Central Tendency and Variability

Question 1

define measures of central tendency

Answer 1

• single value that represents the most typical score
• can be sued to compare different sets of data
• mean, median, and mode

Question 2

define mean

Answer 2

• defines a typical score for a distribution as the sum of all scores divided by the number of total scores
• represents the amount each individual would receive if the whole was divided equally
• balance the distances between it and all the scores: spaces above the mean = the space below the mean
• can calculate the weighted mean for two or more groups

Question 3

what are the characteristics of the mean?

Answer 3

• changing the scores will change the mean
• adding any score will change the mean, unless the score added is equal to the mean

Question 4

define linear transformation

Answer 4

involves adding/subtracting/multipling/dividing by a constant of every score in the set
- adding a constant to every scores adds the same constant to the mean (goes for all operations)

Question 5

define median

Answer 5

• defines a typical score as the midpoint of the distribution when scores are arranged from lowest to highest
• 50% of the scores fall above the median and 50% are below
• P50 = Q2
• no formula, depends on whether we have an odd or even number of spaces
• for continuos variable, it is possible to split one of the categories into fractional parts and find median by locating the precise point that separate the bottom 50% from top

Question 6

what is the main difference between the median and the mean?

Answer 6

mean is the middle of all the distances and median is the middle of all the scores

Question 7

define mode

Answer 7

• typical score as the most frequently occurring
• always corresponds to an actual score in the set
• can have multiple

Question 8

when do you use the mean?

Answer 8

• the best estimate of the population, as it uses every number
• gives the lowest sampling error
• closely related to measures of variability
• use for ratio and interval data that falls on a normally distributed population

Question 9

what are the different kinds of distribution shapes?

Answer 9

symmetrical: mean and median are the same value, sampling error is lower

skewed: positively or negatively (tail of the graphs points to the side associated with the name), mean and median are not the same anymore

Question 10

when do you use the median?

Answer 10

• when the population is skewed or there are extreme outliers
• ordinal scales not having equal intervals between values

Question 11

when do you use the mode?

Answer 11

• nominal data
• always corresponds to an actual score in the set, used for discrete values
• can be used as a supplement for interval.ratio data to determine the distribution shape

Question 12

define variability

Answer 12

• describes the spread of the scores or the spaces between scores
• how much scores cluster together
• how typical the scores in the distribution are
• range, variance, standard deviation

Question 13

define range

Answer 13

difference between the highest score and lowest score
- continuos scale use real limits
- uses only two scores to measure

Question 14

define variance

Answer 14

average amount of squared deviation from the arithmetic mean

Question 15

define standard deviation

Answer 15

average amount of deviation from the arithmetic mean

Question 16

how is variance estimated from a sample?

Answer 16

• due to sampling error, samples with differ from population
• biased stats will under/overestimate
• unbiased stats is where the under/overestimating will balance each other out
• sampling error from mean is random (unbiased)
• sampling error for variance is systematic (biased), consistently underestimate te population variance

Question 17

define least-squared criterion

Answer 17

sum of squared deviation from the mean is less than the sum of squared deviation taken from any other point

Question 18

how deos linear transormations affect varince?

Answer 18

• ading/subtracting a constant C to every score has no effect on the spaces = no effect on variance
• mulitply/dividng a constant C to every score, space will change, variance would need to be multiplied by C2 and standard deviation by C

Question 19

what is the role fo variance in interential statistics?

Answer 19

• determines how easy it is to detect systematic differences between groups
• lots of variability make it difficult to detect, low variability makes it easier
• sample variance called error variance because it is unexplained differnce between cases