Which of the following statements about Z-scores are correct? i) Z-score removes the effect of the scale.ii) Z-score measures a value's distance in the unit of standard deviation relative to the median of a group of valuesiii) Z-score measures a value's distance in the unit of standard deviation relative to the average of a group of valuesiv) Z-score can help identify the existence of outliersv) An observation is not an outlier if the absolute vlaue of its Z-score is higher than 5Question 1Answera.i), ii), iv) and v)b.i), ii) and iv)c.None of the aboved.i), iii), iv) and v)e.i), iii) and iv)
Question
Which of the following statements about Z-scores are correct? i) Z-score removes the effect of the scale.ii) Z-score measures a value's distance in the unit of standard deviation relative to the median of a group of valuesiii) Z-score measures a value's distance in the unit of standard deviation relative to the average of a group of valuesiv) Z-score can help identify the existence of outliersv) An observation is not an outlier if the absolute vlaue of its Z-score is higher than 5Question 1Answera.i), ii), iv) and v)b.i), ii) and iv)c.None of the aboved.i), iii), iv) and v)e.i), iii) and iv)
Solution
The correct answer is d. i), iii), iv) and v).
Here's why:
i) Z-score does indeed remove the effect of the scale. It standardizes different scales by converting them into a standard normal distribution with a mean of 0 and standard deviation of 1.
ii) This statement is incorrect. Z-score measures a value's distance in the unit of standard deviation relative to the mean (not the median) of a group of values.
iii) This statement is correct. As mentioned above, Z-score measures a value's distance in the unit of standard deviation relative to the mean of a group of values.
iv) This statement is correct. Z-scores can help identify outliers because values with a Z-score above 3 or below -3 are usually considered outliers.
v) This statement is also correct. An observation is not necessarily an outlier if the absolute value of its Z-score is higher than 5. However, it is quite unusual and could be considered an extreme value.
Similar Questions
A standardized value, commonly called a z-score relies on the values of Group of answer choicessample standard deviation and the meanmedianmodeaverage distribution
Which of the following statements are TRUE about the normal distribution? Check all that apply.The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.The mean corresponds to the z-score of 1.A z-score is the number of standard deviations a specific data value is from the mean of the distribution.
Based on what you have studied in this unit, reflect and answer the following questions:What are the main characteristics of the normal distribution?Why is it advantageous to use the Z scores?For a standard normal distribution, about 68% of values falls within one standard deviation of the mean; about 95% falls within two standard deviations; and about 99.7% falls within three standard deviations. Suppose the distribution of math scores in the SAT follow a normal distribution with a mean µ=700 and a standard deviation σ=150.Calculate the Z-score for an SAT Math score of 600. Interpret it in your own word.Find the interval [a, b] that captures 68% of the SAT Math score in this example.Find the interval [a, b] that captures 95% of the SAT Math score in this example.Find the interval [a, b] that captures 99.7% of the SAT Math score in this example.
What is the mean of the z-scores?Question 2Answera.0.5b.0c.1
A z-score is most affected by the ______.Choose onemedianmodestandard deviationrange
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