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MEAN:

The Mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations.

Mean 

Mean @focuscivil,     Mean

Mean

MEDIAN

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

Median

Where;

 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

MODE

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)

mode focuscivil

Where;

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:-

Answer: –

Mean

** MODE = MEAN – 3(MEAN – MODE)

         =  34.5  – 3 ( 34.5 – 34.5 )

         =  34.5

Ques 3: – Find the mean, median, also mode and range of the following data set:

8,3,16,3,6,7,13

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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