measures of variability are the spread of values about the mean these are smaller dispersion of scores arising from the comparison often indicates more consistency and reliability it consists of range average deviation variance and standard deviation range is the difference between the largest and the smallest scores this is the formula used r is equal to h minus l where r represents the range h is the highest score and l is the lowest score so let us take this a given given the scores of the following grade 7 students 43 46 40 39 45 42 47 50 49 39 find the range so just simply write the formula then from our given just identify the highest score so in this case it's 50. then the lowest score is 39 so you replace it in our formula then subtract them and that is 11 so this will be our range average deviation gives a better approximation compared to range the formula used is a d is equal to summation of the absolute value of x minus mean all over n where a d is the symbols used to represent average deviation x is the individual score x bar is the mean and capital n is the number of scores so we will be using the same data to solve for the average deviation before we can use the formula in average deviation we need first to set up a table with four columns in our first column we're going to write the given data so then at the end you're going to add all the a number of scores 1 2 3 4 5 6 7 8 9 10. so this capital letter n which represents the number of scores that is 10. then to fill out the second data that the second column that is the mean recall that in solving for mean we will just simply get the sum of all the scores divided by the number of scores so these are the given we'll just add them then divided by the number of scores which is 10 so the sum of the numerators 440 divided by 10 and that is 44 and that will be our mean so we're going to write it in our second column now to get the or to fill out the third column so we will just simply subtract whatever the x or the scores minus the mean so for this row right here we will just subtract 43 minus 44 and that is negative 1. in the second row 46 minus 44 that is positive 2 and so on and so forth then after that to fill out the fourth column so we're going to get the absolute value of the third column so when you say absolute value the number or that is the distance of the number to zero in a number line so when you say distance it is always positive therefore the absolute value of negative one is positive one absolute value of a positive number which is positive 2 is still a positive so that is positive 2. so all the numbers here in this data are all positive so negative 4 that is positive 4 positive 5 positive 1 positive 2 positive 3 positive 6 positive 5 and positive 5. and lastly we're going to sum them up because in our in the numerator of our formula we're going to get its summations it means we're going to sum them up and that is equal to 34 and this is our numerator so we are now ready to use the formula so we'll just simply replace the numerator with 34 and the denominator with 10. then 34 divided by 10 that is 3.4 and this will be our average deviation next is the variance it measure it measures how far each number in the set is from the mean this is the formula sigma squared is equal to summation of quantity x minus mean squared all over n wherein sigma squared is a symbol is the symbol that represents variance commonly and x here represents the individual score x mean is the x bar is the mean capital n is the number of scores so we're going to use the same data to solve for the variance we will be preparing the same table with the same symbols because notice that in solving for average deviation the formula of average deviation and variance are almost similar except in the fourth column so instead of getting the absolute value we're going to square the third column so that we can get the fourth column so it means there's no problem with the first second and third column we'll just fill them out then to square for the third column so negative one squared that is 2 squared that is 4 negative 4 squared that is 16 and so on and so forth then find their sum because we need to get the summation of the fourth column so if we're going to add them all that is 146 and we are now ready to use the formula in finding the variance after preparing the table so we'll just simply divide them 146 divided by the n which is 10 and that is 14.6 and this will be our variance by the way this symbol right here which is sigma this is another greek letter okay so and it is read as sigma last the standard deviation it provides some idea about the distribution of scores around the mean so this is the symbol or this is the formula used sd is equal to square root of the summation of x minus or quantity x minus mean squared all over n wherein sd represents the standard deviation x is the individual score x bar is the mean capital n is the number of scores notice that the radicand or the number inside the radical sign is actually the variance so the difference between the formula of the variance and the standard deviation is in standard deviation we just added the radical sign to get the square root of the variance so it means if our given is the same we will be preparing also the same table with the same content all right so after preparing this table we are now ready to use the formula in finding the standard deviation all right so our numerator here is the summation of quantity x minus mean squared and that is 146. then our n here we will replace it with 10 then 146 divided by 10 that is 14.6 actually this 14.6 was our uh variance a while ago but since we are looking for the standard deviation we need to get its square root so the square root of 14.6 so using calculator that is 3.82 and that will be our standard deviation