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1
Z Score : Brief Overview
2
Normal Distribution
● Represents distribution of random variables
● Represented by symmetric Bell Curve.
● Also known as Gaussian Distribution.
● Peak in middle, tapered towards end.
● Mean is represented by the peak.
For an exam with a highest score
of 1600 & a lowest of 700, the
distribution of marks would be….
3
Standardisation & Standardised Normal Distribution
● Method for comparative study
● Process of putting different variables in a same scale.
● Important parameter : Mean & Standard Deviation
● Predict population statistics from sample data.
● Mean becomes 0
4
The Process of Standardisation : Z-Score
𝒙 = individual value
𝝁 = population mean
𝞼 = standard deviation
Suppose, for the previous problem, the Standard Deviation is 150.
Putting individual values(scores), the mean & the StDev in the formula,
we can represent every scores to their corresponding Z-scores and
construct a graph
Peak (Mean) becomes 0
Standard deviation becomes 1
Z-Score ranges from -3 to +3
5
Z-Score Table & Probabilistic Density
6
Z-Score Table & Probabilistic Density
What do we mean by Probabilistic density??
Q. Find the probability of a student scoring 1380 from the
previous problem. Find the probability of a student scoring
more than 1380.
A. From the formula of z-score, putting 1380 as x, we obtain -
z = (1380 - 1150) / 150 = 1.53
Probability value = 0.93699
The probability of a student scoring 1380 or less is 93.7%
As, Total probability is always 1, hence probability of
a student scoring greater than 1380 is :
(1 - 0.93699) = 0.063
i.e 6.3%
7
Few key points
A. The data is 1𝝈 away from the mean.
B. Null hypothesis & Z-score Table
C. Trilogy of 68-95-99.7
8

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UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
 

Z Score Brief Overview.pptx

  • 1. 1 Z Score : Brief Overview
  • 2. 2 Normal Distribution ● Represents distribution of random variables ● Represented by symmetric Bell Curve. ● Also known as Gaussian Distribution. ● Peak in middle, tapered towards end. ● Mean is represented by the peak. For an exam with a highest score of 1600 & a lowest of 700, the distribution of marks would be….
  • 3. 3 Standardisation & Standardised Normal Distribution ● Method for comparative study ● Process of putting different variables in a same scale. ● Important parameter : Mean & Standard Deviation ● Predict population statistics from sample data. ● Mean becomes 0
  • 4. 4 The Process of Standardisation : Z-Score 𝒙 = individual value 𝝁 = population mean 𝞼 = standard deviation Suppose, for the previous problem, the Standard Deviation is 150. Putting individual values(scores), the mean & the StDev in the formula, we can represent every scores to their corresponding Z-scores and construct a graph Peak (Mean) becomes 0 Standard deviation becomes 1 Z-Score ranges from -3 to +3
  • 5. 5 Z-Score Table & Probabilistic Density
  • 6. 6 Z-Score Table & Probabilistic Density What do we mean by Probabilistic density?? Q. Find the probability of a student scoring 1380 from the previous problem. Find the probability of a student scoring more than 1380. A. From the formula of z-score, putting 1380 as x, we obtain - z = (1380 - 1150) / 150 = 1.53 Probability value = 0.93699 The probability of a student scoring 1380 or less is 93.7% As, Total probability is always 1, hence probability of a student scoring greater than 1380 is : (1 - 0.93699) = 0.063 i.e 6.3%
  • 7. 7 Few key points A. The data is 1𝝈 away from the mean. B. Null hypothesis & Z-score Table C. Trilogy of 68-95-99.7
  • 8. 8

Editor's Notes

  1. In probability theory and statistics, the Normal Distribution, also called the Gaussian Distribution, is the most significant continuous probability distribution. Sometimes it is also called a bell curve. A large number of random variables are either nearly or exactly represented by the normal distribution
  2. Calculate mean & stdev. Subtract each variable from mean & divide by stdev. When you standardize a normal distribution, the mean becomes 0 and the standard deviation becomes 1. This allows you to easily calculate the probability of certain values occurring in your distribution, or to compare data sets with different means and standard deviations.