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09 Jun 2020, 01:37
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Visual solutions is the fastest method to solve this question.
Take 77 as baseline and draw the following number line
Averages 65--------77-----80
Distance -12 -------- 0 ----- +3
Weights 4 -------- 5 ----- 6
Total Distance -48 ------- 0 ------ +18
Distribute the value of total distance from the average into total observations (15):
(-48 + 18 + 0 ) / 15 = -2
Hence the average will be 2 less than our baseline 77:
77-2 = 75
ANS B
Take 77 as baseline and draw the following number line
Averages 65--------77-----80
Distance -12 -------- 0 ----- +3
Weights 4 -------- 5 ----- 6
Total Distance -48 ------- 0 ------ +18
Distribute the value of total distance from the average into total observations (15):
(-48 + 18 + 0 ) / 15 = -2
Hence the average will be 2 less than our baseline 77:
77-2 = 75
ANS B
29 Jun 2020, 08:34
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Please solve this Question both in Details/with Basics and Shortcuts
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. If the average score for the three classes combined is 75 what is the ratio of the numbers of students in each class who took the test?
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A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. If the average score for the three classes combined is 75 what is the ratio of the numbers of students in each class who took the test?
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02 Jul 2020, 02:48
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MahmudulRonee
Understand the concept first: if you have
First observation = 10
Second observation = 10
Third observation = 13
Average = 11
1st method - weighted average
\(\frac{(10 x 2 + 13) }{ 3} = 11\\
\)
2nd method - baseline and visual solution
According to this method, to calculate an average out of multiple observations, you need to calculate the distance of every observation from whatever point you choose as the baseline on the number line that you create (always try to choose a convenient point) and then divide the total distance by the number of observations. What you will find is the distance of the average of the observations from the point that you had originally chosen as the baseline.
In the above-mentioned case we could choose 10 as the baseline:
Observations: 10-------13
Distance from baseline: 0-------3
Number of observations: 2------1
Total difference from baseline = 2x0 +3x1 = + 3
Distance of the average of the observations from baseline = + 3 / 3 = +1
Average = baseline + difference = 10 + 1 = 11
Basically, rather than calculate the weighted average of observations, a calculus that might be time-consuming, you calculate the weighted average of the distances of observations from one determined baseline. The same approach can be used in the problem that you have mentioned. I have simply chosen one of the numbers cited in the text to reduce one of the distances from the baseline (77) to zero, thus simplifying calculations.
*Note: number of observations = weight
Kudos are well accepted if you found my explanation useful
Understand the concept first: if you have
First observation = 10
Second observation = 10
Third observation = 13
Average = 11
1st method - weighted average
\(\frac{(10 x 2 + 13) }{ 3} = 11\\
\)
2nd method - baseline and visual solution
According to this method, to calculate an average out of multiple observations, you need to calculate the distance of every observation from whatever point you choose as the baseline on the number line that you create (always try to choose a convenient point) and then divide the total distance by the number of observations. What you will find is the distance of the average of the observations from the point that you had originally chosen as the baseline.
In the above-mentioned case we could choose 10 as the baseline:
Observations: 10-------13
Distance from baseline: 0-------3
Number of observations: 2------1
Total difference from baseline = 2x0 +3x1 = + 3
Distance of the average of the observations from baseline = + 3 / 3 = +1
Average = baseline + difference = 10 + 1 = 11
Basically, rather than calculate the weighted average of observations, a calculus that might be time-consuming, you calculate the weighted average of the distances of observations from one determined baseline. The same approach can be used in the problem that you have mentioned. I have simply chosen one of the numbers cited in the text to reduce one of the distances from the baseline (77) to zero, thus simplifying calculations.
*Note: number of observations = weight
Kudos are well accepted if you found my explanation useful
