Stats Exam 2 *Focus*
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Advantage of Mean:
-when to use Mean?
2. More uses than median & mode: Necessary for calculating many inferential statistics.
3. ONLY Use the mean for unimodal, symmetrical distributions of interval/ratio level data.
- 1. More informative than median & mode
- -Takes all the observation/scores into account; highest and lowest scores are accounted for
- -Takes the distance & direction of deviations/errors into account.
Limitations of Mean:
- 1. Not always possible to calculate a mean (scale); Mean can only be calculated for interval/ratio level data
- -Need a different measure for nominal or ordinal level data
- 2. Not always appropriate to use the mean to describe the middle of a distribution (distribution)
- -Mean is sensitive to extreme values or “outliers”
- -Mean does not always reflect where the scores “pile up”
- -Need a different measure for asymmetrical distributions: positive or negative distribution
**When to use the Mean:
Use the mean for unimodal, symmetrical distributions of interval/ratio level data.
- -The middle score.
- -the goal is to find the midpoint "score" of the distribution; it can either equal a score or be the point between two middle scores
- -Calculate by: Order the scores from least to greatest, find middle score or avg the two middle scores
- -Divides the distribution exactly in half; 50th percentile
- -Odd # of scores & no “pileup” or ties at the middle.
Advantage of The Median:
-which scales can it be used with?
-what position does it have in skewed distributions
1. Insensitive to extreme values; Can be used when extreme values distort the mean
2. The most central, representative value in skewed distributions
3. Can be calculated when the mean cannot
4.Can be used with ranks/ordinal scales (as well as interval/ratio data)
5. Can be used with open-ended distributions; Example: # of siblings (5+ siblings?)
Limitation of The Median:
-which scale can't be used?
- 1. Not as informative as the mean; just cuts the scores in half
- 2. Takes only the observations/scores around the 50th percentile into account.
- 3.Provides no information about distances between observations.
- 4.Fewer uses than the mean; Median is purely descriptive (rather than informative)
- 5.Not always possible to calculate a median (scale); can only be calculated for ordinal & interval/ratio data
When to use the median:
Use the median when you cannot calculate a mean or when the distributions of interval/ratio data are skewed by extreme values; ordinal scales, open ended distributions
The most frequently occurring score(s); describes where the scores pile up.
Advantages of the Mode:
-which scales? how does this compare with mean/median?
1.Simple to find
2.Can be used with ANY scale of measurement; Median can only be calculated for ordinal & interval/ratio data vs. Mean can only be calculated for interval/ratio data
3. Can be used to indicate >1 most frequent value; Use to indicate bimodality, multimodality
Limitations of the Mode:
- 1. Not as informative as the mean or median;
- -Takes only the most frequently observed X values into account.
- -Provides no information about distances between observations or the # of observations above/below the mode.
- 2. Fewer uses than the mean: Mode is purely descriptive.
- -Need to calculate a mean to use with inferential statistics.
When to use Mode:
- -Use the mode when you cannot compute a mean or median,
- -or with the mean/median to describe a bimodal/multimodal distribution
- Symmetrical: Mean=median=mode
- Bimodial: mean & median is in the middle
- -nominal scale,
- -to get shape of the distribution.
Variability measures used with the mode & median--> Range:
-Used for what categories?
-when is range used?
Range (For Mode): Based on the distance between the highest & lowest observations on the X scale. Only takes the 2 most extreme observations into account.
For interval/ratio data, range = highest score - lowest score
--Range can also be used for ordered categories: Ex:: from “agree” to “disagree strongly,” with modal response = “disagree.”
--The range is typically used with the mode, when the mean & median are inappropriate or impossible to calculate (but may be reported along with a median or a mean).
Variability measures used with the mean
-used with what scales?
-most useful for what kind of distribution?
-SS, variance & standard deviation are based on distances between each of the scores & the mean on the X scale. All scores are taken into account, as with the mean.
-Use only with interval/ratio data.
-Most useful for symmetrical distributions, when the mean is the best measure of central tendency.
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