Question

What is the value of mean deviation about mean for the following observations?
50, 60, 50, 50, 60, 60, 60, 50, 50, 50, 60, 60, 60, 50.
(a) 5
(b) 7
(c) 35
(d) 10​

Answer 1

The correct answer is option (a). 5.

Given:

The given observations = 50, 60, 50, 50, 60, 60, 60, 50, 50, 50, 60, 60, 60, 50.

The number of observations = 14.

To Find:

We have to find the value of the mean deviation about mean for the given observations.

Solution:

The equation for calculating the mean is given by,

$Mean = \frac{Sum of the observations}{Number of observations}$

Substituting the given values in the above equation, it becomes,

$Mean = \frac{50 + 60 + 50 + 50 + 60 + 60 + 60 + 50 + 50 + 50 + 60 + 60 + 60 + 50}{14}$

$= \frac{770}{14} = 55.$

The deviation of all the observations from the mean value is 5.

The sum of deviations of each of the observation from the mean value = $5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 70.$

The equation for mean deviation about the mean is given by,

Mean deviation about mean = $\frac{Sum of deviation of each observation from the mean value}{Number of observations}$

On substituting the given values, the above equation becomes,

Mean deviation about mean $= \frac{70}{14} = 5.$

Hence, the value of mean deviation about mean for the given observations is 5.

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Answer 2

The correct answer is option (a) 5

Mean Deviation

Definition of Mean Deviation: The mean departure is a statistical metric used to compute the average deviation from the mean value of a given data collection. Using the following approach, you can simply determine the mean deviation of the data values.

Step 1: Determine the mean value for the provided data points.

Step 2: Subtract the mean value from each of the provided data values (Note: Ignore the minus symbol)

Step 3: Calculate the average of the data acquired in step 2.

Mean Deviation Formula: The following formula calculates the mean deviation for the supplied data set.

Main content

The equation for calculating the mean is given by,

$Mean = \frac{Sum of the observation}{Number of observation}$

Substituting the given values in the above equation, it becomes,

$Mean = \frac{50, 60, 50, 50, 60, 60, 60, 50, 50, 50, 60, 60, 60, 50}{14} = \frac{770}{14} = 55$

The deviation of all the observations from the mean value is 5.

The sum of deviations of each of the observation from the mean value =

$5+5+5+5+5+5+5+5+5+5+5+5+5+5=70.$

The equation for mean deviation about the mean is given by,

Mean deviation about mean = $\frac{Sum of deviation of each observation from the mean valve}{number of observations}$

On substituting the given values, the above equation becomes,

Mean deviation about mean = $\frac{70}{14} =5.$

Hence, the value of mean deviation about mean for the given observations is 5.

To learn more about Mean Deviation

https://brainly.in/question/51200594

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