**MEAN: **

**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 **

** ,**

**MEDIAN**

**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**

**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**

**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)**

**Where;**

**l = lower limit of the class**

**h = size of the class interval (assuming all class sizes to be equal)**

**f**_{1 }**= frequency of the modal class**

**f**_{0 }**= frequency of the class preceding the modal class**

**f**_{2 }**= 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: –

******** 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= 4^{th} observation.

4^{th }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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