A Brief Version: Elementary Statistics Ch 3
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| What are the four measures of central tendency? | Mean, median, mode, and midrange.
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| Statistic | A characteristic or measure obtained by using the data values from a sample.
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| Parameter | A characteristic or measure obtained by using the data values from a specific population.
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| Mean | Also known as the arithmetic average. Is found by adding the value of the data and dividing by the total number of values.
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| Median | The midpoint of the data array. The symbol for median is MD. It is found by arranging the data in order and selecting the middle point.
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| Mode | The value that occurs most often in a data set.
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| Unimodal | A data set that has only one value that occurs with the greatest frequency.
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| Bimodal | A data set that has two values that occur with the same greatest frequency and both vales are considered to be the mode.
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| Multimodal | A data set that has more than two values that occur with the same greatest frequency and each value is considered to be the mode.
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| No Mode | No data value occurs more than once.
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| Midrange | The sum of the lowest and the highest values in the data set and then divide by 2. The symbol MR is used.
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| Weighted Mean | Find the mean of a variable X by multiplying each value by its corresponding weight and dividing the sum of the products by the sum of the weights.
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| Positively Skewed or Right-Skewed Distribution | The majority of the data values fall to the left of the mean and cluster at the lower end of the distribution; the "tail" is to the right.
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| Negatively Skewed or Left-Skewed | The majority of the data values fall to the right of the mean and cluster at the upper end of the distribution; the "tail" is to the left.
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| Symmetric Distribution | The data values are evenly distributed on both sides of the mean.
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| Range | The highest value minus the lowest value. The symbol R is used.
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| Variance | The average of the squares of the distance each value is from the mean. The symbol is the Greek lowercase letter sigma squared for population and s squared for sample.
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| Standard Deviation | The square root of the variance. The symbol is the Greek lowercase letter sigma for population and s for sample.
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| N = | Population size.
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| n = | Sample size.
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| X = | Individual value.
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| Coefficient of Variation | Denoted by CVar, is the standard deviation by the mean. The result is expressed as a percentage.
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| The Range Rule of Thumb | A rough estimate of the standard deviation is s = range/4.
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| Chebyshev's Theorm | The proportion from a data set that will fall within k standard deviations of the mean will be at least 1- 1/k^2, where k is a number greater than 1 (k is not necessarily an integer).
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| Empirical Rule | About 68% of the data values will fall within 1 standard deviation of the mean, about 95% within 2 deviations, and 99.7% within 3 deviations.
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| Percentiles | Divide the data set into 100 equal groups.
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| Z Score or Standard Score | A value obtained by subtracting the mean from the value and dividing the results by the standard deviation. The symbol is z.
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| Outlier | An extremely high or an extremely low data value when compared with the rest of the data values.
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| Interquartile Range (IRQ) | The difference between the first quartile and the third quartile.
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| Quartile | Position in fourths that a data value holds in the distribution.
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| Decile | Position in tenths that a data holds in the distribution.
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| Boxplot | A graph drawing a horizontal line from the minimum data value to Q1 drawing a horizontal line from Q3 to the max data value, and drawing a box with vertical sides pass through Q1 and Q3 with a vertical line inside the box passing through the median or Q2.
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| Five-Number Summary | The lowest value of the data set, Q1, the median, Q3, and the highest value of the data set.
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You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
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