Standard Deviation & Variance
What is "deviation"?
The distance from the score to the mean (Score - Mean)
What does a z-score of -1 mean?
The raw score is 1 standard deviation below the mean.
A six-sided dice is tossed twice and both results are 6. What is the probability that the next toss is 6?
1/6
What are some features of the normal distribution? (Name any three)
Symmetrical, single peak, frequency highest at the mean and tapers off towards either sides, occurs frequently in real life, known proportions between any two z-scores
What sample size is considered "large enough" for the distribution of sample means to become normal for any population?
30 or more
What does "standard deviation" measure?
The average distance of the scores to the mean. It measures whether the scores are clustered around the mean or scattered widely.
Student A has a z-score of -1 and student B has a z-score of +2. Which student did better?
Student B
What does it mean to sample with replacement?
The same individual can be selected multiple times.
In a normal distribution, what percent of values fall below a z-score of 0?
50%
What is another term for "standard deviation of the distribution of sample means"?
Standard error
Grades of class A has a higher standard deviation than class B. What does that mean?
The grade of students in class A is more variable than class B. More of class B's grades are clustered around the mean than class A.
What is the z-score of a value equal to the mean?
zero
Probability can never be 0. True/False?
False.
In a normal distribution, what proportion of values fall within one standard deviation (+1 or -1) of the mean?
68%
What is at the center (the mean) of the distribution of sample means?
The population mean
5
You can calculate the z-score of any given score given which two parameters?
Mean and standard deviation
Sampling without replacement would create an independent random sample. True/False?
False.
If a student scores 90 on a test with a mean of 70 and a standard deviation of 10, what is their percentile rank?
Around 98th percentile (97.72%)
What happens to standard error as sample size n increases?
It decreases
What is the full name of Sum of Squares?
Sum of Squared Deviations
The class mean grade is 70 with a standard deviation of 5. What is the z-score for a grade of 80?
+2
A bag has 10 red balls and 10 green balls. Kate randomly chose a red ball. Assume the same ball can be selected twice, what is the probability that Kate selects another red ball?
1/2 = 0.5 = 50%
Why is the normal distribution important in inferential statistics?
Central limit theorem tells us that when sample size is large enough, the distribution of sample means for any population turns into a normal distribution, which has known properties for proportions between z-scores.
What does the Central Limit Theorem state about the distribution of sample means (shape, center, spread)?
1. The shape is normal when n is large, regardless of original population 2. Center is at the population mean 3. Standard error gets smaller as n increases