Question

Find the mean and mode of the following frequency distributions.​

Answer 1

Answer:

it's quite simple

if you have enough time to solve it

although there are many formulas which give us direct values but I certainly don't acknowledge them

so I'll show evaluate the value by conventional methods

so first find MEDIAN (obviously because it's easy to find)

So MEDIAN is the middle most observation in the total observations , so here we can see that in the table given the total observations are 25 (basically in this case OBSERVATIONS is NO. OF STUDENTS and roughly OBSERVATIONS means FREQUENCY) so if you doubt try counting it , so that wise if total observations are 25 then the middle most observation will be 13th one , so by the help of table , the mark which represent 13th observation is 22 , so the MEDIAN = 22

So now let's find mean ,

so mean is (total sum of observations / total observations)

So by calculating I found the total sum of observations as 533 and initially we had found the total observations as 25 , so now simply divide 533 with 25 i.e. 533 ÷ 25

so 533/25 = 21.32

THEREFORE , MEAN = 21.32

So now , when we have found MEAN and MEDIAN we can easily find out MODE , because

MODE = (3×MEDIAN) - (2×MEAN)

THEREFORE , MODE = (3×22) - (2×21.32)

THEREFORE , MODE = 66 - 42.64

MODE = 23.36

hope it helps

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