Chapter 6: Standard Deviation

to determine a fraction of SAT score ABOVE a score of 680(which is 1.8 SD's above the mean,) what should you type into "normalcdf" to find the normal percentile

(1.8, 99)

z- score formula

(x-mean)/standard deviation

find z-scores corresponding to... -20 points above mean -10 pts below -15 pts above -30 pts below

- z=2 -z=-1 - z=1.5 -z=-3

standardizing data into z-scores does what to the... -shape? -center? -spread?

-shape=unchanged -center=mean is made zero -spread= makes standard deviation one

z-score of the mean will always be...

0

finding normal percentile for are between two z-scores (say -.5 and 1) with calculator

1. 2nd-DISTR 2. normalcdf 3. "normalcdf(-.5, 1.0) 4. ENTER

Find the cut point for the 25th PERCENTILE in the normal model

1. Look in Table Z for an area of .2500 2. .2514 is pretty close 3. locate -.6 in left margin and .07 in top margin 4. the z-score is -.67

How to Make a Normal Probability Plot with calculator

1. Turn a STATPLOT on 2. choose last icon 3. specify your data list and which axis you want the data on 4. specify the Mark you want the plot to use 5. now ZoomStat does the rest

a positive z-score is found ___ mean

above the

adding a constant to every data value does what to the measures of center and percentiles? how about the spread?

adds same constant to measures of center+percentiles leaves spread unchanged

when we divide or multiply all the data values by any constant value, what happens to measures of location (mean and median) and measures of spread?

both are divided or multiplied by that same value

the higher on a bell curve, the more _______ the value

frequent

What does a z-score tell us?

how many standard deviations a score is from the mean

command for z-score at the 25th percentile in calculator

invNorm (.25)

Z-scores have a mean of _____ and SD of ____

mean of 0 and SD of 1

a larger standard deviation will lead to a ____ set of values and a ___curve, while a smaller standard deviation will lead to a ____set of values and a ___curve.

more spread out and flatter less spread out and sharper

unimodal, symmetric, curve centered at the mean

normal distribution ("bell curve")

if normal probability plot is not straight, what can we interpret this to mean?

normality is certainly questionable

z-score of less than -3 or greater than 3 should be an...

outlier

don't use the mean and standard deviation when

outliers are present

values we choose to specify a model

parameters ("population values")

the standard normal model is extremely useful in finding...

percentiles

what z-score cuts of the highest 10% go a normal model? how would you put this into a calculator

since we want to cut the point for the HIGHEST 10%, we know that 90% is the cut point, as this is the percentage of data BELOW the z-score. invNorm (.9)= 1.28 only 10% of the area in a normal model is more than 1.28 standard deviations above the mean

way to measure distribution of data around a mean

standard deviation

what do we obtain whenever we standardize data?

standard normal model (defined as N (0,1) )

values that are summaries of data

statistics

A normal distribution of scores has a standard deviation of what?

ten

most beneficial use of standard deviation

to standardize data (change from original units to number of standard deviations away from the mean) so we can better compare data and distributions

don't use normal models when the distribution is not

unimodal and symmetric

say you have a z-score of 1.80. how do you find its normal percentile?

using the table of normal percentiles (look down left column for first two digits and then top row for third digit)

To standardize data, we use the...

z-score

notation used for any model to designate center and spread

N (mean, SD)

in a normal model, about ____% of values fall within 1 standard deviation of the mean, about ____% fall within 2 standard deviations of the mean, and about ____% fall within 3 standard deviations of the mean

68-95-99.7 rule