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Psychology statistics chapter 3
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Terms in this set (38)
Central Tendency
-A statistical measure to find a single score that defines the center of a distribution.
Purpose: find the single score that is most typical or best represents the entire group
mean
median
mode
what are the three measures of central tendency?
mean
The___ is the sum of all the scores divided by the number of scores in the data.
population Mean
µ=EX/N
Sample Mean
M=EX/n
population
µ = the mean of a___
sample
M=the mean of a_____
x=mean of a____ also.
The Mean: Three Definitions
Mathematical procedure
________: Sum of the scores divided by the number of scores in the data.
The Mean: Three Definitions
The amount each individual receives when the total is divided equally among all the individuals in the distribution
The Mean: Three Definitions
"arithmetic"
The "______" balance point for the distribution
The weighted mean
Combine two sets of scores
Three steps:
Determine the combined sum of all the scores
Determine the combined number of scores
Divide the sum of scores by the total number of scores
M=EX1+EX2/n1+n2
ΣX = 96
A sample of n = 12 scores has a mean of M = 8. What is the value of ΣX for thissample?
Changing
Characteristics of the Mean:
______ the value of a score changes the mean.
New Score
Characteristics of the Mean:
Introducing a _____ or removing a score usually changes the mean (unless the score added or removed is exactly equal to the mean)
adding or subtracting
Characteristics of the Mean:
____ or ____ a constant from each score changes the mean by the same constant
Multiplying or dividing
Characteristics of the Mean:
_____ or ______ each score by a constant multiplies or divides the mean by that constant.
M=10
A sample of n = 7 scores has M = 5. All of the scores are doubled.What is the new mean?
median
The ____ is the midpoint of the scores in a distribution when they are listed in order from smallest to largest.
The median divides the scores into two groups of equal size.
7
Median is the score in the middle
2 3 6 7 9 10 11
what is the median?
even number of scores
2 3 6 7 9 10 11 12
Indentify the middle pair
2 3 6 7 9 10 11 12
The median is the score half way between them (7 + 9)/2 = 16/2 = 8
8 is the median
Note that 8 is not one of the scores
The Precise Median for a continuous variable.
continuous variable
A ______ can be infinitely divided.
The precise median is located in the interval defined by the real limits of the value.
It is necessary to determine the fraction of the interval needed to divide the distribution exactly in half.
Fraction = #needed to reach 50% / # in the interval
We need 1 out of the three boxes
The interval width is 1
1/3 is (# to reach 50%) / (# in interval)
1/3 = .33
The real limits of 3 are 2.5 and 3.5
So 2.5 + .33 = 2.83
median of a continuous variable
_____ = Real Lower Limit + Fraction
mean
____ is the balance point of a distribution
Defined by distances
Often is not the midpoint of the scores
median
____ is the midpoint of a distribution
Defined by number of scores
Often is not the balance point of the scores
Both (mean/median)
____ measure central tendency, using two different concepts of "middle"
True
It is possible for more than 50% of the scores in a distribution to have values above the mean.
True or False:
It is possible for more than 50% of the scores in a distribution to have values above the mean.
False
It is possible for more than 50% of the scores in a distribution to have values above the median.
It is possible for more than 50% of the scores in a distribution to have values above the median.
mode
The ___is the score or category that has the greatest frequency of any in the frequency distribution
Can be used with any scale of measurement
Corresponds to an actual score in the data
It is possible to have more than one mode
nominal scale
median:
Extreme scores
Skewed distribution
Undetermined values
Open-ended distribution
Ordinal scale
-it should not be used when____.
interval or ratio data, except to accompany mean or median
mode:
Nominal scales
Discrete variables
Describing shape
-it should not be used when___.
no situation precludes it
mean:
it should not be used when Extreme scores
Skewed distribution
Undetermined values
Open-ended distribution
Ordinal scale
Nominal scale
-when is it appropriate to use?
independent variable
dependent variable
Graphs can be used to display measures of central tendency
Allows several means (or medians) to be compared simultaneously
Customarily
X axis is the _____
Y axis the _____
Symmetrical distributions
Mean and median have same value
If exactly one mode, it has same value as the mean and the median
Distribution may have more than one mode, or no mode at all
Mean - Median > 0,
Mean - Median < 0
Central Tendency in Skewed Distributions:
Mean, influenced by extreme scores, is found far toward the long tail (positive or negative)
Median, in order to divide scores in half, is found toward the long tail, but not as far as the mean
Mode is found near the short tail.
If ______, the distribution is positively skewed.
If _______, the distribution is negatively skewed
Negatively skewed
A distribution of scores shows Mean = 31 and Median = 43. This distribution is probably
False
The mean uses all the scores in the data, so it is the best measure of central tendency for skewed data.
True or False:
The mean uses all the scores in the data, so it is the best measure of central tendency for skewed data..
True
The mean and median have the same values, so the distribution is probably symmetrical.
True or False:
The mean and median have the same values, so the distribution is probably symmetrical.
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