Basics of ML & AL Week 2 Challenge

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

ans : 1) measure of central tendency(mean) = 1.4

2) measure of dispersion(variance) = 1.84

3) skewness = 0.568 , therefore positively skewed.

4) kurtosis = -0.976

*calculations attached in document*

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

ans: expected value and simple mean are very similar. they are just used in different context. mean is more of a practical term whereas expected value is a theoretical term. therefore when the sample mean is already present it is easy to predict the expected value.

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

ans: it is neither good or bad. it is simply a measure of distribution. having skewness helps us to better understand the type of data we are dealing with.

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

a)P(X<711) = 84.1%

b)P(X>740) = 2.87%

c)P(600<X<720) = 89.656%

d)P(X=720) = 0: since the value 720 is infinitesimal value under an infinitesimal area it can be assumed as zero. same goes any value of a where p(X = a).

*calculations attached in Document*

5)Explain the curve on the right side.

ans: It is a normal distrubution curve. It is symmeteric about the mean showing that data near the mean sre frequent in occurence than the ones that are further away from the mean. the probability is determined by the area under the curve.