Friday, July 27, 2012

Standard deviation and Variance


Standard Deviation and Variance

Deviation just means how far from the normal

Standard Deviation

The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"

Variance

The Variance is defined as:
The average of the squared differences from the Mean.
To calculate the variance follow these steps:
  • Work out the Mean (the simple average of the numbers)
  • Then for each number: subtract the Mean and square the result (the squared difference).
  • Then work out the average of those squared differences. (Why Square?)

Example

You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:

Answer:

Mean =  
600 + 470 + 170 + 430 + 300
  =  
1970
  = 394
5
5
so the mean (average) height is 394 mm. Let's plot this on the chart:
Now, we calculate each dogs difference from the Mean:
To calculate the Variance, take each difference, square it, and then average the result:
So, the Variance is 21,704.
And the Standard Deviation is just the square root of Variance, so:
Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)

And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean:
So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small.
Rottweilers are tall dogs. And Dachshunds are a bit short ... but don't tell them!

But ... there is a small change with Sample Data

Our example was for a Population (5 dogs were the entire number of dogs we were interested in).
But if the data is a Sample (a selection taken from a bigger Population), then the calculation changes!
When you have "N" data values that are:
  • The Population: divide by N when calculating Variance (like we did)
  • A Sample: divide by N-1 when calculating Variance
All other calculations stay the same, including how we calculated the mean.
Example: if our 5 dogs were just a sample of a bigger population of dogs, we would divide by 4 instead of 5 like this:
Sample Variance = 108,520 / 4 = 27,130
Sample Standard Deviation = √27,130 = 164 (to the nearest mm)
Think of it as a "correction" when your data is only a sample.

Formulas

Here are the two formulas, explained at Standard Deviation Formulas if you want to know more:

The "Population Standard Deviation":
 
The "Sample Standard Deviation": 
Looks complicated, but the important change is to
divide by N-1 (instead of N) when calculating a Sample Variance.


*Footnote: Why square the differences?

If we just added up the differences from the mean ... the negatives would cancel the positives:
 
4 + 4 - 4 - 40
4
So that won't work. How about we use absolute values?
 
|4| + |4| + |-4| + |-4|  =  4 + 4 + 4 + 4  = 4
44
That looks good, but what about this case:
 
|7| + |1| + |-6| + |-2|  =  7 + 1 + 6 + 2  = 4
44
Oh No! It also gives a value of 4, Even though the differences are more spread out!
So let us try squaring each difference (and taking the square root at the end):
 
42 + 42 + 42 + 42644
44
 
72 + 12 + 62 + 22904.74...
44
That is nice! The Standard Deviation is bigger when the differences are more spread out ... just what we want!
In fact this method is a similar idea to distance between points, just applied in a different way.
And it is easier to use algebra on squares and square roots than absolute values, which makes the standard deviation easy to use in other areas of mathematics.

Wednesday, July 25, 2012

Why Reforms are so important to a nation


For India to try to get back on the growth path the following may need to happen
 
1)Inflation moderates
  
2)Interest rates soften
  
3)Growth picks up
  
For this to happen, the reform process needs to be re-kindled. People are talking about renewing reforms but why are reforms vital?

Let's say there is a small factory that is manufacturing goods and services.
The population of the town buys everything from this factory. As the population grows, the demand for goods also grows. Naturally, the factory raised prices because of the excess demand. This is how inflation steps in.

So how does one fight inflation and bring prices down?
One way may be to reduce the amount of money people have so that they buy less.
To make this happen the Central Bank will increase interest rates.
This way, money is less and prices are controlled.

But people may not be satisfied because they cannot buy much.
But if money is supplied cheaply, prices could go up and inflation could be back.
So what does the government do?

The government may need to make it easy for people to set up more factories and increase supply.

To set up more factories, entrepreneurs would need
 
1)Land
  
2)Good quality people
  
3)Reasonably cheap capital
  
4)Good infrastructure
  
In order to make the above available the government has to initiate reforms as explained:-
 
Land: To get land, the government has to make policies so that both buyer and seller of land are happy.
  
Labour: To get good people, the government has to make policies that will encourage entrepreneurs to set up educational and vocational colleges. This would also include FDI in the Education sector. Since we need to be efficient and competitive with the rest of the world, our labour needs to be productive. For this to happen, we need Labour Reforms.
  
Capital: To get reasonably cheap capital the government can do one of the following:-
  
 1. Frame policies to encourage people to invest so that capital is formed. However, people will invest if they have sufficient funds and if they are optimistic about the future. To have adequate funds, money should be available cheaply which means interest rates should be low. But if interest rates are low without commensurate economic production, inflation is likely to step in. Nevertheless reducing interest rates can spur investments.
  
 2. Frame policies that attract foreigners to invest in India. When foreign capital comes in, the value of the rupee goes up and inflation is kept at bay. With inflation at bay, the government can take measures to reduce interest rates. However, the profits arising out of foreign investments have to be shared with them. Either people share and move forward or stay standstill. Hence the need of reforms in the retail sector such as FDI in retail.
  
Infrastructure
  
 To be competitive, the manufacturer may need to be efficient; gets supplies in time and can deliver finished goods in time and needs to hold minimum inventory. This is possible on the back of good infrastructure like roads and railways, storehouses, refrigerated vans etc. For infrastructure to come up, we need land reforms so that people are clear what they will get when they hand over their land for infrastructure projects.
  
So when we have reforms in place, more factories will come up. When more factories come up, the country will produce more goods. When more goods are produced, more money can be printed without losing value.

When more money is printed, the interest rates can be reduced. When interest rates are reduced more entrepreneurs jump into the fray creating more production and more jobs. With more jobs, people have more money and are in a good position to consume the additional production. This gives rise to more investment and thereby a virtuous cycle kicks in.

With adequate supply, inflation is kept at bay even as people have cheap money for investment and for consumption. With interest rates low, inflation low, value of rupee stable, high production, the GDP of the country improves. With higher GDP, more jobs and prosperity in place, the tax collection increases. With higher taxes from higher GDP the situation turns win – win.

People don't mind paying more taxes because they are earning more. Higher taxes help the government keep its fiscal deficit in check. In the meanwhile, the government is in a good position to invest in bigger infrastructure projects and improve the productivity of the nation.

The moot point of the above explanation is that if the country wants to get a glimpse of utopia, it must reform its policies to infuse efficiency and productivity in the system.

Wednesday, July 11, 2012

CEO’s morning meetings


More often than not, companies tend to attribute downslide in business to external factors. My own experience suggests that it is mostly on account of internal factors that a company is not able to align itself to emerging needs of customers, product ranges and pricing of products, leading to downslide. Often leadership keeps managing today’s need with yesterday’s methodology and mindset. They are found wanting to change the prevailing culture of excessive bureaucracy, risk aversion, turf war between different functions, lack of coordination and insensitivity to communicate with customers and employees. The internal factors that support status quo are the biggest barriers to innovation and hassle free service. As Einstein said, “We cannot solve problems by using the same kind of thinking we used when we created them.”
One of the key challenges in pursuing a transformation agenda is to improve the prevailing internal environment characterized by constraints. Everyone in the management, especially at the top, has to learn the new habits of collaboration. In the competitive reality, where speed very often determines the business outcome, our traditional ways of working and communication style could be the biggest handicaps in our transformational program. It is like pushing a giant wheel. No matter how gifted a leader is, the organizational transformation cannot be successful without the support, engagement and commitment of the top team.
The top management needs to pursue the change agenda with grit and determination. They need to see the larger picture, pull together as a team, reinvent themselves and work in coordination with each other, to deliver results. Transformation program will yield good results when the top team thinks together, acts in unison and delivers on time.. Rudolf Giuliani, the legendary Mayor of New York city during the 9/11 crisis, used collective genius of key functionaries by organizing morning meetings with various departmental heads such as health, operations, fire, sanitation to effectively coordinate the successful running of the city post-terrorist attacks.
In the transformation program, one of my major challenges was to rid the corporate office of its culture of red-tapism, finger pointing, lack of accountability and ineffective communication, which affected our business relationship with customers, resulting in negative business outcomes. The need was to move on to a facilitative and open culture mode in shaping a new future and identity for the bank.
To bring radical changes in the way we do business, I introduced the system of ‘morning meetings’ as powerful means of constructively engaging the top management team to pursue the fast track transformation agenda with vigor and commitment. There was certain discipline about these meetings. We met for an hour from 9.30 am to 10.30 am, and membership was confined to general managers, advisors and my executive secretary. Later on, we brought in deputy general managers too. Ground rules were that anyone can place any item or point for discussion, even if it was beyond one’s own area of responsibility.
Problem solving
Rigorous discussions took place on anything or everything that mattered especially processes - speed of response, pattern of response, our successes, our failures, competitor’s strategies, regulatory environment, talent stock taking, issues of leadership, etc.
After a slow start, these meetings became effective vehicles for generation of ideas, exploration of solutions, problem solving, strategy formulation and learning. For example, when our credit portfolio was not picking up, these morning meeting debates led us to take some key decisions relating to structure of credit department, targeting new corporates, reviewing credit delivery mechanism, rehashing training of credit officers, reviewing outlook for interest rates, etc. This allowed us to achieve around 40 percent growth in our credit portfolio – highest in 2005-06 among the public sector banks.
Promoting strategic thinking
The morning meetings also helped us promote strategic thinking, as we laid great emphasis on diagnosis as the starting point for problem solving. In our discussion on any live problem, the emphasis was always on diagnostic questions like: Did we analyse the root cause of the problem; did we provide a bandaged solution or take long lasting corrective steps to avoid recurrence of the problems; did we handhold the managers in solving the problem; did we show knee-jerk reaction to a situation or did we explore alternate ways of handling the problem? Further, the collective creativity helped in making possible many customer centric innovations.
A forum for business review
Morning meetings became the forum for setting in motion the spade work needed for our vision exercise 2005-2010. We discussed our ambition for the future in relation to the economic environment, competitors’ growth strategy and our unique strengths. Every week, we also reviewed our business growth, merits and demerits of our products in relation to competitors’ products. These sessions were very intense with arguments and counter arguments. There was an increasing openness in the group. It was in these meetings that we discussed our aspirations for rapid expansion globally and many other strategies such as revamping our subsidiaries and creating new joint ventures for life insurance and mutual funds.
Set the tone for execution
Napoleon Bonaparte is famously quoted as saying, “Take time to deliberate, but when the time for action has arrived, stop thinking and go in.” So was it for Bank of Baroda. During 2005-08, we had an ambitious agenda for transformation that included introduction of core banking solutions, and doubling the business mix of the bank. These projects required impeccable treatment and time-bound implementation. They also required a high degree of coordination amongst various functionaries across the bank. The morning meetings allowed us to collectively discuss the implementation details of each project, identifying owners for each, support required and implementation schedules. The coordinated efforts helped in achieving extraordinary results, including doubling of business in just 3 years.
In effect, these morning meetings created an environment of espirit de corps in the ranks of management and helped stitch many loose ends in our programs and policies. It invigorated the top management and helped in de-bureaucratizing the working of the bank. It enforced the discipline of execution and promoted the culture of accountability for outcomes. They allowed us to function as a learning organization where new and expansive pattern of thinking was nurtured, where collective aspiration was set free and where we continuously learnt how to learn together – all in the setting of our aspiration to reach new milestones of achievement.
I feel truly gratified that as many as ten of my colleagues rose to become chairman or executive directors in public sector banks, and the training and grooming through these conversations helped them manage their transition and play leadership roles with great elan. A general manager who rose to become an executive director of a public sector bank had this to say, “I have learnt many management lessons at the morning meetings in Bank of Baroda, what even a regular MBA would have not taught me. These meetings helped me to transform myself into a better person and a better banker/business manager.”
Personally for me, morning meetings were sessions of exploration, discovery, coaching, guiding and persuading everyone to raise their aspirations. I truly feel that much of what we could achieve in the 3 years of my tenure, can be attributed to our informed and engaged sessions in the morning meetings. I personally benefited a lot as these meetings provided me deep insights into many operational and organizational issues. Truly, morning meetings were my ‘sapiental circles’ (knowledge generating group). Finally, leadership grooming is all about engaged conversations about real life issues and distilled learning derived from such engaged sessions, where people benefit from their own collective wisdom in solving problems and architecting the future for their organizations.
 By Dr. Anil K. Khandelwal