0.02, 0.03, \cdots \cdots, 1$
Series Mean Calculation
The question asks for the mean of the series: $0.01, 0.02, 0.03, \cdots \cdots, 1$. This is an arithmetic progression.
Arithmetic Progression Properties
To find the mean of an arithmetic progression, we can use the formula:
$ \text{Mean} = \frac{\text{First Term} + \text{Last Term}}{2} $
Identifying Series Terms
- First Term ($a$) = $0.01$
- Last Term ($l$) = $1$
Calculating the Mean
- Substitute the values into the formula:
$ \text{Mean} = \frac{0.01 + 1}{2} $
- Simplify the expression:
$ \text{Mean} = \frac{1.01}{2} $
- Calculate the final value:
$ \text{Mean} = 0.505 $
The question requires the answer rounded to three decimal places. The calculated mean $0.505$ is already in this format.
Final Result
The mean of the series is 0.505.
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?
