Z-Score, T-Score, Percentile Rank and Box-Plot Graph

Thiyagu K.

Z-Score, T-Score, Percentile Rank and Box-Plot Graph

Thiyagu K.

visibility

…

description

33 pages

link

1 file

Z-Score, T-Score, Percentile Rank and Box-Plot Graph

Z-Score T-Score Percentile Rank & Box-Plot Graph ThiyaguSuriya K.THIYAGU, Assistant Professor, Department of Education, Central University of Kerala, Kasaragod 1 Z-Score ThiyaguSuriya 2 Z-Score Z-Score (Z-value, Standard Score, and Normal Score) Z-score is the number of standard deviations from the mean, a data point is It’s a measure of how many standard deviations below or above the population mean The basic Z score formula for a sample is: Z= ThiyaguSuriya (𝒙#𝝁) 𝝈 Z - score = DeviationScore Std .Deviation 3 ThiyaguSuriya 4 https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/what-is-a-z-score-what-is-a-p-value.htm Z-score (Standard Deviations) p-value (Probability) Confidence level < -1.65 or > +1.65 < 0.10 90% < -1.96 or > +1.96 < 0.05 95% < -2.58 or > +2.58 < 0.01 ThiyaguSuriya 99% 5 Example # 1 Let’s say you have a test score of 190. The test has a mean (µ) of 150 and a standard deviation (σ) of 25. Assuming a normal distribution, Your Z-score would be: Z = (x – µ) / σ = 190 – 150 / 25 = 1.6. The Z score tells you how many standard deviations from the mean your score is. In this example, Your score is 1.6 Standard Deviations above the Mean. ThiyaguSuriya 6 Example # 2 Ahalya has secured 50 marks in English; the class mean is 60, and the standard deviation is 10. What is the Z-score of Ahalya? Answer: The raw score of 50 may be converted to Z-score by applying the formula. So, Ahalya’s Z-score is X -M Z= S .D 50 - 60 - 10 Z= = = -1s 10 10 Ahalya’sThiyaguSuriya score is 1-Sigma distance below the Mean.7 T-Score ThiyaguSuriya 8 T-Score T-score is a type of standard score computed by multiplying a Z-score by 10 and adding 50. T-scores tell individuals How far is their score from the mean? T-scores have a mean of 50 and a standard deviation of 10. T-score was 70 it would, in turn, mean that their score was 20 points above the mean. ThiyaguSuriya 9 ThiyaguSuriya 10 T-Score vs Z-Score ThiyaguSuriya https://www.educba.com/z-score-vs-t-score/ 11 T-Score vs Z-Score https://www.educba.com/z-score-vs-t-score/ ThiyaguSuriya 12 T = (Z x 10) + 50. T = 10 Z + 50. ThiyaguSuriya 13 Example Amartya secured 60 marks in English, which has a mean of 40, and an S.D. of 8. She secured 50 marks in the mother tongue test, having a mean of 50 and an S.D. of 6. Convert all raw scores into T-scores. In which subject has Amartya done better? T = 10 Z + 50 ThiyaguSuriya 14 Answer: Answer: Amartya secures 60 in English. Where Mean = 40 and S.D = 8 Amartya secures 50 in Mother Tongue Where Mean = 50 and S.D = 6 𝑥−𝑀 𝑇 = 10 [ ] + 50 𝑆𝐷 T = 10 [ $"#%" & ] + 50 𝑥−𝑀 𝑇 = 10 [ ] + 50 𝑆𝐷 !"#!" T= /0 10 [ ] + 50 1 T = 10 [ T= 2 10 [ ] + 50 / T = 10 [ ] + 50 $ ] + 50 " T = 25 + 50 = 75 $ T = 0 + 50 T = 50 From the above two T-Scores, Amartya Secures better in English subject than Mother Tongue ThiyaguSuriya 15 . T-Score vs. Z-Score: When to Use Each Do you know the population SD? Is the sample size (n) greater than 30? N o Use a t-score s Ye o N Use a t-score ThiyaguSuriya https://www.statology.org/t-score-vs-z-score/ Ye s Use a z-score 16 Percentile Rank ThiyaguSuriya 17 Percentile Rank The nth percentile is that scale value or score point below which ‘n’ percent of the cases in the distribution fall. The scale value is the percentile, while its corresponding percentage value is its percentile rank. Percent ile Rank ThiyaguSuriya 18 Percentile Rank Calculation of Percentile Rank from Ungrouped Data é100 R - 50 ù PR = 100 - ê ú N û ë Where, PR = Percentile Rank R = Rank position of the score of an individual whose percentile rank is to be determined. ThiyaguSuriya 19 Example Find out the percentile rank of score ‘25’ from the following scores. 65, 46, 58, 32, 25, 14, 15, 10, 9, 7, 5, 3 ThiyaguSuriya 20 ThiyaguSuriya 21 Group Data 100 é æK -Lö ù PR = cfb + ç ÷ fw ú ê N ë è i ø û • Cf b=cumulative frequency below the class interval which k lies / containing k • K = Score for which we want to find percentile rank • L = Actual exact lower limit of the class interval containing K • Fw= frequency within the class interval containing k ThiyaguSuriya 22 Find out the percentile rank of 82 scores of the following frequency distribution. CI ECI /CCI f 91 – 100 90.5 – 100.5 3 cf 30 81 – 90 80.5 – 90.5 7 27 71 – 80 70.5 – 80.5 8 20 61 – 50 60.5 – 50.5 5 12 51 – 60 50.5 – 60.5 4 7 41 – 50 40.5 – 50.5 3 3 ThiyaguSuriya K 23 ThiyaguSuriya 24 Box Plot Graph ThiyaguSuriya 25 Box Plot The box plot (box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summaries: Minimum, First Quartile, Median, Third Quartile, and ThiyaguSuriya Maximum. 26 Box Plot ThiyaguSuriya 27 ThiyaguSuriya 28 ThiyaguSuriya 29 ThiyaguSuriya 30 https://www.labxchange.org/library/items/lb:LabXchange:d8863c77:html:1 ThiyaguSuriya 31 Boxplots allow us to evaluate whether a data set is symmetrical, right-skewed, or left-skewed. https://www.labxchange.org/library/items/lb:LabXchange:d8863c77:html:1 ThiyaguSuriya 32 Histograms and boxplots of symmetric, right-skewed, and left-skewed unimodal data sets Thank You ThiyaguSuriya 33

Log In

Z-Score, T-Score, Percentile Rank and Box-Plot Graph

Related papers

Related papers

Related topics