The Mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations.
The Median is a measure of Central tendency which gives the value of the middle-most observation in the data.
Ascending order. Then if n is odd, the median is the
If is even, then the medium will be the average of the
l = lower limit of median class
n =number of observation
cf = cumulative frequency of class preceding the median class
f = frequency of median class Data #DI
h= class size (assuming class size to be equal)
* 3 MEDIAN = MODE + 2 MEANs
A Mode is that value among the observations which occurs most often, that is, the value of the observations having the maximum frequency.
MODE = MEANS – 3(MEAN – MODE)
l = lower limit of the class
h = size of the class interval (assuming all class sizes to be equal)
f1 = frequency of the modal class
f0 = frequency of the class preceding the modal class
f2 = frequency of the class succeeding the modal class.
Ques 1: – Calculate mode for the following data: –
Answer; – As the frequency for class 30 – 40 is maximum. This class is also the modal class. Classes 20 – 30 are pre- modal and 40 – 50 are post – modal classes.
The mode is: – m
Ques 2: – Find the arithmetic mean, median and also mode of the following data:-
** MODE = MEAN – 3(MEAN – MODE)
= 34.5 – 3 ( 34.5 – 34.5 )
Ques 3: – Find the mean, median, also mode and range of the following data set:
Finding the mean:
First sum of numbers: 8+3+16+3+6+7+13 = 56
Then divide 56 by the total number of data points, 7,
and you get 8. Also The mean is 8.
Finding the median:
First put the numbers in ascending order: 3, 3, 6, 7, 8, 13, 16
Total number of data is 7. which is odd (n+1)÷2= 4th observation.
4th observation is 7.
The middle number is 7. There for the median is also 7.
Finding the mode:
Remember the mode is also the number that appears the most. It can help to put the numbers in order so we don’t miss anything: 3, 3, 6, 7, 8, 13, 16
number 3 appears twice and the rest of the numbers only appear once. The mode is 3.
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