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07 Jul 2025, 14:04
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Option C and Option D are the correct answers.
Before diving into solving the question lets understand the mentioned mentioned in it first and lets see what we need to find in order to answer the question.
The question begins by telling us that during a scientific experiment their has been some error while measuring the results and each of the error was affected by the same error and it needs to be adjusted in order to get the answer. Then it tells us that 'm ' is the correct result for each of the measurement and m = -0.5n + 10, where n is the original measurement which is incorrect then it moves forward and tells us the original measurement of average and standard deviation which are 7.3 and 2.9 respectively. And now the questions asks us to find the correct measurement of mean and standard deviation.
First to solve for the mean i.e. the average of the measurements, so as mentioned in the question original mean is 7.3 and original measurements are marked as n which we need to put into the formula i.e. m = -0.5n + 10 in order to find the correct measurement. So lets see by putting the value in the formula what will be our answer.
m = -0.5n + 10
m = -0.5*(7.3) + 10
m = -3.65 + 10
m = 6.35 (Option C)
So from here we get that the correct value of average is Option C i.e. 6.35.
Now lets move on to the second part of the question i.e. finding the correct Standard Deviation. Now here comes the tricky part because most of the people will make calculation mistake in this part of the question. Lets understand how and why.
Fist of all lets understand what is Standard Deviation. So, in simple terms Standard Deviation basically means the distance between the numbers and average of the set. And we all know that distance can never be negative as we as addition and deduction does not affect the Standard Deviation of the set. So equation find the correct Standard Deviation will m = l-0.5nl.
So as per the above discussion Correct Standard Deviation =>m = l-0.5*2.9l =>m = 1.45 (Option D)
Before diving into solving the question lets understand the mentioned mentioned in it first and lets see what we need to find in order to answer the question.
The question begins by telling us that during a scientific experiment their has been some error while measuring the results and each of the error was affected by the same error and it needs to be adjusted in order to get the answer. Then it tells us that 'm ' is the correct result for each of the measurement and m = -0.5n + 10, where n is the original measurement which is incorrect then it moves forward and tells us the original measurement of average and standard deviation which are 7.3 and 2.9 respectively. And now the questions asks us to find the correct measurement of mean and standard deviation.
First to solve for the mean i.e. the average of the measurements, so as mentioned in the question original mean is 7.3 and original measurements are marked as n which we need to put into the formula i.e. m = -0.5n + 10 in order to find the correct measurement. So lets see by putting the value in the formula what will be our answer.
m = -0.5n + 10
m = -0.5*(7.3) + 10
m = -3.65 + 10
m = 6.35 (Option C)
So from here we get that the correct value of average is Option C i.e. 6.35.
Now lets move on to the second part of the question i.e. finding the correct Standard Deviation. Now here comes the tricky part because most of the people will make calculation mistake in this part of the question. Lets understand how and why.
Fist of all lets understand what is Standard Deviation. So, in simple terms Standard Deviation basically means the distance between the numbers and average of the set. And we all know that distance can never be negative as we as addition and deduction does not affect the Standard Deviation of the set. So equation find the correct Standard Deviation will m = l-0.5nl.
So as per the above discussion Correct Standard Deviation =>m = l-0.5*2.9l =>m = 1.45 (Option D)
Bunuel
07 Jul 2025, 14:41
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We can plug the average value on the formula provided:
m = -0.5n + 10
So
m = -0.5*(7.3) + 10
m = -3.65 + 10
m = 6.35
When we have this modification in a list of values (multiplying the average per a constant and add/subtracting another constante) in the formate a*x + b, where x is the previous average, the "+b" does not influences the standard deviation. The "a*" term, on the other hand, modify the previous sd by multiplying the value by the "a" and taking the absolute value.
Therefore:
m = -0.5*(7.3) + 10
newSD = | -0.5*(previousSD) |
newSD = | -0.5*(2.9) |
new SD = | - 1.45 |
new SD = 1.45
Answers
Corrected Mean = 6.35
Corrected Standard Deviation = 1.45
m = -0.5n + 10
So
m = -0.5*(7.3) + 10
m = -3.65 + 10
m = 6.35
When we have this modification in a list of values (multiplying the average per a constant and add/subtracting another constante) in the formate a*x + b, where x is the previous average, the "+b" does not influences the standard deviation. The "a*" term, on the other hand, modify the previous sd by multiplying the value by the "a" and taking the absolute value.
Therefore:
m = -0.5*(7.3) + 10
newSD = | -0.5*(previousSD) |
newSD = | -0.5*(2.9) |
new SD = | - 1.45 |
new SD = 1.45
Answers
Corrected Mean = 6.35
Corrected Standard Deviation = 1.45
07 Jul 2025, 14:48
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Correction of each value: m = -0.5n + 10
Given mean of n values = 7.3
If all values are adjusted, actual mean will be 7.3*-0.5 + 10 = 6.35
S.D = (((v1-mean)^2 + (v2-mean)^2....(vn-mean)^2)/observations)^0.5
Each value will be adjusted by *-0.5. The adjustment of +10 will get neautralised. This means, actual SD will be old SD * 0.5 = 1.45
Corrected mean = 6.35
Corrected S.D. = 1.45
Given mean of n values = 7.3
If all values are adjusted, actual mean will be 7.3*-0.5 + 10 = 6.35
S.D = (((v1-mean)^2 + (v2-mean)^2....(vn-mean)^2)/observations)^0.5
Each value will be adjusted by *-0.5. The adjustment of +10 will get neautralised. This means, actual SD will be old SD * 0.5 = 1.45
Corrected mean = 6.35
Corrected S.D. = 1.45
Bunuel
