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23 Cards in this Set
- Front
- Back
arithmetic mean
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computed by adding all the values of the variable in the data set and dividing by the number of observations.
generally just referred to as the mean. It is sensitive to extreme values. usually uses the symbol xbar |
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population arithmetic mean
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(μ pronounced mew) is computed using all of the individuals in the population. It is a parameter.
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sample arithmetic mean (x with a bar over the top pronounced x-bar)
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is computed using sample data. The sample mean is static.
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median
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the value that lies in the middle of the data when the the data is arranged in ascending order. We use M to represent the median. Median is resistive to extreme values.
to help remember think of the median of the road. It divides the road in half. |
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distribution shape in relation to mean and median
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skewed left mean smaller than median
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mode
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a variable is the most frequent observation of the variable that occurs in the data set. Use this when the data are qualitative or the most frequent observation is needed.
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range
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the difference between the largest and the smaller data value. range is not resistant to change and it does not consider all of the data values.
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standard deviation is based on
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the deviation from the mean
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population standard deviation
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of a variable is the square root of the sum of squared deviations about the population mean divided by the number of observations in the population, N. That is, it is the square root of the mean of the squared deviations about the population mean. The population standard deviation is usually lower case greek sigma, σ
N is the number of observations μ is the population |
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conceptual formula
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because it allow us to see how standard deviation measures are spread
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sample standard deviation, s
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s of a variable is the square root of the sum of squared deviations about the sample mean divided by n-1 where n is the sample size.
standard deviation is not resistant |
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deviation about the mean
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the ith observation is xi- u
For a sample, the deviation about the mean for the ith observation is xi - xbar |
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computational formula
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σ =√ ∑x²i - [ (∑xi)² / N ] ÷ N
where ∑x²i means to square each observation and then sum these squared values and (∑xi)² means to add up all the observations and square the sum. |
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degrees of freedom
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n-1 because from the first n-1 observation have freedom to be whatever value they wish, but the nth value has no freedom. It must be whatever value forces the sum of the deviations about the mean to equal zero.
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the larger the standard deviation
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the more dispersion the distribution has (when comparing 2 populations.)
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variance
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the variance of a variable is the square of the standard deviation.
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The population variance is
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σ²
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the sample variance is
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s²
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z-score
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represents the distance that a data value is from mean in terms of standard deviations.
we find it by subtracting the mean from the data value and dividing this result by the standard deviation. There is both a population z-score and a sample z-score The z score is unitless It has a mean of 0 and a standard deviation of 1. it allows us to compare apples to oranges. |
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kth percentile
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denoted Pk of a set of data is a value such that k percent of the observations are less than or equal to the value.
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quartiles are
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resistant to extreme values
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interquartile range IQR
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the range of the middle 50% of the observations in the data set. That is, the IQR is the difference between the third and first quartiles and is found using the formulate IQR= Q3 - Q1
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outlier
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If a data value is less than the lower fence or greater than the upper fence, it is considered an outlier.
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