chapter 6 Flashcards
Differentiate between empirical and theoretical frequency. What kind of distribution is on a normal curve?
Empirical: Based on real observations
Theoretical: Based on theoretical or hypothetical observations
The normal curve is a theoretical distribution.
What are the properties of a standard normal curve?
-It is symmetrical.
- It is unimodal; the mean, median, and mode are equal.
- The values along the abscissa are continuous.
- The curve is asymptotic to the abscissa: Because there are an infinite number of values in the distribution, the curve never touches the abscissa.
- The mean is zero.
- The variance and standard deviation equal 1.
- The area under the curve is 1.
What do the x-axis and y-axis of a normal standard curve consist of?
x-axis: z-scores
y-axis : relative frequency
What are z scores?
A z-score tells you how far a number is from the average (mean) in terms of standard deviations.
If the z-score is 0, the number is exactly the average.
A positive z-score means the number is above the average.
A negative z-score means the number is below the average.
How to find the area under a curve when given the z score?
A z-score tells you how far a number is from the average (mean) in terms of standard deviations.
If the z-score is 0, the number is exactly the average.
A positive z-score means the number is above the average.
A negative z-score means the number is below the average.
How to solve when z score is unknown?
Look up the value in the table B1.
find the two z scores that separate the middle 95% of the area from the extreme 5%.
0.025 in each tail . Look up the z score of 0.025 in table b1.
How to find the proportion of scores below a certain value.
use z = (X - µ)/σ formula where x is our score and mu is the average.
Solving this gives you the z score. Look up the value of the z score and write it in percentage form. That is the percentage or proportion of scores below the given score.
how to find percentile rank when given z scores?
To determine the percentile rank of each z-score, we need to look at the cumulative area to the left of each z-score on the standard normal distribution curve, which gives us the percentile rank.
Differentiate between percentile and percentile rank.
The main difference between percentile and percentile rank is that a percentile refers to a point, while a percentile rank covers an interval.
A percentile is a score below which a given percentage of scores in the distribution falls.
Percentile rank refers to data point’s position in a set of data when the data points are ordered from smallest to largest.
