Measures of central tendency

There are 3 common measures of central tendency
1. Mean
2. Median
3. Mode

---

Mean :
The mean (or average) of number of observations is the sum of the values of observations divided by the total number of observations.
It is denoted by `bar x` and read as x bar.

So if `x_1,x_2,...,x_n` are n observations, then mean is

`bar x=(x_1+x_2+...+x_n)/n=(sum x)/n`

Here greek symbol `sum` (sigma) is used for summation.

---

1. Find the Mean of `3,13,11,15,5,4,2`

Solution:
Mean `bar x=(sum x)/n`

`=(3+13+11+15+5+4+2)/7`

`=53/7`

`=7.5714`

---

2. Find the Mean of `10,50,30,20,10,20,70,30`

Solution:
Mean `bar x=(sum x)/n`

`=(10+50+30+20+10+20+70+30)/8`

`=240/8`

`=30`

---

3. Find the Mean of `69,66,67,69,64,63,65,68,72`

Solution:
Mean `bar x=(sum x)/n`

`=(69+66+67+69+64+63+65+68+72)/9`

`=603/9`

`=67`

---

If values of observations are large, then to simplify calculation, Assume any number A and subtract it from all the observations.
Then mean is `bar x=A+(sum d_i)/n`, where `d_i=x_i-A`

4. Find the Mean of `69,66,67,69,64,63,65,68,72`

Solution:

x	`d=x-A=x-65`
69	4
66	1
67	2
69	4
64	-1
63	-2
65	0
68	3
72	7
---	---
`n=9`	`sum d=18`

`bar x=A+(sum d_i)/n`
`=65+18/9`
`=65+2`
`=67`

---

---