Basics of ML & AL Week 2 Challenge

1)Calculate all 4 business moments using pen and paper for the below data set?

The solution is as follows:

1. Measure of central tendency:
Mean = (0 + 0.25 + 0.3 + 0.45 + 0.4)/5 = 0.28

2. Measure of dispersion:
Variance = ((0-0.28)^2)(0.35) + ((1-0.28)^2)(0.25) + ((2 - 0.28))^2(0.15) + ((3-0.28)^2)(0.15) + ((4-0.28)^2)(0.10)
= 0.02744 + 0.1296 + 0.44376 + 1.10976 + 1.38384
= 3.0944

Std Dev: 1.176367289582637

3. Measure of skewness:

sk = -0.004724111866969 + 0.0796861851779446 + 0.46930440925503 + 1.8559915983609 + 3.1652415235149

sk = 5.565499604441806

4. Measure of Kurtosis:

Kt = 0.0011247840406071 + 0.0351267653476 + 0.686388155482665 + 4.292731301001 + 10.012431516365

Kt = 15.02780252223687

2)What is the significance of expected value when simple mean (Sum of all observations/number of observations) is already in place.

Two terms that which are used interchangeably in statistics are expected value and mean.

In general, we use the following terms in different situations:
Expected value is used when we want to calculate the mean of a probability distribution. This represents the average value we expect to occur before collecting any data. Mean is typically used when we want to calculate the average value of a given sample. This represents the average value of raw data that we’ve already collected. We can calculate the mean (or expected value) of a discrete random variable as the weighted average of all the outcomes of that random variable based on their probabilities. We interpret expected value as the predicted average outcome if we looked at that random variable over an infinite number of trials.

3)Having skewness in the curve considered to be bad in the analysis?

Skewness is not bad nor is it good. Skewness may be a violation of assumptions of a test, in which case either figure out a way to fix it, or use a different test. So, when is the skewness too much? The rule of thumb seems to be: If the skewness is between -0.5 and 0.5, the data are fairly symmetrical. If the skewness is between -1 and -0.5(negatively skewed) or between 0.5 and 1(positively skewed), the data are moderately skewed. In a distribution that is negatively skewed, the exact opposite is the case: the mean of negatively skewed data will be less than the median. If the data graphs symmetrically, the distribution has zero skewness, regardless of how long or fat the tails are. Also, skewness tells us about the direction of outliers. You can see that our distribution is positively skewed and most of the outliers are present on the right side of the distribution. And one should remember that skewness does not tell us about the number of outliers. It only tells us the direction.

4)Evaluate the probabilities for continuous normal distribution with given mean = 680 and standard deviation = 31

a)P(X<711) = 0.84

b)P(X>740) = 0.0265

c)P(600<X<720) = 0.8966

d)P(X=720) = 0

5)Explain the curve on the right side

It is a bell curve. It is a common type of distribution for a variable, also known as the normal distribution. The term "bell curve" actually originates from the fact that the graph used to depict a normal distribution consists of a symmetrical bell-shaped curve. Let's dive in a little deep. The highest point on the curve, or the top of the bell, represents the most probable event in a series of data (its mean, mode, and median), while all other possible occurrences are symmetrically distributed around the mean, creating a downward-sloping curve on each side of the peak. The width of the bell curve is described by its standard deviation.

The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:

• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
• The mean, mode and median are all equal.
• The curve is symmetric at the center (i.e. around the mean, μ).
• Exactly half of the values are to the left of center and exactly half the values are to the right.
• The total area under the curve is 1.