Chapter 2 - Central Tendency G+W

in most situations with numerical scores from an interval or ratio scale, the mean is the preferred measure of _____________________ _________________________.

central tendency

the normal distribution is the most _____________________________ distribution.

common

the mean is usually the best measure of central tendency when your data distribution is ____________________ and ______________________, such as when your data is normally distributed.

continuous . . . symmetrical

the mode is the most frequently occurring score in a

distribution

Conceptually, the mean is obtained by:

dividing the total (EX) equally among the number of individuals (N or n).

if the data set is perfectly normal, the mean, median and mean are __________________ to each other.

equal (the same value)

a distribution with a mean of 70 and a median of 75 is probably positively skewed. true or false?

false. the mean is displaced toward the tail on the left-hand side.

If you have a score of 52 on an 80 point exam, then you definitely scored above the median (true or false)

false. the value of the median would depend on where all the scores are located.

the gaol of central tendency is to:

find the single score that is most typical or most representative of the entire group

the mode is easily located by:

finding the peak in a frequency distribution graph

in skewed distributions (especially distributions for continuous variables) there is a strong tendency:

for the mean median and mode to be located in predictably different positions.

When should you NOT use the mean to measure Central Tendency?

in the presence of extreme outliers

if a symmetrical distribution has only one mode:

it is also in the center of the distribution

A sample of n = 6 scores has a mean of M = 40. One new score is added to the sample and the new mean is found to be M = 35. What can you conclude about the value of the new score?

it must be less than 40

a left skewed distribution has a long _______________ tail

left

Which measure of central tendency is most affected if one extremely large score is added to a distribution? (mean, median, mode)

mean

best measure of central tendency for not skewed interval/ratio variables

mean

the three standard measures of central tendency are:

mean, median and mode

If scores in a distribution are listed in order from smallest to largest, the _________________ is the midpoint of the list.

median

best measure of central tendency for ordinal variables

median

best measure of central tendency for skewed interval/ratio variables

median

for symmetrical distributions, the mean is equal to the _________________, if there is only one mode, then it has __________ _________________ value ________.

median . . . same . . .too

Best measure of central tendency for nominal variables:

mode

nominal data only has a ______________.

mode

a left skewed distribution is also known as a _______________________ skewed distribution.

negatively

a peak that leans right is ________________________ skewed, or ___________________ skewed.

negatively . . . left

a rectangular distribution has

no mode because all X values occur with the same frequency. still the mean and median are in the center of the distribution

for data measured on a _______________ scale, the mode is the appropriate measure of central tendency.

nominal

discrete variables are those that exist:

only in whole indivisible categories. often numerical values, such as the number of children in a family or the number of rooms in a house

the median also is used for:

open-ended distributions and when there are undetermined (infinite) scores that make it impossible to compute a mean.

a right skewed distribution is also known as a _________________ skewed distribution

positively

a peak that leans left is ______________________ skewed, or _____________________ skewed.

positively . . . right

a right skewed distribution has a long __________________ tail

right

overall mean is also known as

the weighted mean

the purpose of central tendency is:

to determine the single value that identifies the center of the distribution and best represents the entire set of scores.

for skewed distributions, the mode is located:

toward the side where the scores pile up, the mean is pulled toward the extreme scores in the tail. the median is usually located between these two values.

changing the value of a score in a distribution always changes the mean

true.

When to use the mode:

-nominal scales -discrete variables (whole values) -describing a shape

when constructing a graph of any type, you should recall the two basic rules:

1) the height of a graph should be approximately two-thirds to three-quarters of its length 2) normally, you start numbering both the X-axis and the Y-axis with zero at the point where the two axes intersect. However, when a value of zero is part of the data, it is common to move the zero point away from the intersection so that the graph does not overlap the axes.

what two values do we need to calculate the overall mean of a distribution?

1) the overall sum of the scores for the combined group (EX) 2) the total number of scores in the combined group (n)

more specifically, the median is the point on the measurement scale below which _______% of the scores in the distribution are located.

50

find the mean for the following sample of n = 5 scores: 1, 8, 7, 5, 9

EX = 30 and M=6

A sample of n = 6 scores has a mean of M = 8. What is the value of EX for this sample?

EX = 48

In a perfectly symmetrical distribution, the mean, the median, and the mode will all have the same value - True/False?

False, if the distribution is bimodal

Adding a new score to a distribution always changes the mean. True or false?

False. if the score is equal to the mean, it does not change the mean

a sample mean is identified by the letter:

M

when defining the midpoint, we are:

NOT locating the midpoint between the highest and lowest x-values

the median is the preferred measure of central tendency when:

a distribution has a few extreme scores that displace the value of the mean

a bimodal distribution that is symmetrical has:

a mean and median together in the center with the modes on each side.

central tendency

a statistical measure to determine a single score that defines the center of a distribution.

Find the median for each distribution of scores: a) 3, 4, 6, 7, 9, 10, 11 b) 8, 10, 11, 12, 14, 15

a) the median is X=7 b) the median is X=11.5

the mean is computed by:

adding all of the scores and then dividing by the number of scores

for a perfectly symmetrical distribution with one mode:

all three measures of central tendency (the mean, median and mode) have the same value

the distance above the mean is exactly ___________________ by the distance below the mean.

balanced . . .

why is a left skewed distribution sometimes called a negatively skewed distribution?

because it's long tail is on the negative direction on a number line.

how do you find the total number of scores in the combined group?

by adding the number of scores in the first sample (n1) and the number of scores in the second sample (n2).

the mean is:

the arithmetic average, the balance point for the distribution

One sample has n = 5 scores with a mean of M = 4. A second sample has n = 3 scores with a mean of M = 10. If the two samples are combined, what is the mean for the combined sample?

the combined sample has n = 8 scores that total EX = 50. the M=6.25

Why is it usually considered inappropriate to compute a mean for scores measured on an ordinal scale?

the definition of the mean is based on distances (the mean balances the distances) and ordinal scales do not measure distance.

left skewed boxplot

the left whisker is longer than the right whisker

if every score is multiplied by a constant:

the mean is multiplied by the same constant

changing any score in the distribution causes:

the mean to change

the following is a distribution of measurements for a continous variable. Find the precise median that divides the distribution exactly in half. Scores: 1, 2, 2, 3, 4, 4, 4, 4, 5

the median is 3.70 (one-fifth of the way into the interval from 3.5 to 4.5)

the median is:

the midpoint of a distribution of scores

a population has a mean of m=40. If every score were multiplied by 3, what would be the value for the new mean?

the new mean would be 120.

a population has a mean of m=40. If 5 points were added to every score, what would be the value for the new mean?

the new mean would be 45

A sample of n = 4 scores has a mean of 9. If one person with a score of X = 3 is removed from the sample, what is the value for the new sample mean?

the original sample has n = 4 and EX = 36. The new sample has n = 3 scores that total EX = 33. The new mean is M = 11.

right skewed histogram

the peak of the histogram veers to the left . . tails have positive skew to the right

left skewed histogram

the peak of the histogram veers to the right . . tails have a negative skew to the left

right skewed boxplot

the right whisker looks longer and the mean is greater than the median

when a constant value is added to or subtracted from every score in the distribution:

the same constant value is added to or subtracted from the mean

the midpoint of a distribution means:

the scores are divided up into two equal sized groups.