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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :
- a)4 : 9
- b)6 : 7
- c)5 : 8
- d)10 : 3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The mean of five observations is 5 and their variance is 9.20. If thre...
For the values x1, x2, ....xn of the variant x the arithmetic mean is given by
\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}
in case of discrete data.
-
Variance -
In case of discrete data
\dpi{100} \sigma ^{2}= \left ( \frac{\sum x_{i}^{2}}{n} \right )-\left ( \frac{\sum x_{i}}{n} \right )^{2}
-
Let 5 bservation are 1,3,8,1 and b
mean = \frac{\Sigma x_{i}}{5} = 5
1 + 3 + 8 + a + b = 25
a+ b = 13 ..... (1)
Variance (\sigma^{2}) = \frac{\Sigma x_{i}^{2}}{5} -2 5 = 9.20
Sigma x_{i}^{2} = 171
a2 + b2 = 97..... (2)
from (1) and (2)
(a+b)2 - 2ab = 97
ab = 36
a:b = 9:4 or 4:9
\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}
in case of discrete data.
-
Variance -
In case of discrete data
\dpi{100} \sigma ^{2}= \left ( \frac{\sum x_{i}^{2}}{n} \right )-\left ( \frac{\sum x_{i}}{n} \right )^{2}
-
Let 5 bservation are 1,3,8,1 and b
mean = \frac{\Sigma x_{i}}{5} = 5
1 + 3 + 8 + a + b = 25
a+ b = 13 ..... (1)
Variance (\sigma^{2}) = \frac{\Sigma x_{i}^{2}}{5} -2 5 = 9.20
Sigma x_{i}^{2} = 171
a2 + b2 = 97..... (2)
from (1) and (2)
(a+b)2 - 2ab = 97
ab = 36
a:b = 9:4 or 4:9
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Community Answer
The mean of five observations is 5 and their variance is 9.20. If thre...
Given Data:
- Mean of five observations = 5
- Variance of five observations = 9.20
- Three observations are 1, 3, and 8
Calculating the Sum of all Five Observations:
- We know that the sum of five observations is equal to the mean multiplied by the total number of observations.
- Sum of five observations = 5 * 5 = 25
- Sum of the three given observations (1, 3, and 8) = 1 + 3 + 8 = 12
- Sum of the other two observations = Total sum - Sum of given observations
- Sum of the other two observations = 25 - 12 = 13
Calculating the Variance of all Five Observations:
- Variance is the average of the squared differences from the mean.
- Variance = (sum of squares of differences from mean) / total number of observations
- Using the given variance, we can calculate the sum of squares of differences from the mean.
- Sum of squares of differences from the mean = Variance * Total number of observations
- Sum of squares of differences from the mean = 9.20 * 5 = 46
Calculating the Squared Differences of the Other Two Observations:
- Sum of squares of differences from the mean = (observation1 - mean)^2 + (observation2 - mean)^2 + (observation3 - mean)^2 + (observation4 - mean)^2 + (observation5 - mean)^2
- Substituting the given values and calculated values, we get:
- 46 = (1-5)^2 + (3-5)^2 + (8-5)^2 + (observation4-5)^2 + (observation5-5)^2
- Solving the above equation for the other two observations, we get:
- (observation4-5)^2 + (observation5-5)^2 = 27
Calculating the Ratio of the Other Two Observations:
- Let the other two observations be x and y.
- We have (x-5)^2 + (y-5)^2 = 27
- Since the observations are real numbers, the only possible solution is x=4 and y=9
- Therefore, the ratio of the other two observations is 4:9
Therefore, the correct answer is option 'A' (4:9).
- Mean of five observations = 5
- Variance of five observations = 9.20
- Three observations are 1, 3, and 8
Calculating the Sum of all Five Observations:
- We know that the sum of five observations is equal to the mean multiplied by the total number of observations.
- Sum of five observations = 5 * 5 = 25
- Sum of the three given observations (1, 3, and 8) = 1 + 3 + 8 = 12
- Sum of the other two observations = Total sum - Sum of given observations
- Sum of the other two observations = 25 - 12 = 13
Calculating the Variance of all Five Observations:
- Variance is the average of the squared differences from the mean.
- Variance = (sum of squares of differences from mean) / total number of observations
- Using the given variance, we can calculate the sum of squares of differences from the mean.
- Sum of squares of differences from the mean = Variance * Total number of observations
- Sum of squares of differences from the mean = 9.20 * 5 = 46
Calculating the Squared Differences of the Other Two Observations:
- Sum of squares of differences from the mean = (observation1 - mean)^2 + (observation2 - mean)^2 + (observation3 - mean)^2 + (observation4 - mean)^2 + (observation5 - mean)^2
- Substituting the given values and calculated values, we get:
- 46 = (1-5)^2 + (3-5)^2 + (8-5)^2 + (observation4-5)^2 + (observation5-5)^2
- Solving the above equation for the other two observations, we get:
- (observation4-5)^2 + (observation5-5)^2 = 27
Calculating the Ratio of the Other Two Observations:
- Let the other two observations be x and y.
- We have (x-5)^2 + (y-5)^2 = 27
- Since the observations are real numbers, the only possible solution is x=4 and y=9
- Therefore, the ratio of the other two observations is 4:9
Therefore, the correct answer is option 'A' (4:9).
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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer?
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The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer?.
The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :a)4 : 9b)6 : 7c)5 : 8d)10 : 3Correct answer is option 'A'. Can you explain this answer?.
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