If the mean deviation about the mean of the numbers 1, 2, 3, …. n, where n is odd, is \(\frac{5(n + 1)}{n}\), then n is equal to ______.
Correct Answer: 21
Solution and Explanation
The correct answer is: 21
Mean
\(=\frac{\frac{n(n+1)}{2}}{n}=\frac{n+1}{2}\)
\(⇒((n-1)+(n-3)+(n-5)+...0=5)=5(n+1)\)
\(⇒(\frac{n+1}{4})(n-1)=5(n+1)\)
So, n = 21.
Top Questions on Mean Deviation
- The mean of 6 numbers is 15, and the standard deviation is 2. If each number is increased by 5, what is the new standard deviation?
- AP EAPCET - 2025
- Mathematics
- Mean Deviation
- Let the mean and variance of the observations \( 2, 3, 3, 4, 5, 7, a, b \) be 4 and 2, respectively. Then, the mean deviation about the mode of the observation is:
- JEE Main - 2025
- Mathematics
- Mean Deviation
Find the mean deviation of the following data:
- KEAM - 2025
- Mathematics
- Mean Deviation
- If the variance of the data \( 2,3,5,8,12 \) is \( \sigma^2 \) and the mean deviation from the median for this data is \( M \), then \( \sigma^2 - M \) is:
- BITSAT - 2024
- Mathematics
- Mean Deviation
- The mean of \( n \) items is \( X \). If the first item is increased by 1, second by 2, and so on, the new mean is:
- BITSAT - 2024
- Mathematics
- Mean Deviation
Questions Asked in JEE Main exam
- Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:
- JEE Main - 2025
- Solutions
In the given circuit the sliding contact is pulled outwards such that the electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 Ω, the value of the current in the circuit will be A.- JEE Main - 2025
- Electrical Circuits
- Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k} \) and \( \vec{b} = 2\hat{i} + 7\hat{j} + 3\hat{k} \). Let \( L_1 : \vec{r} = (-\hat{i} + 2\hat{j} + \hat{k}) + \lambda \vec{a}, \lambda \in {R} \) and \( L_2 : \vec{r} = (\hat{j} + \hat{k}) + \mu \vec{b}, \mu \in \mathbb{R} \) be two lines. If the line \( L_3 \) passes through the point of intersection of \( L_1 \) and \( L_2 \), and is parallel to \( \vec{a} + \vec{b} \), then \( L_3 \) passes through the point:
- JEE Main - 2025
- Vectors
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
For $ \alpha, \beta, \gamma \in \mathbb{R} $, if $$ \lim_{x \to 0} \frac{x^2 \sin \alpha x + (\gamma - 1)e^{x^2} - 3}{\sin 2x - \beta x} = 3, $$ then $ \beta + \gamma - \alpha $ is equal to:
Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution