fundamental of statistics mid-term study guide

7/29/2019 Fundamental of Statistics Mid-term study guide

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Measures of Central Tendency: Categories or scores that describe what is average or typical of

the distribution

Mode=category or score with the highest frequency of percentage in distribution

Largest # or proportion of cases fall in mode/ not necessarily category with the majorityUsed for nominal variables and is the only measure that can be used with nominal

MEAN

x x = y

N

1. x = mean 2. = frequency 3. y = value of each variable 4. N= # of observations

Most widely used and best known measure of central tendency (average) and is typicallyused to describe interval ratio variable (age/income/education)

Only for IR level because involves addition and division (only level that provides #s thatcan be added or divided)

Mean for frequency table

1. Multiply freq by value for each row2. Add up totals for each row3. Divide by total freq for the table

Unlike mode or median, incorporates all scores in distribution. If subtract mean from each score

and add up all differences, it will always =0Every score figures into mean so is sensitive to extreme scores (disproportionately affected by

outliers)

Median is not and mode so mean shouldnt be used in these cases

Add up all the scores together and then divide by the # of scores

MEDIAN

When N is ODD N+1/2 When N is EVEN N+1/2 tells the two numbers the median is between Take value +value/2= median

Score that divides distribution into 2 equal parts so that half is above and half is below

Represents the EXACT middle of distribution Can only be used with ordinal or interval ration variables (scores can be at least rank

ordered)

Can be used to compare groups


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Special case of a percentilescore at or below which a specific percentage ofdistribution falls

Response associated with middle case*Remember must order categories or scores first (lowest to highest or highest to lowest)

** If data is ordinal, theres no need to average 2 middle scores isnt appropriate because it

simply falls between two middle values.

Q1

Must first find position of value at 25th percentile Multiply N by .25 which gives the values the 25th percentile is between value 1 + value 2/ 2= Q1

Q3Same but multiply by .75 instead of .25

IQR

Subtract Q1 from Q3

VARIANCE

Average of squared deviations from the mean

y

2

s =(y -y)2

N- 1

STANDARD DEVIATION

(y -y)2

N- 1

STANDARD (z) SCORESThe # of Standard deviations that a given raw score is above or below the mean

Z=Y - Y

Sy

Finding area between mean and positive Z score

1. Looking for a range from the mean to a value2. Convert value to a Z score (value minus the mean and divided by the standard deviation)3. Look up Z score in the chart (Column A)4. Convert the proportion (.000) to a percentage= 0%

Finding the area between the mean and a negative Z score1. Looking for a range from the mean to a value2. Covert to a Z score (which turns out negative)


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3. The is symmetrical on both sides so a negative area doesnt exist so use the positive ofthe Z score in the standard normal table in column A

4. Convert proportion to a percentage

Finding the area between 2 Z scores on the same side of the mean1. Looking for value between two numbers (percentage between value A and value B)2. Find Z scores for both values3. Look up in Z score table4. To find the area between two value that are above the mean SUBTRACT the smaller

number from the larger number

5. This is percentage between these two valuesFinding the area between 2 Z scores on the opposite side of the mean

1. Looking for value between two numbers (percentage between value A and value B)2. Find Z scores for both values3. Look up in Z score table4. Look up areas between these 2 Z scores and the mean5. Add the two areas together6. Convert to a percentageFinding the area above a positive Z score OR below a negative Z score

1. Looking for percentage between high values and low values2. Convert value 1 to a z score and look up in column C3. Convert value 2 to a z score and look up in column CFinding a z score bounding an area above it1. Looking for raw score that bounds the top X% of distribution2. Make X% into a proportion3. Look for the percentage converted to a proportion (decimal) in column C4. Then take value in Column A5. This is the z score6. Convert z score to a raw score7. X + z score (standard deviation)=raw score8. Raw score= area that bounds upper X% of distributionFinding a z score bounding an area below it

1. Looking for lower percentage of distribution=X%2. Convert percentage to a proportion (decimal) .X3. Look in column C of z score table for .X4. Then take value from column A which is the z score (negative because on left side)5. Convert Z score to raw score


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6. Mean + a score times standard deviationFinding percentile rank of score higher than the mean

1. Raw score is X and can to calculate the percentile2. Convert raw score to z score3.

Find area beyond Z (column C)4. Subtract area from 1.00-value from column C

5. Result = proportion of scores less than X6.

Finding percentile rank of score lower than the mean

1. Raw score= X which is less than mean2. Convert to z score3. Find area beyond z (column C)4. Multiply by 100 to get a percentileFinding raw score of percentile higher than 501. We need the Xth percentile so where is the cutoff2. Find area associated with percentile= x/100=.x3. SUBTRACT area from 1.00 to find area above and beyond percentile rank 1.00-x4. Convert z score to a raw score

Finding raw score of percentile lower than 501. What about the Xth percentile below the mean2. Find area BELOW the percentile X/1003. Find the z score associated with this area (column C) BUT REMEMBER that this is a

negative Z score since it is less than the mean so Sy is negative -.X

4. Convert z score to raw score

fundamental of statistics mid-term study guide

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