Psychology statistics chapter 3

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.

Negatively skewed

A distribution of scores shows Mean = 31 and Median = 43. This distribution is probably

ΣX = 96

A sample of n = 12 scores has a mean of M = 8. What is the value of ΣX for thissample?

M=10

A sample of n = 7 scores has M = 5. All of the scores are doubled.What is the new 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.

Sample Mean

M=EX/n

sample

M=the mean of a_____ x=mean of a____ also.

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

7

Median is the score in the middle 2 3 6 7 9 10 11 what is the median?

mean median mode

what are the three measures of central tendency?

population

µ = the mean of a___

population Mean

µ=EX/N

The Mean: Three Definitions Mathematical procedure

________: Sum of the scores divided by the number of scores in the data.

median of a continuous variable

_____ = Real Lower Limit + Fraction

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 > 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

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.

Changing

Characteristics of the Mean: ______ the value of a score changes the mean.

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

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 _____

The Mean: Three Definitions "arithmetic"

The "______" balance point for the distribution

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.

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

The Mean: Three Definitions

The amount each individual receives when the total is divided equally among all the individuals in the distribution

mean

The___ is the sum of all the scores divided by the number of scores in the data.

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.

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.

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..

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

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"

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?

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___.