Mean Deviation MCQ Quiz - Objective Question with Answer for Mean Deviation - Download Free PDF

Explanation:

The mean of 10 natural numbers 

⇒  

=  = 5.5

Mean deviation = 

∴ Option (b) is correct.

Concept Used:

• Mean deviation about the mean =

• Mean deviation about the median =

• Mean deviation of m and M = where is the mean of m and M.

Calculation:

First, arrange the data in ascending order: 2, 3, 5, 7, 11, 15, 20

Mean

Median = 7 (middle value)

Mean deviation about the mean (m):

Mean deviation about the median (M):

Mean of m and M:

Mean deviation about the mean of m and M:

Hence option 1 is correct

Concept Used:

Mean deviation about the mean is calculated using the formula:

Mean Deviation =

where fᵢ is the frequency of the i-th class, xᵢ is the midpoint of the i-th class interval, x̄ is the mean of the data, and N is the total frequency.

Calculation:

First, we find the midpoints (xᵢ) of each class interval:

0-2: x₁ = 1

2-4: x₂ = 3

4-6: x₃ = 5

6-8: x₄ = 7

8-10: x₅ = 9

Next, we calculate the mean (x̄) of the data:

x̄ =

x̄ =

x̄ = = 5

Now, we calculate the absolute deviations |xᵢ - x̄|:

|x₁ - x̄| = |1 - 5| = 4

|x₂ - x̄| = |3 - 5| = 2

|x₃ - x̄| = |5 - 5| = 0

|x₄ - x̄| = |7 - 5| = 2

|x₅ - x̄| = |9 - 5| = 4

Next, we calculate Σfᵢ|xᵢ - x̄|:

Σfᵢ|xᵢ - x̄| = 1×4 + 3×2 + 5×0 + 3×2 + 1×4 = 4 + 6 + 0 + 6 + 4 = 20

Mean Deviation = =

Hence option 4 is correct

Explanation -

x + y = 10 .........(1)

Median = 18 = M

M.D. = 

1.25 = 

x + 2y = 14 .........(1)

by (1) & (2)

x = 6, y = 4

⇒ 4x + 5y = 24 + 20 = 44 

Hence Option(2) is correct.

Formula

Median = (n + 1)/2

Calculation

Median = value of (n + 1)/2^th item

⇒ (48 + 1)/2 = 24.5^th item

24.5 lies in cf of 36

∴ Median = 12

Mean deviation about median = (1/48)(36)

⇒ 0.75

∴ Mean deviation about median is 0.75

Concept:

Mean deviation about the mean = , Where  is mean.

Calculation:

Given numbers are 10, 9, 21, 16, 24

Total numbers = 5

We know that mean deviation about the mean = 

Mean deviation from the mean = 

CONCEPT:

Mean Deviation for ungrouped data about the median:

For ‘n’ observation x₁, x₂………….. x_n, the mean deviation about their mean  is given by . where N is the number of observations and M is the median.

CALCULATIONS:

Arrange data in ascending order –

2, 3, 4, 6, 7, 9, 11

No. of observation n = 7 (odd)

Median will be  term i.e. 4^th term = 6.

Mean deviation about their median M is given by 

Here, M = 6

Concept:

Mean: It is the average of given observation. Let x₁, x₂, …, x_n be n observations, then

Mean

Mean deviation: Let x₁, x₂, …, x_n be n observations, then:

Mean deviation

Calculation:

Given: Data: 4, 7, 8, 9, 10, 12, 13, 17.

Mean

⇒ X̅ = 10

Mean deviation

= 3

Concept:

Mean deviation from mean =  

Coefficient of mean deviation = 

where N is the number of observation

x̅ is the mean of the data

x is the value of the observation.

Calculation:

⇒ x̅ = 

 Sum of deviation from mean is given by Σ∣xi​ − x̅∣,

⇒ Σ∣x_i​ − x̅∣ = ∣21 − 30∣ + ∣34 − 30∣ + ∣23 − 30∣ + ∣39 − 30∣ + ∣26 − 30∣ + ∣37 − 30∣ + ∣40 − 30∣ + ∣20 − 30∣ + ∣33 − 30∣ + ∣27 − 30∣

⇒ Σ∣xi​ − x̅∣ = 9 + 4 + 7 + 9 + 4 + 7 + 10 + 10 + 3 + 3

⇒ Σ∣xi​ − x̅∣ = 66
Mean deviation from mean =  =  ​= 6.6
Coefficient of mean deviation =  = 0.22

∴ Coefficient of mean deviation = 0.22

Concept:

To find the mean deviation, use the following steps

Step 1: Find the mean value for the given data values

Step 2: Now, subtract mean value form each of the data value given (Note: Ignore the minus symbol)

Step 3: Now, find the mean of those values obtained in step 2.

Mean deviation 

Calculations:

Given data is 2, 9, 9, 3, 6, 9, 4 

⇒ n = 7

Mean 

⇒  

Mean deviation 

⇒ Mean deviation 

⇒ Mean deviation =  2.57

Hence, the mean deviation of the data 2, 9, 9, 3, 6, 9, 4 is 2.57

Formula used

Mean Deviation about median= 

Where, 

x_i = individual term 

M = Median

n = total number of terms

Calculation:

52, 56, 66, 70, 75, 80, 82

Median = 70

⇒  M = 70

⇒ The value of (x_i - M) are

⇒ -18, -14, -4, 0, 5, 10, 12

⇒ Mean Deviation = 

∴ The mean deviation about median is 9

Important Points

The mean is the average of a data set.

The median is the middle of the set of numbers.

Mean deviation about mean 

 where x̅ = mean 

x_i = individual term 

n = total number of terms

Concept:

Deviation = |data value - mean|

Calculation:

Let, data value be 

 and 

Now,

-50 + 3.5n = 50 + 2.5n

⇒ n = 100

⇒ n = 100

Hence, option (4) is correct. 

Concept:

• Mean of a distribution =  
• Mean deviation about mean x̅ = 

where fi are frequencies and xi are the mid points of class

Calculation:

Calculating mean

⇒ Mean =  =  = 34.5

CONCEPT:

Mean Deviation for ungrouped data:

For ‘n’ observation x₁, x₂………….. x_n, the mean deviation about their mean  is given by .where N is the number of observations

CALCULATIONS:

Given data of numbers are p, 6, 6, 7, 8, 11, 15, and 16.

Mean 

⇒ p + 69 = 24p

⇒  23p = 69                  

∴  p = 3

So given data is 3, 6, 6, 7, 8, 11, 15, 16 and mean is 3p, i.e. 9.

∴ Mean deviation 

Mean deviation