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50 Cards in this Set
- Front
- Back
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What is ordered array?
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Numerical data sorted by order of magnitude.
Data collected from smallest to largest. |
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What is ordered array usually display on?
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stem-and-leaf diagram
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What is a stem-and-leaf diagram?
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A simple way to see distribution details in a data set.
Stem: leading digits (10, 100) Leaves: trailing digits (11, 24, 190) |
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What is a frequency distribution?
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A lsit or table containing class groupings (ranges within which the data fall) and the corresponding frequencies within which data fall in each grouping or category.
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How do you calculate the width interval of class intervals?
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width of interval =
range/no. of desried class groupings. |
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What graph is used for numerical data?
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Histogram.
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What does a histogram display on its horizontal axis?
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The class boundaries (midpoints).
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What do the bars represent on a histogram?
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The number or percentage of observations within each class.
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What are the 4 summary measures that describe data numerically?
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1. Central Tendency
2. Quartiles 3. Variation 4. Shape |
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What are the measures of central tendency?
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1. Arithmetic mean
2. Median 3. Mode |
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Which is the most common measure of central tendency?
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The mean. However as it is affected by outliers, the median is also often used as it is not sensitive to extreme outliers.
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What is the mean?
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The average value.
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How do you calculate the mean?
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mean=
sum of all values/no. of values |
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What is the median?
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The middle value in an array.
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How do you find the median?
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median position=
no. of values +1/2 |
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What difference does the number of values (odd or even) make to the median?
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Odd: the median is the middle value.
Even: the median is the average of the two middle numbers. |
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What is the mode?
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The most frequent value in an array.
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How many mode's are there in an array?
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There may be no modes or several modes, it depends on the array.
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What are quartiles?
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They split the ranked data into four parts, each with an equal number of values.
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What are the five measures of variation?
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1. Range
2. Interquartile range 3. Variance 4. Standard deviation 5. Coefficient of variation |
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What do measures of variation give information on?
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The spread or variablility of the data values.
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How do you calculate the range?
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Range=
Xlargest - X smallest |
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What does the interquartile range show?
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estimatses some high and low value observations and calculates the range from the remaining values.
It can eliminate some of the outlier problems. |
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How do you calculate the interquartile range?
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interquartile range=
3rd quartile - 1st quartile IR = Q3 - Q1 |
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What is variance?
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The approximate average of squared deviations of values from the mean. It is directly related to the standard deviation.
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How do you calculate variance?
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Variance =
(the sum of ((i'th value of the variable x) - mean) / (sample size - 1) |
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What is standard deviation?
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The most commonly used meausre of variation.
It is the square root of the variance and has the same units as the orginial data. It shows variation about the mean. |
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How do you calculate standard deviation?
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standard deviation =
the square root of variance. |
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What is the coefficient of variation?
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The relative measure of variation.
Always in percentage form. Can be used to compare two or more sets of data measured in different units. |
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How do you calculate the coefficient of variation?
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Coefficient of variation =
standard deviation/mean |
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What is a Z score?
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A measure of relative standing.
The number of standard deviations that given data values are from the mean. |
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What would a Z score of 2.0 mean?
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This means that a value is 2.0 standard deviations from the mean.
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How do you calculate the Z score?
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Z score =
value (x) - mean/standard deviation |
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What does the shape of a distribution show?
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It describes how data is distributed.
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What are the measures of shape?
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1. symmetric
2. skewed |
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What does a left-skewed distribution show?
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mean < medain
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What does a symmetric distribution show?
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mean = median
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What does a right-skewed distribution show?
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mean > median
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What is the Empirical Rule?
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It gives the distribution of data values in terms of standard deviations from the mean for bell-shaped distributions.
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What does m(+ or -)10 mean according to the empriical rule?
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That 68% of the values in the population are within a distance of plus or minus one standard deviation from the mean.
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What does m(+ or -)20 mean according to the empirical rule?
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That 95% of the values in the population are within a distance of plus or minus two standard deviation from the mean.
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What does m(+ or -)30 mean according to the empirical rule?
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That 99.7% of the values in the population are within a distance of plus or minus three standard deviation from the mean.
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What is a box-and-whisker plot?
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It is a graphical display of data using the 5 number summary.
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What is the 5 number summary?
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1. Minimum
2. Q1 3. Median 4. Q3 5. Maximum |
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What is a scatter diagram used for?
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To examine possible relationships between two numerical variables.
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What is the coefficient of correlation?
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It measures the relative strength of the linear relationship between two variables.
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Which formula is used for the coefficient of correlation?
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r = cov(X,Y)/SxSy
where: cov(X,Y) is the sum of variance x plus variance y Sx is the standard deviation of variable x Sy is the standard deviation of variable y |
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What does p = -1 mean?
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Perfect negative correlation.
It means that the larger values of X tend to paired with the smaller values of Y. |
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What does p = 0 mean?
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No correlation.
Larger values of X have no influence of the values of Y. |
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What does p = +1 mean?
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Perfect positive correlation.
It means that larger values of X tend to be paired with the larger values of Y. |
