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The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.?
Most Upvoted Answer
The following figures are the heights in cm of 7 children chose at ran...
Calculating the Mean Height of Children
Direct Method:
- Add up all the heights: 64+59+67+69+65+70+68 = 462
- Divide the sum by the number of children: 462/7 = 66
- The simple arithmetic mean of the heights is 66cm.
Assumed Mean Method:
- Choose an assumed mean, typically a value close to the actual mean. Let's assume the mean height is 65cm.
- Calculate the deviation of each height from the assumed mean: -1,-6,2,4,0,5,3
- Square each deviation: 1,36,4,16,0,25,9
- Add up the squared deviations: 91
- Divide the sum by the number of children: 91/7 = 13
- Take the square root of the result: √13 = 3.61
- Multiply the square root by a constant factor, typically 0.6745 for 7 observations: 3.61 x 0.6745 = 2.43
- Add the assumed mean to the product: 65 + 2.43 = 67.43
- The simple arithmetic mean of the heights is 67.43cm.
Step Deviation Method:
- Choose a convenient step value, let's use 2.
- Find the mean of the heights: (64+59+67+69+65+70+68)/7 = 66
- Calculate the deviation of each height from the mean and divide by the step value: -1/-1, -7/-2, 1/2, 3/2, -1/2, 4/2, 2/2
- Simplify the fractions: 1, 3.5, 0.5, 1.5, -0.5, 2, 1
- Add up the simplified deviations: 8
- Multiply the sum by the step value: 8 x 2 = 16
- Divide the product by the total number of observations: 16/7 = 2.29
- Add the result to the mean: 66 + 2.29 = 68.29
- The simple arithmetic mean of the heights is 68.29cm.
Direct Method:
- Add up all the heights: 64+59+67+69+65+70+68 = 462
- Divide the sum by the number of children: 462/7 = 66
- The simple arithmetic mean of the heights is 66cm.
Assumed Mean Method:
- Choose an assumed mean, typically a value close to the actual mean. Let's assume the mean height is 65cm.
- Calculate the deviation of each height from the assumed mean: -1,-6,2,4,0,5,3
- Square each deviation: 1,36,4,16,0,25,9
- Add up the squared deviations: 91
- Divide the sum by the number of children: 91/7 = 13
- Take the square root of the result: √13 = 3.61
- Multiply the square root by a constant factor, typically 0.6745 for 7 observations: 3.61 x 0.6745 = 2.43
- Add the assumed mean to the product: 65 + 2.43 = 67.43
- The simple arithmetic mean of the heights is 67.43cm.
Step Deviation Method:
- Choose a convenient step value, let's use 2.
- Find the mean of the heights: (64+59+67+69+65+70+68)/7 = 66
- Calculate the deviation of each height from the mean and divide by the step value: -1/-1, -7/-2, 1/2, 3/2, -1/2, 4/2, 2/2
- Simplify the fractions: 1, 3.5, 0.5, 1.5, -0.5, 2, 1
- Add up the simplified deviations: 8
- Multiply the sum by the step value: 8 x 2 = 16
- Divide the product by the total number of observations: 16/7 = 2.29
- Add the result to the mean: 66 + 2.29 = 68.29
- The simple arithmetic mean of the heights is 68.29cm.
Community Answer
The following figures are the heights in cm of 7 children chose at ran...
Direct Method
Mean =total number of observation/number of observation
Mean = 64+59+67+69+65+70+68/7
Mean = 462/7
Mean = 66
Mean =total number of observation/number of observation
Mean = 64+59+67+69+65+70+68/7
Mean = 462/7
Mean = 66
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The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.?
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The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.?.
The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following figures are the heights in cm of 7 children chose at random. 64,59,67,69,65,70,68 Calculate the simple arithmetic mean of the heights by Direct method , assumed mean method and Step deviation method.?.
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