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The standard deviation for the data 7, 9, 11, 13, 15 is
- a)2.4
- b)2.5
- c)2.7
- d)2.8
Correct answer is option 'D'. Can you explain this answer?
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The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7...
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The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7...
To calculate the standard deviation for the given data, we need to follow the steps mentioned below:
Step 1: Find the Mean
- Add up all the given numbers: 7 + 9 + 11 + 13 + 15 = 55
- Divide the sum by the total number of data points: 55 / 5 = 11
The mean of the data is 11.
Step 2: Find the Deviation from the Mean
- Subtract the mean from each data point:
- Deviation for 7 = 7 - 11 = -4
- Deviation for 9 = 9 - 11 = -2
- Deviation for 11 = 11 - 11 = 0
- Deviation for 13 = 13 - 11 = 2
- Deviation for 15 = 15 - 11 = 4
Step 3: Square the Deviations
- Square each deviation:
- (-4)^2 = 16
- (-2)^2 = 4
- 0^2 = 0
- 2^2 = 4
- 4^2 = 16
Step 4: Find the Variance
- Add up all the squared deviations: 16 + 4 + 0 + 4 + 16 = 40
- Divide the sum by the total number of data points: 40 / 5 = 8
The variance of the data is 8.
Step 5: Find the Standard Deviation
- Take the square root of the variance: √8 ≈ 2.83
Rounding to one decimal place, the standard deviation for the given data is approximately 2.8.
Therefore, the correct answer is option 'D' - 2.8.
Step 1: Find the Mean
- Add up all the given numbers: 7 + 9 + 11 + 13 + 15 = 55
- Divide the sum by the total number of data points: 55 / 5 = 11
The mean of the data is 11.
Step 2: Find the Deviation from the Mean
- Subtract the mean from each data point:
- Deviation for 7 = 7 - 11 = -4
- Deviation for 9 = 9 - 11 = -2
- Deviation for 11 = 11 - 11 = 0
- Deviation for 13 = 13 - 11 = 2
- Deviation for 15 = 15 - 11 = 4
Step 3: Square the Deviations
- Square each deviation:
- (-4)^2 = 16
- (-2)^2 = 4
- 0^2 = 0
- 2^2 = 4
- 4^2 = 16
Step 4: Find the Variance
- Add up all the squared deviations: 16 + 4 + 0 + 4 + 16 = 40
- Divide the sum by the total number of data points: 40 / 5 = 8
The variance of the data is 8.
Step 5: Find the Standard Deviation
- Take the square root of the variance: √8 ≈ 2.83
Rounding to one decimal place, the standard deviation for the given data is approximately 2.8.
Therefore, the correct answer is option 'D' - 2.8.
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The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7d)2.8Correct answer is option 'D'. Can you explain this answer?
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The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7d)2.8Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7d)2.8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The standard deviation for the data 7, 9, 11, 13, 15 isa)2.4b)2.5c)2.7d)2.8Correct answer is option 'D'. Can you explain this answer?.
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