Standardized (z) scores - STATS

In your psychology class, the mean exam score is 72 and the standard deviation is 12. You scored 78. In your biology class, the mean exam score is 56 and the standard deviation is 5. You scored 66. If your professors grade "on a curve" (i.e., according to the distribution of scores), for which exam would you expect to get a better grade? (Hint: Convert your exam scores to z-scores). -biology -psychology

Biology

The standard deviation can be negative. True or false

False

Z-scores close to 0 are located on the tails of a normal distribution. True or false

False

Use both the graphs FB and Twitter and compare to see who's more unpopular?

Fb

For a normal distribution of scores, which of the following z-scores represent the most extreme location on the left side of the distribution? -2.17 -1.89 1.65 2.99

LEFT! -2.17

Last week Sarah had exams in Math and in Spanish. These exams were curved, so the grades were based on z-scores. On the math exam, the mean was M = 30 with SD = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was M = 60 with SD = 6 and Sarah had a score of X = 65. For which class should Sara expect the better grade? Math Spanish

Math

If we standardize a distribution by converting every value to a z-score, what will be the new mean of this standardized distribution?

Mean = 0

Convert histograms to

Relative frequency n/total (same things as proportions)

If we standardize a distribution by converting every value to a z-score, what will be the new standardized deviation?

The z-score of any value, that's 1 standard deviation away from the mean, will be 1 after we standardize it

A score equal to the mean has a z-score of 0. True or false

True

It is rare to find scores more than 3 standard deviations above or below the mean. True or false

True

Within a single population, two equivalent raw scores will always have the same z-score. True or false

True

Z-scores can be negative. True or False

True

When it says a (number) above or below the mean that is the?

Z-score

Finding x with z-score formula: FB friends of Chris is 2.5 standard deviation above the mean. The standard deviation = 36 and the mean = 190. How many FB friends does Chris have?

z-score = 2.5;standard deviation = 36;mean = 190 z = x - mean/standard deviation -> 2.5 = x-190/36 (solve for x) -> 2.5(36)+190 = x -> x=280

How many standard deviations above the mean is an IQ of 150? (In other words, what is the z-score for 150?) IQ data: μ = 100.8 sd=14.9

3.3

For a population with a mean of 80 and standard deviation of 12, what is the z-score corresponding to 71?

-0.75

What is the z-score for a score of 17? X = 17 μ = 20 sd = 3

-1

What is the z-score for a score of 12.5? X = 12.5 μ = 20 sd = 3

-2.5

What does the negative z-score mean?

-The original value is less than the mean -The original value mines the mean is negative

What is the z-score for a score of 20? X = 20 μ = 20 sd = 3

0

A theoretical normal distribution is = to

1 or 100%; therefore the area = 1

How do you convert a normal distribution to a standardized normal distribution? Given FB friends mean=190; standard deviation=36; x=210 Popularity score (look at graph)

1. find z-score: z= z-mean/standard deviation z=210-190/36 z=0.56 2. convert to a new popularity score: z= z-mean/standard deviation 0.56 = x-50/10(solve for x) 0.56(10)=x-50; 0.56(10)+50=x-50+50 x=55.6 -took a spread out distribution and converted that to a normal distribution

How many standard deviations above the mean is an IQ of 125? (In other words, what is the z-score for 125?) Round to two decimal places. IQ data: μ = 100.8 sd=14.9

1.62

How many standard deviations is Katies number of FB friends from the mean number of FB friends? (look at notes)

1.Find how many fewer friends than mean 2.Divide answer by standard deviation to figure out how many standard deviations away from the mean

For a population with mean of 100 and standard deviation of 20, what is the X value corresponding to z = 1.50?

130

A population of scores has a mean of 40. In this population, a score of X = 46 has a Z-score of Z = 3.0. What is the population standard deviation (σ)?

2

A population of scores has a mean of 55 and standard deviation of 6. In this population, a score of X = 68 corresponds to z =

2.17

Your score on the first statistics exam was 48 and the average was μ= 36. Which value for standard deviation would give you a higher position in the grade distribution for this exam?

5

Standardizing the distribution

When you compare (mount them on top of each other) two graphs to each other to compare individual scores

In N = 25 games last season, the college basketball team averaged M = 78 points with a standard deviation of 12. In their final game of the season, the team scored 89 points. Based on this information, the number of points scored in the final game was ____. a little above average There is not enough information to compare last year with the average. far above average

a little above average

The San Jose State University football team played 12 games last season (N = 12) and averaged 24.5 points per game with standard deviation 9.5. Their first game of the new season, they scored 33 points. If we compare this with the points scored last season, then this score is: a little above average far above average above average, but it's impossible to tell how much need more information

a little above average bc σ =9.5. average is 24.5. 24.5+9.5=34 so its higher than the new score 33

Last week Tom had exams in Statistics and in English. He scored 10 points above the mean on both exams. From this information, you can conclude that ____. Tom will have a higher z-score for the exam with the lower mean None of the other choices are correct. Tom has identical z-scores for the two exams both of Tom's z-scores are positive

both of Tom's z-scores are positive

Formula for how many standard deviations away from the mean

difference/standard deviation

A z-score of z = +3.00 indicates a location that is ____. The location depends on the mean and standard deviation for the distribution. far above the mean in the extreme right-hand tail of the distribution near the center of the distribution slightly above the mean

far above the mean in the extreme right-hand tail of the distribution

On an exam with M = 52, you have a score of X = 48. Which value for the standard deviation would give you a higher position in the class distribution?

s=4

z is

the number of standard deviations away from the mean