Midterm 2

Question 1

Descriptive statistics

Answer 1

• Helps us organize, summarize, and describe data (usually based on samples)
• Without distorting the info it provides about the world

Question 2

Inferential statistics

Answer 2

-Helps us generalize from the sample to the population

Question 3

Graphical representations

Answer 3

• Pie chart = categorical, nominal/ordinal
• Bar graph = categorical, nominal/ordinal
• Histogram = quantitative data
• Frequency polygon = quantitative, continuous data

Question 4

Histogram

Answer 4

• Shows the frequency of occurrence of each score
• X-axis contains RANGES of scores
• Y-axis represents the frequency of occurrence

Question 5

Percentile rank

Answer 5

-Percentile rank of a score value is the percent measurements in the distribution BELOW that value

Question 6

Characteristics of frequency distributions

Answer 6

• Shape
• Central tendency
• Variability

Question 7

Shape of frequency distributions

Answer 7

• Symmetric = two equal halves
• Positively skewed = has score values with low frequencies that trail off towards the positive end
• Negatively skewed = has score values that trail off towards the negative end

MODALITY

• Unimodal = one peak
• Bimodal = two peaks
• Multimodal = multiple peaks
• Uniform = does not have a well define MODE

Question 8

Central tendency

Answer 8

• Central tendency of a distribution is the score of a value that corresponds to the center of that distribution
• A typical or representative score
• Summarizes a distribution
• Allows comparison to other distributions
• Used in inferential statistics procedures

Question 9

What are the 3 main measures of central tendency?

Answer 9

1. Mean
2. Median
3. Mode

Question 10

Mean

Answer 10

-numerical average, obtained by summing all the data scores and then dividing by the number of scores

• Population mean (u) vs sample mean (M)
• A PARAMETER is the true value of a quantity in the population
• A STATISTIC is the value of the same quantity based on a sample
• a statistic (ex. M) is used to estimate a parameter (ex. u)
• M is an unbiased estimator of u

Question 11

Limitations of mean as a central tendency measure

Answer 11

• sensitive to outliers
• poor measure of central tendency for highly skewed distributions
• NOT suitable for ordinal or nominal data

Question 12

Median

Answer 12

• 50th percentile of a distribution
• The middle score with half the measurements above it and half the measurements below it

ADVANTAGES

• Robust against outliers
• A better summary of skewed data
• Can be used with ordinal data

LIMITATIONS
-Median is NOT an unbiased estimator of any population parameter

Question 13

Mode

Answer 13

• The score with the highest frequency
• A distribution with two frequently occurring mode values is bimodal

ADVANTAGES
-Can be used with any type of data, including nominal

LIMITATIONS

• Ignores much of the data
• Is NOT an unbiased estimator of any population data

Question 14

Which measure of central tendency is best to use?

Answer 14

Mean

• Preferred for interval and ratio data
• symmetric distribution

Median

• Use for skewed distribution
• Outliers
• Limits the applicability of statistical tests

Mode

• Categorical data
• Multimodal distributions

Question 15

Variability

Answer 15

-Is the extent to which scores in a frequency distribution differ from one another

Two measures of variability:

• Range
• Variance

Question 16

Variance

Answer 16

-Is the average of the squared deviations of each score from the mean

• Population variance (sigma^2) vs standard deviation (s^2)
• s^2 is an unbiased estimator of sigma^2

Question 17

Standard deviation

Answer 17

• Is an estimate of the average deviation of scores around the mean
• It is the SQUARE ROOT OF VARIANCE