T-Score of a particular score in a data set is 50. If each score of the data set is multiplied by 10, what will be the new T-score of that particular score ? 

The correct answer is - 50

Key Points

• T-Score Calculation
  • The T-score is a standard score that indicates how many standard deviations a data point is from the mean.
  • It is calculated using the formula: T = 50 + 10 * z, where z is the z-score of the data point.
• Effect of Multiplying Scores
  • Multiplying each score by a constant scales both the mean and the standard deviation by the same factor.
  • However, the z-score (which is the number of standard deviations away from the mean) remains unchanged.
• Impact on T-Score
  • Since the z-score remains the same, the T-score, which is derived from the z-score, also remains unchanged.
  • Hence, if the original T-score is 50, the new T-score will still be 50.

Additional Information

• Standard Scores
  • Standard scores, such as z-scores and T-scores, are used to compare data points from different distributions.
  • These scores help in understanding the position of a data point relative to the mean of the distribution.
• Z-Score
  • The z-score is calculated using the formula: z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.
  • A z-score indicates how many standard deviations a data point is from the mean.
• Implications in Data Analysis
  • Understanding transformations such as multiplication is crucial for data normalization and standardization.
  • These concepts are widely used in statistical analysis, machine learning, and other data science applications.