Data Interpretation: Descriptive Statistics (College Board AP® Psychology): Flashcards
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What are the three measures of central tendency?
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What are the three measures of central tendency?
The three measures of central tendency are the mean, the median, and the mode.
Define mean.
The mean is the arithmetic average of a data set, calculated by adding all values and dividing by the number of values.
True or False?
The mean score always appears as one of the actual values in the data set.
False.
The mean is a calculated average and may not appear in the data set itself, for example a mean of 6.5 from a set of whole-number scores.
Define median.
The median is the middle value of a data set when all values are arranged in numerical order.
When a data set has an even number of values, the median is calculated by averaging the two __________ values.
When a data set has an even number of values, the median is calculated by averaging the two middle values.
Define mode.
The mode is the most frequently occurring value in a data set.
True or False?
The mode is the only measure of central tendency that can be used with categorical data.
True.
The mode identifies the most frequent category, so it can summarize non-numerical data such as eye color or survey responses, which the mean and median cannot.
When is the median the most appropriate measure of central tendency?
The median is most appropriate when a data set is skewed or contains outliers, because it is not distorted by extreme scores.
When is the mean the most appropriate measure of central tendency?
The mean is most appropriate when data is normally distributed and contains no extreme outliers that would distort the average.
The mean takes every score in a data set into account, making it the most ______________ measure of central tendency.
The mean takes every score in a data set into account, making it the most sensitive measure of central tendency.
Define measures of dispersion.
Measures of dispersion calculate the spread of scores in a data set, showing how much scores vary from one another and from the central measure.
Define range.
The range is the difference between the highest and lowest scores in a data set, calculated by subtracting the lowest value from the highest.
What is a key limitation of the range as a measure of dispersion?
The range only takes two scores into account, so it provides no information about how the other scores are distributed and can be distorted by a single outlier.
Define standard deviation.
Standard deviation measures how much the scores in a data set deviate from the mean, indicating how clustered or spread out scores are around that average.
True or False?
Standard deviation uses every score in the data set, which makes it a more sensitive measure of dispersion than the range.
True.
Because standard deviation incorporates every score, it is a more valid and sensitive representation of the overall spread than the range, which uses only two values.
What does a low standard deviation tell you about a data set?
A low standard deviation indicates that scores are clustered tightly around the mean, showing that participants responded consistently and the data is reliable.
Define percentile rank.
Percentile rank indicates the percentage of scores in a data set that fall at or below a given score, showing where that score sits relative to all others.
A score at the 50th percentile corresponds to the __________ of the data set.
A score at the 50th percentile corresponds to the median of the data set.
A z-score of +1 corresponds to approximately which percentile?
A z-score of +1 corresponds to approximately the 84th percentile, meaning the score is higher than roughly 84% of all scores in the distribution.
Define regression toward the mean.
Regression toward the mean is the statistical tendency for extreme scores on an initial measurement to be closer to the average when the same participants are measured again.
Why does regression toward the mean matter in psychological research?
Regression toward the mean is a significant confounding variable, because an apparent improvement in participants selected for extreme scores may be due to chance rather than the intervention.
A z-score of 0 means that the score is exactly at the ______ of the distribution.
A z-score of 0 means that the score is exactly at the mean of the distribution.
Define distribution.
A distribution refers to the way in which scores are spread across a data set, including how they cluster around the mean and whether that spread is symmetrical or asymmetrical.
Define normal distribution.
A normal distribution is a symmetrical, bell-shaped distribution in which most scores cluster around the mean, with progressively fewer scores toward the extremes.
In a normal distribution, approximately what percentage of scores fall within one standard deviation of the mean?
In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean.
True or False?
Approximately 95% of scores in a normal distribution fall within two standard deviations of the mean.
True.
In a normal distribution, roughly 95% of scores lie within two standard deviations of the mean, so scores beyond this range occur in only about 5% of cases.
In a perfect normal distribution, where do the mean, median, and mode fall?
In a perfect normal distribution, the mean, median, and mode are all equal and located at the peak of the bell curve.
Define skewed distribution.
A skewed distribution is one in which scores are not distributed symmetrically around the mean, with one tail longer than the other.
In a positively skewed distribution, the order of central tendency is mode < median < ______.
In a positively skewed distribution, the order of central tendency is mode < median < mean.
In a negatively skewed distribution, what is the order of the mean, median, and mode?
In a negatively skewed distribution, the order is mean < median < mode, because the extreme low scores in the left tail pull the mean below the other measures.
Define bimodal distribution.
A bimodal distribution has two distinct peaks, where two values occur with equal or near-equal frequency and both more often than any other value in the data set.
True or False?
The mean is the measure of central tendency that is most affected by skew in a data set.
True.
Because the mean uses every score, it is pulled toward the extreme values in the longer tail, while the median and mode remain more stable.
What does a bimodal distribution typically suggest about the sample?
A bimodal distribution suggests that the data set contains two distinct subgroups who responded differently, such as younger and older participants on a memory test.
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