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A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 , then the mean deviation is
- a)6.4
- b)9.6
- c)10.6
- d)8.6
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 ...
Arranging the given data in ascending order,
we have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, Median M = (46+48)/2
=47
(∵ n = 10, median is the mean of 5th and 6th items)
∴ Mean deviation = ∑|xi−M|/n
=∑|xi−47|/10
= (13+9+5+3+1+1+7+8+16+23)/10
=8.6
we have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, Median M = (46+48)/2
=47
(∵ n = 10, median is the mean of 5th and 6th items)
∴ Mean deviation = ∑|xi−M|/n
=∑|xi−47|/10
= (13+9+5+3+1+1+7+8+16+23)/10
=8.6
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A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 ...
Mean deviation is a measure of statistical dispersion. It measures how spread out a set of data is from its mean. The formula for mean deviation is:
Mean deviation = (Σ|X - μ|) / n
Where Σ is the sum, X is the variable, μ is the mean, and n is the number of observations.
Given the following data: 38,70,48,34,42,55,63,46,54,44
Step 1: Find the mean
μ = (38+70+48+34+42+55+63+46+54+44)/10
μ = 50.4
Step 2: Find the absolute deviation for each observation
|38-50.4| = 12.4
|70-50.4| = 19.6
|48-50.4| = 2.4
|34-50.4| = 16.4
|42-50.4| = 8.4
|55-50.4| = 4.6
|63-50.4| = 12.6
|46-50.4| = 4.4
|54-50.4| = 3.6
|44-50.4| = 6.4
Step 3: Find the sum of the absolute deviation
Σ|X - μ| = 12.4+19.6+2.4+16.4+8.4+4.6+12.6+4.4+3.6+6.4
Σ|X - μ| = 91.4
Step 4: Find the mean deviation
Mean deviation = (Σ|X - μ|) / n
Mean deviation = 91.4 / 10
Mean deviation = 9.14
Therefore, the correct option is D) 8.6.
Mean deviation = (Σ|X - μ|) / n
Where Σ is the sum, X is the variable, μ is the mean, and n is the number of observations.
Given the following data: 38,70,48,34,42,55,63,46,54,44
Step 1: Find the mean
μ = (38+70+48+34+42+55+63+46+54+44)/10
μ = 50.4
Step 2: Find the absolute deviation for each observation
|38-50.4| = 12.4
|70-50.4| = 19.6
|48-50.4| = 2.4
|34-50.4| = 16.4
|42-50.4| = 8.4
|55-50.4| = 4.6
|63-50.4| = 12.6
|46-50.4| = 4.4
|54-50.4| = 3.6
|44-50.4| = 6.4
Step 3: Find the sum of the absolute deviation
Σ|X - μ| = 12.4+19.6+2.4+16.4+8.4+4.6+12.6+4.4+3.6+6.4
Σ|X - μ| = 91.4
Step 4: Find the mean deviation
Mean deviation = (Σ|X - μ|) / n
Mean deviation = 91.4 / 10
Mean deviation = 9.14
Therefore, the correct option is D) 8.6.
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A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 , then the mean deviation isa)6.4b)9.6c)10.6d)8.6Correct answer is option 'D'. Can you explain this answer?
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