the mean is equal to 23.76471
the variance is equal to 23.3564
the standard deviation is equal to 4.832846096.
you can round your answers as needed.
you are basically using the same procedures for frequency tables with the additional step that you need to take the midpoint of each interval and use that as your data point.
the steps are:
find the midpoint of each interval and use that for each data point.
multiply each data point by its frequency
take the sum of the data points times their frequency and divide that by the sum of the frequencies.
that's your mean which is equal to 23.76471.
to find the standard deviation, do the following:
subtract the mean from each data point and then square it.
multiply that by the frequency.
take the sum of of that and then divide it by the sum of the frequencies.
that would be the population variance which is equal to 397.0588235 / 17 = 23.35640138 shown as 23.3564 in the spreadsheet.
take the square root of the population variance to get the population standard deviation.
i stressed that it was the population variance because the population variance and the sample variance are calculated differently.
the population variance is found by dividing by the sum of the frequencies.
the sample variance is found by dividing by the sum of the frequencies minus 1.
i'm assuming you're dealing with a population and not a sample from a population.
there is an online calculator you can use once you have found the midpoint of each interval.
that calculator can be found at http://knowpapa.com/sd-freq/
my inputs to that calculator are shown below:
my outputs from that calculator are shown below:
the results agree with my calculations in excel.
the primary thing to do is to find your data points by taking the midpoint of each interval and then using that for all further calculations.
let me know if you have any questions regarding this.