Compute all the measures of central tendency, dispersion and...

Compute all the measures of central tendency, dispersion and quartile position of the following ungrouped sample data. Then organize and graph the ungrouped data using an appropriate chart and table. 70 17 20 38 9 37 14 99 14 53 35 41 59 83 91 74 40 89 53 49 74 15 35 47 3 58 62 75 100 39 14 62 16 28 30 99 66 11 65 15 6 72 6 82 29 98 76 47 56 100 20 87 30 18 46 Table 1: Sample Data

Transcript

00:01 Hello everyone so this is the question that we have we have this set of data with us and we have to compute all the measures which are compute of central tendency compute measures of central tendency dispersion and quartile position now let's compute the measures of central tendency so it will cover main, median and mode.

00:55 So let's find mean first.

01:01 Or arithmetic mean you may call it.

01:06 So how do we give mean? we give it by a formula which is sum of all observations when divided by number observations.

01:29 The sum of observations in this data is 2672 divided by there are 55 because there is one two two three four five six seven eight nine ten and eleven and five one two three four five seven it would try eleven multiplied by five which is fifty five two six seven two divided by 55.

01:56 This gives me a mean of value of 48 .5 so this is my meet data which i have so let's find more mode is nothing but the data entry or the data entity used most or repeated most so are the frequency repeated the most number of times so mode is nothing but frequency repeated most number of times so here the mode is according to data is equal to 14 mode is 14 now let's come on to median so medium in order to find median i have to arrange the set of data which i have in ascending order so arrange the data set in ascending order.

03:14 So let us write the theta in ascending order.

03:18 So this would be 3, 6, 6, 11, 14, 14, 14, 15, 15 15, 15, 16, 17, 17, 18, 18, 20, 20, 20, 27, 29, 30, 30, 35, 37, 38, 39, 401, 46, 47, 49, 47, 49, 53, 56, 58, 59, 58, 59, 59, 50, 59, 58, 59, 62 65 66 70 72 74 75 66 70 72 72 75 76 86 82 83 87 89 91 95 98 99 99 99 99 99 and 100 100 so these are my 55 entries and as 55 entries i have which is an odd number so how to find a medium of median of an odd number value or terms? so it is given by the formula and plus one by n plus one divided by tweth term.

05:19 So here 55 plus 1 divided by 2oth term which is equal to 28th term or observation so the 28th term over here is 47 so median is equal to 47 right so let's move on to the other question that we have so median is 47 to dispersion so two of the question to dispersion.

06:02 Now to compute the measures of dispersion, i need to find range first, range of the data.

06:10 So, in order to find the range, i have to find the difference between the highest frequency in the data set, highest frequency, and the lowest frequency.

06:30 Lowest frequency so highest frequency over here if you have a look is hundred and the lowest is three so pretty easy hundred minus three which is equal to ninety now let's find variance so variance would be given by the formula submission of x i squared divided by n number of entities minus the mean square here x bar is denoted as mean n is number of frequencies data sets that we have data values data increase and submission of x i will square each and every data or the frequency that we have.

07:30 So this would give me a value for variance which is 1767767 when divided by 55 minus the mean which we have was mean was 48 .58 whole square.

07:51 So this would be equal to variance which is 8 .4.

08:01 4 .79.

08:07 So this is my proximate variance...

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