determine the mean,variance and standard deviation for the following data

100,133,87,101,88,98,145,52,83,120

asked by guest
on Nov 19, 2024 at 5:13 am



You asked:

Find the arithmetic mean, sample variance, and sample standard deviation of the following data: \(100, 133, 87, 101, 88, 98, 145, 52, 83, 120\)

MathBot Answer:

The arithmetic mean (often referred to as the average, arithmetic average, or the mean) is a value indicating the typical value of the elements in a given data set. It is computed by summing the numbers in a data set and dividing that number by the amount of numbers in the set.\[\overline{x} = \frac{1}{n}\sum_{i=1}^{n}{x_i}\] where \(x_i\) represents the individual values and \(n\) represents the number of values in the data set.


The arithmetic mean of \(100, 133, 87, 101, 88,...\) is \(\frac{1007}{10} = 100.7\).

The sample variance measures the spread of values around the arithmetic mean in a data set. It is calculated with the formula: \[S^2 = \frac{1}{n-1}{\sum_{i=0}^{n}{(x_i - X)^2}}\] where \(x_i\) represents the individual values, \(n\) represents the number of values in the data set, and \(X\) represents the arithmetic mean.


The sample variance of \(100, 133, 87, 101, 88,...\) is \(713.344444444444\).

The sample standard deviation is a measure of the spread of values around the arithmetic mean in a data set. It is the square root of the sample variance, and it is calculated with the formula: \[S = \sqrt{\frac{1}{n-1}{\sum_{i=0}^{n}{(x_i - X)^2}}}\] where \(x_i\) represents the individual values, \(n\) represents the number of values in the data set, and \(X\) represents the arithmetic mean.


The sample standard deviation of \(100, 133, 87, 101, 88,...\) is \(26.708508839777\).

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