Bollinger band--the measure of volatility.

Bollinger band-
This theory is developed by John Bollinger. It measures the volatility of stock under observation. It predicts oversold & overbought conditions of stock.
It consists of three lines
1. The simple moving average (SMA) over a predetermined period (n) is plotted on stock price chart.
2. The upper & lower bollinger band lines are calculated by adding & subtracting standard deviation from simple moving average price(SMA).
As standard deviation uses average of price range,hence SMA line is used in Bollinger band,instead EMA line can also be used.
Generally  20-day SMA & 2 standard deviation above & below SMA line are plotted.
If the period of SMA is changed, the standard deviation should be changed accordingly. If we use 50-period SMA, standard deviation should be 2.1,& if we are using 10-period SMA standard deviation used should be 1.9.
The look-back period for SMA & standard deviation should be same.
What is standard deviation -
Standard deviation tells by how much the values of a given set differs from mean(average) of a given set of values.
Low standard deviation denotes values of a given set are close to mean (average)  of a given set.
High standard deviation denotes values are more spread from the mean(average).
How to calculate standard deviation -
The standard deviation is calculaed by the following formula-
SD = √1/N*€(x1-u) ²
Where
          N= total number of values in a given set.
x1,x2,x3...= values of given set.
           u= mean(average) of values of a given set.
The mean value(u) is subtracted from each value indivisually& then summation of all these values are taken, then dividing by number of values, it's square root is taken.
Now-a-days, standard deviation calculator is available on internet & not needed to calculate it manually.
How to calculate Bollinger band-
The billing band is calculated by following formula,
Middle line(20-day SMA line) = addition of previous 20 closing prices of stock price /20
Upper line= 20-day SMA + 2*(standard deviation) 
Lower line=20-day SMA-2*(standard deviation) 
The region between middle line & upper line is called upper band, while the region between middle line & lower line is called lower band.

W-bottom pattern -
It occures before strong uptrend. It contains two lows within the band, second of which may be lower than the first.
The first low may be slightly below the lower band, then stock proceeds above, may go above middle line(SMA line), then reverses back making lower low than the first, but rests on the lower band & then proceeds to overbought condition.

M-top pattern-
It occurs before strong downtrend. In this pattern, the first high can be higher or lower than the second top.
The first high may be created above the upper band, then price reverses & touches or go below middle line, then again the second top is formed but fails to touch the upper band & then price proceeds to oversold region.

In strong uptrend or downtrend the stock price may remain above or below the upper or lower band respectivally for a certain period, which may create confusion to traders.
When the band shrinks, it does mean, the closing prices are near to average value(SMA line)  because standard deviation is used to calculate the upper & lower bands. It indicates volatility is less. Less volatility suggests variation in stock price is less, indicating stock will remain sideways.
On the other hand, when bollinger band expands, it indicates the closing prices are far spread out from mean(SMA line), volatility is increasing. Volatility is increasing means more variation in stock price.
The demerit of bollinger band is that, it predicts the volatility but unable to predict the direction that is uptrend or downtrend.
Hence bollinger band should not be used alone,but should be coupled with other indicators.