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![Answer:
Amartya secures 60 in English.
Where Mean = 40 and S.D = 8
Answer:
Amartya secures 50 in Mother Tongue
Where Mean = 50 and S.D = 6
𝑇 = 10 [
𝑥 − 𝑀
𝑆𝐷
] + 50
T = 10 [
!"#!"
$
] + 50
T = 10 [
"
$
] + 50
T = 0 + 50
T = 50
𝑇 = 10 [
𝑥 − 𝑀
𝑆𝐷
] + 50 T = 10 [
$"#%"
&
] + 50
T = 10 [
/0
1
] + 50
T = 10 [
2
/
] + 50
T = 25 + 50 = 75
From the above two T-Scores, Amartya Secures better in English subject than Mother Tongue.
ThiyaguSuriya 15](https://image.slidesharecdn.com/zscoretscorepercentialrank-240430124917-3dedf2a2/75/Z-Score-T-Score-Percential-Rank-and-Box-Plot-Graph-15-2048.jpg){kind=icon}
Uploaded byThiyagu K
Z Score,T Score, Percential Rank and Box Plot Graph
The document explains statistical concepts such as z-scores, t-scores, and percentile ranks, providing formulas and examples for their calculation. It outlines the differences between z-scores and t-scores, including when to use each based on sample size and population standard deviation. Additionally, it discusses the construction and interpretation of box plots for visualizing data distribution.
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Z Score,T Score, Percential Rank and Box Plot Graph
- 1. Z-Score T-Score Percentile Rank & Box-Plot Graph K.THIYAGU, AssistantProfessor, Department of Education, Central University of Kerala, Kasaragod ThiyaguSuriya 1
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- 3. Z-Score Z-Score (Z-value, StandardScore, 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 = (𝒙#𝝁) 𝝈 Deviation Std core DeviationS score Z . = - ThiyaguSuriya 3
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- 5. 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 99% https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/what-is-a-z-score-what-is-a-p-value.htm ThiyaguSuriya 5
- 6. Example # 1 Let’ssay 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
- 7. Ahalya has secured50 marks in English; the class mean is 60, and the standard deviation is 10. What is the Z-score of Ahalya? D S M X Z . - = s 1 10 10 10 60 50 - = - = - = Z Example # 2 Answer: The raw score of 50 may be converted to Z-score by applying the formula. So, Ahalya’s Z-score is Ahalya’s score is 1-Sigma distance below the Mean. ThiyaguSuriya 7
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- 9. T-Score T-score is atype 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
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- 13. T = (Zx 10) + 50. T = 10 Z + 50. ThiyaguSuriya 13
- 14. Example Amartya secured 60marks 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
- 15. Answer: Amartya secures 60in English. Where Mean = 40 and S.D = 8 Answer: Amartya secures 50 in Mother Tongue Where Mean = 50 and S.D = 6 𝑇 = 10 [ 𝑥 − 𝑀 𝑆𝐷 ] + 50 T = 10 [ !"#!" $ ] + 50 T = 10 [ " $ ] + 50 T = 0 + 50 T = 50 𝑇 = 10 [ 𝑥 − 𝑀 𝑆𝐷 ] + 50 T = 10 [ $"#%" & ] + 50 T = 10 [ /0 1 ] + 50 T = 10 [ 2 / ] + 50 T = 25 + 50 = 75 From the above two T-Scores, Amartya Secures better in English subject than Mother Tongue. ThiyaguSuriya 15
- 16. T-Score vs. Z-Score:When to Use Each https://www.statology.org/t-score-vs-z-score/ Do you know the population SD? Use a t-score Is the sample size (n) greater than 30? N o Y e s Use a t-score Use a z-score N o Yes ThiyaguSuriya 16
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- 18. Percentile Rank The nthpercentile 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. Percentile Rank ThiyaguSuriya 18
- 19. Percentile Rank Calculation ofPercentile Rank from Ungrouped Data ú û ù ê ë é - - = N R PR 50 100 100 Where, PR = Percentile Rank R = Rank position of the score of an individual whose percentile rank is to be determined. ThiyaguSuriya 19
- 20. Example Find out thepercentile rank of score ‘25’ from the following scores. 65, 46, 58, 32, 25, 14, 15, 10, 9, 7, 5, 3 ThiyaguSuriya 20
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- 22. Group Data ú û ù ê ë é ÷ ø ö ç è æ - + =w b f i L K cf N PR 100 • Cfb=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
- 23. CI ECI /CCIf cf 91 – 100 90.5 – 100.5 3 30 81 – 90 80.5 – 90.5 7 27 K 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 Find out the percentile rank of 82 scores of the following frequency distribution. ThiyaguSuriya 23
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- 26. Box Plot The boxplot (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 Maximum. ThiyaguSuriya 26
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- 31. Boxplots allow usto evaluate whether a data set is symmetrical, right-skewed, or left-skewed. https://www.labxchange.org/library/items/lb:LabXchange:d8863c77:html:1 ThiyaguSuriya 31
- 32. Histograms and boxplotsof symmetric, right-skewed, and left-skewed unimodal data sets https://www.labxchange.org/library/items/lb:LabXchange:d8863c77:html:1 ThiyaguSuriya 32
- 33.