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9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percentageof the 8 number's are within 1 standard deviation?
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percentageof the 8 number's are within 1 standard deviation?
- a)90%
- b)85%
- c)80%
- d)75%
- e)70%
Correct answer is option 'D'. Can you explain this answer?
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9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5The mean and the standard de...
10-0.3=9.7 10+0.3=10.3 the number within 1 standard deviation should be between 9.7-10.3 so there are six numbers within 1 standard deviation 6/8=75%
Answer is D
Answer is D
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9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5The mean and the standard de...
Mean and Standard Deviation
The given set of numbers are: 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5
The mean of these numbers = (9.4 + 9.9 + 9.9 + 9.9 + 10.0 + 10.2 + 10.2 + 10.5)/8 = 10
The standard deviation can be calculated using the formula:
σ = √[Σ(x-μ)²/N]
where σ is the standard deviation, x is the individual data point, μ is the mean, and N is the total number of data points.
Plugging in the values, we get:
σ = √[((9.4-10)² + (9.9-10)² + (9.9-10)² + (9.9-10)² + (10-10)² + (10.2-10)² + (10.2-10)² + (10.5-10)²)/8] = 0.3
Percentage within 1 Standard Deviation
To find out the percentage of the numbers within 1 standard deviation of the mean, we need to find out the range of values that lie within one standard deviation from the mean.
In this case, one standard deviation from the mean (10) would be:
10 + 0.3 = 10.3
10 - 0.3 = 9.7
Therefore, the range of values within one standard deviation from the mean is 9.7 to 10.3.
Out of the 8 numbers given, 6 numbers fall within this range. Therefore, the percentage of numbers within 1 standard deviation is:
(6/8) x 100% = 75%
Hence, the correct answer is option D (75%).
The given set of numbers are: 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5
The mean of these numbers = (9.4 + 9.9 + 9.9 + 9.9 + 10.0 + 10.2 + 10.2 + 10.5)/8 = 10
The standard deviation can be calculated using the formula:
σ = √[Σ(x-μ)²/N]
where σ is the standard deviation, x is the individual data point, μ is the mean, and N is the total number of data points.
Plugging in the values, we get:
σ = √[((9.4-10)² + (9.9-10)² + (9.9-10)² + (9.9-10)² + (10-10)² + (10.2-10)² + (10.2-10)² + (10.5-10)²)/8] = 0.3
Percentage within 1 Standard Deviation
To find out the percentage of the numbers within 1 standard deviation of the mean, we need to find out the range of values that lie within one standard deviation from the mean.
In this case, one standard deviation from the mean (10) would be:
10 + 0.3 = 10.3
10 - 0.3 = 9.7
Therefore, the range of values within one standard deviation from the mean is 9.7 to 10.3.
Out of the 8 numbers given, 6 numbers fall within this range. Therefore, the percentage of numbers within 1 standard deviation is:
(6/8) x 100% = 75%
Hence, the correct answer is option D (75%).
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