## Seven Fundamentals of Stats

**Mean** is average of numbers. E.g. 3,5,7,9 It’s mean would be 6. Another E.g. 1,1,3,3 It’s mean equal to 2.5. So question may arise how we calculate mean. It’s first statistical formula which a person learn in Grade I.

**Step by Step**

- Sum up all the observations
- Divide with number of observations(N)

**Mode** is a number which appear most often in the set. E.g 2,21,23,21,22,24 It’s Mode would be 21. Another E.g. 1,1,22,3,3 It’s mean is bimodal mean two modes in a set, 3 & 1.

**Step by Step**

- Most Repeating number exists in data set.

**Median** first rearrange the order then check the middle value. E.g. 1,5,3. We are rearranging its order 1,3,5 and then we find out that 3 is the middle value.

In case of set consists of even number 1,2,3,4,5,6,7,8,9,10 then we take average of fifth and sixth values that would be our mean value. 5+6 =11/2 = 5.5

**Variance** is deviation of numbers from its mean value. In stock market, numbers fluctuate rapidly due to shift in demand/supply of stocks.

It’s quite simple to calculate variance of any thing. We actually need to understand the formula. As variance is related to mean, so obviously it exists into formula. So we first calculate the mean, then subtract mean from every number(item) then take square of each values and then we sum up all these values and finally divide with N (Number of items).

**Step by Step**

- Take Mean/Average
- Deduct mean from every individual values
- Then take square of values which we obtain from step 2
- Sum up all values which we get from step 3
- Divide it by Number of observation

Variance is fluctuations of stock prices from its intrinsic value(Fair Value) which we calculate through many different ways, E.g. Dividend Discount model.

**Standard Deviation** is square root of Variance. It means that Standard deviation is always lower than its variance.

**Step by Step**

- Take Mean/Average
- Deduct mean from every individual values
- Then take square of values which we obtain from step 2
- Sum up all values which we get from step 3
- Divide it by Number of observation
- Take square root of value obtain from step 5

**Co Variance **

For calculating covariance, both data set should contain same number of observations.

E.g If stock A has positive returns while Stock B and vice versa then there is positive covariance.

**Step by Step**

- Take Average of both data sets X & Y
- Deduct Mean from Observations
- Deduct X Mean from Xth Observations
- Deduct Y Mean from Yth Observations

- Then Multiply Step 2.a &2.b results
- Accumulate all numbers obtained from step 3
- Step 4 results should be divide by number of observations.

**Correlation**

It’s standardized form of Co variance. It tell us the direction and strength of relationship in between two variables.

Correlation coefficients are always in between -1 to 1. -1 depicts negative correlation while +1 represent positive correlation. And O shows that there is no correlation among two data set or variables. E.g If Karachi Stock Exchange Index rises, So Lahore and Islamabad Index will rise. Which gave us the example of positive correlation. And If Gold prices rises there is possibility of fall in Pakistani Stock Exchanges which describe negative correlation.

**Step by Step**

- Calculating the Covariance of X & Y
- Divide the obtain number from step by Standard deviation of X and Standard deviation of Y.