Question:
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
Show Hint
To find the variance, first calculate the mean, then determine the squared deviations from the mean, and finally divide the sum of these squared deviations by the total number of data points.
Updated On: Jan 22, 2025
- \( 22.1 \)
- \( 23.0 \)
- \( 20.2 \)
- \( 21.2 \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Compute the mean (\( \bar{x} \)) of the given data.
\[
\bar{x} = \frac{\sum x_i}{n} = \frac{8 + 12 + 13 + 15 + 22}{5} = 14.
\]
Step 2: Calculate the squared deviations from the mean.
\[
(x_i - \bar{x})^2 = \{(8-14)^2, (12-14)^2, (13-14)^2, (15-14)^2, (22-14)^2\}.
\]
\[
(x_i - \bar{x})^2 = \{36, 4, 1, 1, 64\}.
\]
Step 3: Find the variance.
\[
\text{Variance (Var(x))} = \frac{\sum (x_i - \bar{x})^2}{n} = \frac{36 + 4 + 1 + 1 + 64}{5} = \frac{106}{5} = 21.2.
\]
Final Answer:
The variance of the data is:
\[
\boxed{21.2}
\]
Was this answer helpful?
0
0
Top Questions on Limits
- The area of the region \( \{(x, y): 0 \leq y \leq x^2 + 1, \, 0 \leq y \leq x + 1, \, 0 \leq x \leq 2\ \) is:}
- Evaluate \( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \):
- Let \(k\in R\). If \(\)\(\)\(\)\(\lim\limits_{x→0+}(\sin(\sin kx)+\cos x+x)^{\frac{2}{x}}=e^6\), then the value of k is
- If \(\lim\limits_{x \to1}(\frac {x^2-2ax+b}{x-1})=8\)
then \((a-b)\) is _____ . (Answer in integer) - Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:
View More Questions
Questions Asked in MHT CET exam
- Which of the following is correct?
- MHT CET - 2024
- Vector Algebra
- If the vector equation of the line \[ \frac{x - 2}{2} = \frac{2y - 5}{-3} = z + 1, \] is given by: \[ \vec{r} = \left(2\hat{i} + \frac{5}{2}\hat{j} - \hat{k}\right) + \lambda\left(2\hat{i} - \frac{3}{2}\hat{j} + p\hat{k}\right), \] then \( p \) is equal to:
- MHT CET - 2024
- Random Variables
- The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:
- MHT CET - 2024
- Geometric Progression
- Let \( X \) be the discrete random variable representing the number (\( x \)) appeared on the face of a biased die when it is rolled. The probability distribution of \( X \) is as follows: \[ X = x: \quad 1, \, 2, \, 3, \, 4, \, 5, \, 6 \] \[ P(X = x): \quad 0.1, \, 0.15, \, 0.3, \, 0.25, \, k, \, k \] The variance of \( X \) is:
- MHT CET - 2024
- Differential equations
- A spherical iron ball \( 10 \, \text{cm} \) in radius is coated with a layer of ice of uniform thickness that melts at a rate of \( 50 \, \text{cm}^3/\text{min} \). When the thickness of ice is \( 15 \, \text{cm} \), then the rate at which the thickness of ice decreases is:
- MHT CET - 2024
- Matrices
View More Questions