week 2 (central tendency, variance and z scores)

Question 1

mode

Answer 1

the most common score in a data set. The mode is unaffected by extreme scores. Reflects a score which actually occurred

Question 2

median

Answer 2

score corresponding to the point at which 50% of the scores fall below, when data is arranged in numerical order. unaffected by extreme scores. If have even data, median is the average of the middle 2 placements. eg data 4, 8, 10, 12. median is 9.

Question 3

mean

Answer 3

the average score in a data set. (sum all X’s and then divide by N). Most common measure for describing central tendency, but is affected by extreme scores. Easier to work with and manipulate with statistics. The sample mean is usually a better measure of a population mean, compared with mode and median.

Question 4

trimmed means

Answer 4

mean where some of the extreme data scores have been discarded.

Question 5

variability

Answer 5

tells us how far the scores vary from the mean.

Question 6

range

Answer 6

reports minimum and maximum scores for a data set

Question 7

inter-quartile range

Answer 7

extreme scores (upper 25% and lower 25%) removed, and then report the remaining minimum and maximum which is the inter-quartile range

Question 8

average deviation

Answer 8

calculate each deviation from the mean, sum them, then divide by N to give the average deviation BUT this is likely to equal zero, THEREFORE do MEAN ABSOLUTE DEVIATION (m.a.d.) where use absolute deviations (no negatives) and then sum them, then divide by N.

Question 9

variance (S²)

Answer 9

S²=SS/(N-1)

SS = sum of the squared deviations

SS= Σ(X-X^-)²

Note the (N-1) is a statistical correction because the variance in a sample will be less than the population.

Question 10

S=standard deviation

Answer 10

S= square root of (S²)

this is the most common statistic for variability. Provides a measure of the averagedeviation from the mean

Question 11

Normal distribution

Answer 11

Standard normal distribution has a mean of 0 and a standard deviation of 1. Any score in a normally distributed data set, can be converted to a standard normal distribution by using the formula for Z scores. This converts each score, into how many standard deviation units it is from the mean. eg. A z-score of +2 indicates the score is 2 standard deviations above the mean, and a z-score of -1.5 indicates it is 1.5standard deviations below the mean.

Z= deviation from mean/ standard deviation

Z=(X-mean) / S

Note that is data is skewed, and not normally distributed, cannot make use of z scores.

Note that when an attribute is normally distributed, there will always be 34.13% of the population between the mean and +1 standard deviation, 13.59% population scoring between +1 standard deviation and +2 standard deviations, and 2.28% scoring above 2 standard deviations from the mean.

Question 12

Z table

Answer 12

When look at Z table, find the Z score and then can see larger portion and smaller portion. The smaller portion would be the same for same magnitude but negative z. The smaller portion tells us the probability of obtaining the said score or higher, by chance.

Question 13

Confidence limits around Z

Answer 13

To be 95% certain that a score will lie between 2 values, need to remove 2.5% of scores from either end.

1. consult Z table. Find smaller portion of 0.025 (this is 2.5%), here see that Z= 1.96.
2. Calculate scores that represent 1.96 standard deviations below and above the mean.

X= X^-+/-1.96S. This will give you the values within which you are 95% confident any score should randomly score between in a normal distribution.