Find the mean deviation about median for the following continuous distribution: Marks Obtained No. of Boys 0 - 10 6 10 - 20 8 20 - 30 14 30 - 40 16 40 - 50 4 50 - 60 2

Class (fi-hi) frequency fi cumulative frequency cfi Midpoint ( 1 + h ) / 2 fi|xi-M| 0 - 10 6 6 5 137 . 16 10 - 20 8 6 + 8 = 14 15 102 . 88 → 20 - 30 14 14 + 14 = 28 25 40 . 04 30 - 40 16 28 + 16 = 44 35 114 . 24 40 - 50 4 44 + 4 = 48 45 68 . 56 50 - 60 2 48 + 2 = 50 55 54 . 28 N = ∑ fi = 50 ∑ fi | xi - M | = 517 . 16 Here, N 2 = 50 2 = 25 which lies in the class 20 - 30 Therefore, the median class is 20 - 30 ∴ Median M = 1 + N 2 - c f f × h where l is the lower limit of the median class. c f is the cumulative frequency of the class interval proceeding the median class. f is the frequency of median class. h is the width of the median class. ∴ M = 20 + 25 - 14 14 × 10 = 20 + 11 14 × 10 = 20 + 55 7 ⇒ M = 27 . 86 Mean deviation about median = ∑ fi | xi - M | ∑ fi = 517 . 16 50 = 10 . 343 (approximately)

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The mean deviation of the data is when measured from the median.

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Important Questions on Statistics

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The probability distribution of random variable $X$ is given by:

$X$	$1$	$2$	$3$	$4$	$5$
$P (X)$	$K$	$2 K$	$2 K$	$3 K$	$K$

Let $p = P (1 < X < 4 ∣ X < 3)$ . If $5 p = λ K$ , then $λ$ is equal to

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

10

is the mean of the data

2, 3, 5, 18, 17, 15, 13, x, 9

and

7,

then the mean deviation of this data about its mean is

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Let

O

be the mean deviation of the first five odd natural numbers about their mean and

P

be the mean deviation of the first five prime numbers about their mean. Then

P - O =

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation about median for the following continuous distribution:

$\begin{matrix} Marks Obtained & No. of Boys \\ 0 - 10 & 6 \\ 10 - 20 & 8 \\ 20 - 30 & 14 \\ 30 - 40 & 16 \\ 40 - 50 & 4 \\ 50 - 60 & 2 \end{matrix}$

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The mean deviation from the mean of the set of observations,

- 1, 0, 4

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation about the mean for the following data :

$3, 6, 10, 4, 9, 10$

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

M_{1}

and

M_{2}

are the mean deviations from mean and median of the first

15

even integers then

M_{1} + M_{2} =

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation about the mean for the following data:

$x_{i}$	$2$	$5$	$7$	$8$	$10$	$35$
$f_{i}$	$6$	$8$	$10$	$6$	$8$	$2$

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The mean deviation about the mean for the following data is

Class Interval	$0 - 4$	$4 - 8$	$8 - 12$	$12 - 16$
Frequency	$4$	$3$	$2$	$1$

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The approximate value of the mean deviation about the mean for the following data is

Class Interval	$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$
Frequency	$1$	$2$	$3$	$2$	$1$

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation from the mean of the following discrete data:

$3, 6, 10, 4, 9, 10$

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

If the mean deviation of the numbers

1, 1 + d, \dots, 1 + 100 d

from their mean is

255

, then a value of

d

is :

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation from the mean of the following discrete data

6, 7, 10, 12, 13, 4, 12, 16

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

What is the mean deviation about the mean for the following data?

$x_{i}$	$1$	$2$	$3$	$4$
$f_{i}$	$5$	$10$	$15$	$20$

HARD

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation from the mean of the following data, using the step deviation method :

$\begin{matrix} Marks & No. of Students \\ 0 - 10 & 6 \\ 10 - 20 & 5 \\ 20 - 30 & 8 \\ 30 - 40 & 15 \\ 40 - 50 & 7 \\ 50 - 60 & 6 \\ 60 - 70 & 3 \end{matrix}$

EASY

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation about the median for the following data:

$4, 6, 9, 3, 10, 13, 2$

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Find the mean deviation about the mean for the following data:

$\begin{array}{lccccc} Marks obtained & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 \\ No. of students & 5 & 8 & 15 & 16 & 6 \end{array}$

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The mean of three positive numbers is

9 .

The mean is larger than only one of these numbers. The mean deviation about mean is

2 .

The smallest number is

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

Let the data

4, 10, x, y, 27

be in the increasing order. If the median of the data is

18

and its mean deviation about mean is

7.6,

then the mean of this data is

MEDIUM

Mathematics>Mathematical Reasoning and Statistics>Statistics>Mean Deviation

The mean deviation of the data

2, 9, 9, 3, 6, 9, 4

from the mean is

The mean deviation of the data is when measured from the median.

Important Questions on Statistics

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