Compute the range, sample variance, and sample standard deviation for the following scores: 25,

Compute the range, sample variance, and sample standard...

Key Concepts

Range

The range is a basic measure of dispersion that indicates the spread of a dataset by calculating the difference between the maximum and minimum values. It provides a simple sense of the total spread within the data but is sensitive to outliers.

Sample Variance

Sample variance quantifies the degree of spread in a sample data set by calculating the average of squared deviations from the sample mean. It uses the formula that divides the sum of the squared differences by n-1, where n is the number of observations, to serve as an unbiased estimator of the population variance.

Sample Standard Deviation

The sample standard deviation is the square root of the sample variance, providing a measure of spread that is expressed in the same units as the original data. It offers insight into the typical distance of the data points from the sample mean and is crucial for understanding the variability within a dataset.

Transcript

00:01 Dear student, the question is that compute the range, simple variance and simple standard definition of the fulon score.

00:10 Here is the given score in the question.

00:13 Let's first find the range.

00:18 As we know that range means the maximum minus the minimum value in the data.

00:31 So by looking at the data we see that 41 is the maximum value and 25 is the minimum.

00:43 So let's subtract these two, we get 60.

00:47 So the range is 60.

00:54 Secondly, we have to find the simple variation.

00:57 For finding the simple variation, what we need is the formula for simple variation.

01:08 That is variance equals to summation of xi minus x all square divided by n minus 1.

01:34 Now here we can see that there are two things we have to find.

01:39 First is mean, simple mean and second is we have to subtract each of the xi value from the mean and then take square of it.

01:53 So let's first find the mean.

01:55 For finding the mean of this data, we simply add x bar equals to the data 25 plus 36 plus 41 plus 28 plus dot dot dot on the data and 31 plus 31.

02:31 And then we will divide it with the number of observation that is 60.

02:39 So the x bar will be equal to 505 divided by 16 that is equal to 31 .5625.

02:56 So simply the mean for it is mean equals to 31 .5625.

03:09 Now here we can see that we require the mean x bar and then xi value will be subtracted from it.

03:19 So let's do it...

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