Probability distribution that describes the likelihood of getting a certain number of successes in a fixed number of independent trials, each with only two possible outcomes: success and failure We calculate the probability of getting a specific number of successes…
Central limit theorem describes the behavior of the sampling distribution of the mean of a random variable, It allows to make inferences about populations based on samples, distributions of sample means approaches normal distributions, even when the original experiment doesn’t…
Suppose, we are calculating sample mean, as the number of samples increases the output accuracy increases, this theory says that as the samples/iterations/trials approach infinity we get most accurate output Applications of law of large numbers
Expected value helps us find average value we can expect from an random event Formula: E = Σ(x * P(x)) Example: I roll a fair six-sided dice. What’s the expected value from the dice? There are six possible outcomes (1,…
Bayes’ theorem is a powerful tool in probability that deals with conditional probabilities It helps to calculate the probability of an event (A) happening given that we already know another event (B) has occurred Formula: P(A | B) = (P(B…
We have seen probablity, now lets learn addition and multiplication rule Addition rule: This rule applies when we are dealing with mutually exclusive events (two or more events that cannot happen simultaneously), i.e., independent events – if one event occurs,…
Probability tells how likely an event is going to happen How to write or represent probability? P(event) = percentage Eg: fair coin for events, P(Head) = 0.5 = P(Tail) Note: Sum of all events is always equal to 100% ie,…
Why Z Score? We have already Empirical rule of normal distribution, that gives approximate percentile, but z score gives more accurate percentile What is z Score? A z Score (standard score / normalized score) this describes, how many standard deviations…
The empirical rule, also known as the 68-95-99.7 rule, this is a statistical principle that applies to normal distributions The empirical rule states that in a normal distribution: Note: Standard deviation (σ or SD): This measures data is spread out…
Histogram & Frequency distributions: A histogram is a bar chart that represents the distribution of data. This groups data into ranges (bins) and shows the frequency (count) of each data points that fall within each bin Example: Ages of class…
Population Vs Sample What is population? A population is the whole group that we want to draw conclusions What is a sample? A sample is a part of the population, typically it shall represent majority of population Example: Weather forecast…
Inter Quartile Range (IQR) IQR helps to understand spread of data, by dividing the data in to 4 pieces (also known as quarters) Example: Imagine there are some set of numbers give, we wanted to understand the data spread, obviously…
Kurtosis we measure the shape of cure w.r.t height. It describes how much the deviation is from a normal (bell-shaped) curve Note: Kurtosis is analyzed alongside skewness, this describes the asymmetry of a distribution. While skewness tells you if the…
Skewness describes how the data points spread around the mean, particularly whether they lean more towards one side (left or right) or are relatively symmetrical Types of Skewness: Positive Skewness: The tail of the distribution extends to the right. Larger…
What is measure of dispersion? (Data spread – range, variance and standard deviation) Here we see how the data points are spread, it tells us how much variation is there from central tendency Range: Here we see minimum and maximum…
Scales of measurements of data Nominal Scale: Represents categories with no ranking, it only represents categories of data. Example: Blood group, customer segments What operation can we do on nominal scale? We can perform count operation on categories. Ordinal scale:…
Descriptive statistics Here we are summarizing the data, we are describing the characteristics of data and finding relation among the variables in data What do we perform in descriptive statistics? Inferential statistics Here we are coming with conclusions over population…
What is Mean? Mean is known as average, which represents middle point in data. We can say that mean is most common value in the data. Example: Age of 3 students are, 12, 15, 18. Average age of those 3…
In statistics variable is something that can change or vary, with or without any conditions Note: Values of variable could be measured w.r.t numerical scale (could be either continuous or discrete) or non measurable as well Examples of variables: Types of…
What is data? Data is essentially a collection of anything from numbers and figures to text and symbols. It is basically unprocessed information. Example of data: Note: data should be stored either in digital or physical format. Data ——–> Processed——->…
