Statistical MeasuresIn this section we will take into consideration the an interpretation and calculation of miscellaneous statistical measures. Us will usage the following data set to perform the suggested calculations.Data Set: ( 121,144,169,196, )

## Measures the variation

Sum

Sum. The aggregate of a group of numbers. The formula is:Sum = , where the prize ∑ represents including all the data values.

You are watching: 121,144,169,196

0+121=121121+144=265265+169=434434+196=630630+0=630

Adding up the 5 numbers gone into we come at a amount of 630(In words: 6 hundred thirty )

Arithmetic typical (Simple Average)

Definition: the accumulation (sum) of every the data values divided by the variety of data points.Where µ represents the mean of a population, and also ∑ to represent the amount of all the data values, and also N to represent the variety of data values. If the data collection refers to a sample (part of a population), the calculation stays the same but the symbols room different. This is important due to the fact that it shows to anyone whether us are handling a populace or a sample. A data set always has a mean and it is unique.

Find the mean value

To uncover the typical value, divide the amount by the number of values.In ours case, we discovered in the previous step that the sum is 630 and we have the right to count the 5 values so:

Mean=630/5=126

Median

Definition: the middle (center) worth of a data set after the data has been i ordered it from low to high value. The is, 50% of the data values are below the median value and 50% the the data worths are over the average value. A straightforward formula deserve to be applied. The position (P) the the average is: P=. If n the variety of data points is odd, the median value is just one of the data points. If n is even, then the median is the median of the data worths directly below and over the position calculation. A data collection always has a median and also it is unique.

Find the typical value

To discover the typical value, we start by sorting Or arranging our number In ascending Or diminish order.

0,121,144,169,196

As we have an odd variety of numbers, our median is the center number in our sorted list.

Median=144(In words: one hundred forty-four )

Range

The number difference between the maximum and also minimum worths of a data set.R = best – minimum values

Find the Range

Using our sorted list of numbers 0,121,144,169,196 we subtract the very first (smallest/min) from the last (biggest/max) Range=196-0=196

VarianceDefinition: the typical of the squared distinctions from the median of a data set. The is a measure of the spread of a data set from the mean.

In probability theory and also statistics, variance actions how far a set of number is spread out out. A variance the zero indicates that all the values are identical.

Find the VarianceTo calculation the variance follow these steps:Now, for each number: subtract the Mean and square the an outcome (the squared difference).(0-126)2=15876(121-126)2=25(144-126)2=324(169-126)2=1849(196-126)2=4900Find the average of those squared differences.0+15876=1587615876+25=1590115901+324=1622516225+1849=1807418074+4900=22974

The sum of the 4 squared distinctions is 22974 We have the right to now calculate the Variance as 22974/4=5743.5

Standard DeviationDefinition: The square source of the variance. It steps the spread out of the data collection from the mean. Keep in mind that the unit measure up of the standard deviation is the same as the data se. The is, if the data is in feet the traditional deviation is also in feet. This is no true for the variance.

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In statistics, the traditional deviation (SD, also represented by the Greek letter sigma, σ) is a measure the is used to quantify the lot of sport or dispersion that a set of data values.