Question:
Consider the following frequency distribution:
The mean deviation about the mean is:
Consider the following frequency distribution:
The mean deviation about the mean is:
Show Hint
Always calculate the Mean first. If the Mean is an integer (like 9 here), the absolute deviations become very easy to calculate. If the mean is a decimal, keep at least two decimal places for accuracy.
Updated On: Apr 6, 2026
- 4.23
- 5.23
- 2.32
- 3.23
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Mean deviation about the mean is the arithmetic mean of the absolute deviations of the observations from their arithmetic mean.
Step 2: Key Formula or Approach:
1. Mean ($\bar{x}$) $= \frac{\sum f_i x_i}{\sum f_i}$ 2. Mean Deviation (M.D.) $= \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i}$
Step 3: Detailed Explanation:
1. Calculate $\sum f_i$: $4 + 8 + 2 + 3 + 9 = 26$. 2. Calculate $\sum f_i x_i$: $(5 \times 4) + (6 \times 8) + (8 \times 2) + (11 \times 3) + (13 \times 9) = 20 + 48 + 16 + 33 + 117 = 234$. 3. Mean $\bar{x} = 234 / 26 = 9$. 4. Calculate $\sum f_i |x_i - 9|$: $4|5-9| + 8|6-9| + 2|8-9| + 3|11-9| + 9|13-9|$ $= 4(4) + 8(3) + 2(1) + 3(2) + 9(4) = 16 + 24 + 2 + 6 + 36 = 84$. 5. M.D. $= 84 / 26 \approx 3.23$.
Step 4: Final Answer:
The mean deviation about the mean is 3.23.
Was this answer helpful?
0
0
Top JEE Main Mathematics Questions
- For a positive integer $n$, if the mean of the binomial coefficients in the expansion of $(a + b)^{2n - 3}$ is 16, then $n$ is equal to :
- JEE Main - 2018
- Mathematics
- binomial expansion formula
- The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, $x^2 = 4y$, internally in the ratio 1 : 2, is :
- JEE Main - 2020
- Mathematics
- Conic sections
- If a hyperbola passes through the point $P(10,16)$ and it has vertices at $( ? 6,0)$, then the equation of the normal to it at P is :
- JEE Main - 2020
- Mathematics
- Conic sections
- Axis of a parabola lies along $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin, on the positive $x$-axis then which of the following points does not lie on it ?
- JEE Main - 2019
- Mathematics
- Conic sections
- Equation of the tangent to the circle, at the point $(1, -1)$, whose centre is the point of intersection of the straight lines $x - y = 1$and $+ y = 3$is :
- JEE Main - 2016
- Mathematics
- Conic sections
View More Questions
Top JEE Main Calculus Questions
- Let \( f(x) = 2^x - x^2, \, x \in \mathbb{R} \). If \( m \) and \( n \) are respectively the number of points at which the curves \( y = f(x) \) and \( y = f'(x) \) intersect the x-axis, then the value of \( m + n \) is
- If\[\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1 - \sin 2x} \, dx = \alpha + \beta \sqrt{2} + \gamma \sqrt{3},\]where \( \alpha \), \( \beta \), and \( \gamma \) are rational numbers, then \( 3\alpha + 4\beta - \gamma \) is equal to ______.
- Let \( f \) be a differentiable function in the interval \( (0, \infty) \) such that \( f(1) = 1 \) and \(\lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1\) for each \( x > 0 \).
Then \( 2f(2) + 3f(3) \) is equal to _________. The area of the region enclosed by the parabolas \( y = x^2 - 5x \) and \( y = 7x - x^2 \) is _________.
- For the function $f(x) = (\cos x) - x + 1, x \in \mathbb{R}$, find the correct relationship between the following two statements
(S1) $f(x) = 0$ for only one value of x is $[0, \pi]$.
(S2) $f(x)$ is decreasing in $\left[0, \frac{\pi}{2}\right]$ and increasing in $\left[\frac{\pi}{2}, \pi\right]$.
View More Questions
Top JEE Main Questions
- For a positive integer $n$, if the mean of the binomial coefficients in the expansion of $(a + b)^{2n - 3}$ is 16, then $n$ is equal to :
- JEE Main - 2018
- binomial expansion formula
- Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance $C$ if the equivalent capacitance between point $A$ and $B$ is to be $1\, \mu F$ is :
- JEE Main - 2016
- electrostatic potential and capacitance
- Given the masses of various atomic particles $m _{ p }=1.0072 u$ , $m _{ n }=1.0087 \,u$ $m _{ e }=0.000548 u$ , $m _{\overline{ v }}=0$, $m _{ d }=2.0141 u$ where $p \equiv$ proton, $n \equiv$ neutron, $e \equiv$ electron, $\overline{ v } \equiv$ antineutrino and $d \equiv$ deuteron. Which of the following process is allowed by momentum and energy conservation ?
- Find the binding energy per nucleon for ${ }_{50}^{120} Sn$. Mass of proton $m _{ p }=1.00783\, U ,$ mass of neutron $m_{n}=1.00867 \,U$ and mass of tin nucleus $m _{ Sn }=119.902199 \,U $ (take $1U = 931 \,MeV)$
- The locus of a point which divides the line segment joining the point (0, -1) and a point on the parabola, $x^2 = 4y$, internally in the ratio 1 : 2, is :
- JEE Main - 2020
- Conic sections
View More Questions