The standard deviation of the weight in kg of the student of a class of 50 students was calculated to be 4.5 later on it was found that due to some fault in weighing machine the weight of each student was under measured by 0.5 kg the correct standard deviations of the weight will be?

Question

Answer

Explanation:

What is Standard Deviation?

Standard deviation is a measure of the amount of variation or dispersion of a set of values. It shows how much variation there is from the average (mean) value. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

Effects of Faulty Weighing Machine

In the given problem, the weight of each student was under-measured by 0.5 kg due to some fault in the weighing machine. This means that the recorded weight of each student was 0.5 kg lower than their actual weight. Therefore, the mean weight of the class would also be 0.5 kg lower than the actual mean weight.

How to Find Correct Standard Deviation?

To find the correct standard deviation, we need to adjust the recorded weights of the students by adding 0.5 kg to each weight. Then, we can calculate the new mean weight and the new standard deviation based on the adjusted weights.

Formula for Standard Deviation

The formula for standard deviation is:

s = sqrt [(Σ(xi - x)^2) / (n-1)]

where:

s = standard deviation

Σ = sum of

xi = each value in the data set

x = mean of the data set

n = number of values in the data set

Calculation

Let's assume that the mean weight of the class before adjustment was 60 kg, and the standard deviation was 4.5 kg. After adjusting the weights, the new mean weight would be:

60 + 0.5 = 60.5 kg

Now, we can calculate the new standard deviation using the formula:

s = sqrt [(Σ(xi - x)^2) / (n-1)]

where:

Σ(xi - x)^2 = sum of squared deviations from the mean

n = number of values in the data set = 50

Since we do not have the individual weights of the students, we cannot calculate the sum of squared deviations from the mean directly. However, we know that the standard deviation is a measure of the spread of the data, and adding a constant value to each data point does not change the spread. Therefore, we can use the following formula to adjust the standard deviation:

s' = s / k

where:

s' = new standard deviation

s = old standard deviation = 4.5 kg

k = adjustment factor = 1.0 + (0.5 / 60.5) = 1.008

Answer

There is no change sd because sd is affected by change scale but by change in origin

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