Statistics Test 1 (1-4) – Flashcards
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characteristics of people or things
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In statistics variables are
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population
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In statistics, the data we work with is just one part of a bigger picture called the
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How where the variables measured? What variables were measured? Who collected the data?
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What are some things that should be asked when developing an understanding of data?
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Numerical and Categorical
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What are two basic types of variables in statistics?
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qualitative
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Categorical values are also referred to as ____ variables.
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quantitative
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Numerical values are also referred to as ____ variables.
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Variation and data
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The study of statistics rest on what two major concepts?
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context
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Data are more than just numbers, because data have _____
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Variation
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The circles shown are similar, but not exactly the same. This is an example of?
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frequency
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The number of times a value is observed in a data set is called a ___
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They take into account possible differences among the sizes of the groups.
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Why are percentages or rates often better than counts for making comparisons?
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The response variable
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The outcome variable in a question about causality is also referred to as what?
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The Control Group
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In an experiment studying the association between a treatment variable and an outcome variable, the group of people who do NOT receive the treatment are called what?
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Controlled Experiments
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Of the following, which is the only method of data collection suitable for making conclusions about causal relationships? Observational Studies Anecdotes Controlled Experiments All three are suitable
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A confounding variable
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A differences between two groups in an observational study that can explain why the outcomes were very different between the groups is called what?
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To make the groups as similar as possible, minimizing bias.
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Why is random assignment used to assign people to treatment groups and control groups in a controlled experiment?
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Equal sample sizes for control and treatment group
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Which of the following is NOT one of the criteria for the "gold standard" for experiments? Large Sample Size Random assignment of subjects to treatment or control groups Double-blinding Equal sample sizes for control and treatment group
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distribution of a sample
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The ____ organizes data by recording all the values observed in a sample as well as how many times each values was observed.
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See the data and summarize it
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What two-step process is used to examine distributions?
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bins
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In a histogram, observations are grouped into intervals called _____.
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changes the shape of the histogram
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Changing the width of bins in a histogram ______
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proportion
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"Relative frequency" is the same as?
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When technology is not availiable and the data set is not large
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A stemplot is often useful when?
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How many numbers are in the data set
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When examining the shape of a distribution of numerical data, which of the following is NOT one of the three basic characteristics of a distribution's shape? Whether the distribution is symmetric of skewed How many numbers are in the data set How many mounds appear Whether any unusually large or small values are present
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Two very different groups have been combined into a single collection
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The existence of multiple mounds in a distribution is sometimes a sign of what?
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Outliers
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Values so large or so small that they do not fit into the pattern of the distribution are called what?
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Bar graph and pie chart
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Two commonly used graphs to display the distribution of a sample of categorical data are?
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A bar chart is used for numerical variables while a histogram is used for categorical variables.
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What is the main difference between a bar chart and a histogram?
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They are not commonly used by statisticians or in scientific settings
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Because the human eye has a difficult time judging how much area is taken up by the wedge-shaped slice of a pie chart, which of the following is true of pie charts? They are only used for small data sets They are only used if they are made by a computer They are not commonly used by statisticians or in scientific settings They are preferred over bar graphs
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mode
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When describing the distribution of a categorical variable, the category that appears most often is called the ____
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Make an appropriate graph
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What is the first step in almost every investigation of data?
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Change the scale of the vertical axis so that it does not start at 0
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What is the most common trick to mislead readers of bar graphs?
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Decreasing the use of misleading graphics
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Which of the following is NOT a way in which the Internet is influencing statistical graphics? Decreasing the use of misleading graphics Increasing the use of interactive displays Allowing for a greater variety of graphical displays None of the above
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mean
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The ____ is another term for the arithmetic average.
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How many standard deviations away an observation is from the mean
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A standard unit measures what?
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The observation is equal to the mean
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If an observation has a z-score of 0, what does that mean?
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Z-Score
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What is used to compare values measured in different units, such as inches and pounds?
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Mean and Median
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What are two measures of the center of distribution?
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The median is preferred when the data is strongly skewed or has outliers
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Under what conditions is the use of the median preferred?
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The mean is preferred when the data is relatively symmetric
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Under what conditions is the use of the mean preferred?
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median
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The value that would be right in the middle if you were to sort the data from smallest to largest is called the ____
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median interquartile range
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When a distribution is skewed, the ____ is used to measure the center and the ____ is used to measure variation.
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resistant
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Because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is _____ to outliers.
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The mean tends to be greater than the median
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In a right-skewed distribution which of the following is true? The mean tends to be less than the median The mean and median are approximately the same The mean tends to be greater than the median None of these
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median
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In a boxplot, the vertical line inside the box marks the location of the _____.
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IQR
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The length of the box in a boxplot is proportional to what?
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1.5
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In a boxplot, potential outliers are points that are more than _____ IQRs from the edges of the box.
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To the most extreme values that are not potential outliers
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In a boxplot, the whiskers extend to?
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The minimum Q1 The Median Q3 The mamimum
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What are the fiver numbers needed to make a boxplot?
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Variation
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Which of the following is NOT something that one looks for when studying scatterplots? Shape Variation Strength Trend
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a positive association
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Since, in general, the longer a car is owned the more miles it travels one can say there is a ______ between age of car and mileage.
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weak
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A large amount of scatter in a scatterplot is an indication that the association between the two variables is ____.
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trend shape strength context
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When describing two-variable associations, a written description should always include what?
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correlation coefficient (r)
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The _____ is a number that measures the strenth of the linear association between two numerical variables.
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variables are numerical
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The correlation coefficient (r) makes sense only if the trend is linear and the ____
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-1 and 1
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The correlation coefficient (r) is always a number between ____
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Never
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When can a correlation coefficient (r) based on an observational study be used to support a claim of cause and effect?
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It has no effect on r
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When computing the correlation coefficient (r), what is the effect of changing the order of the variables on r?
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regression equation
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The ____ is a tool for making predictions about future observed values and is a useful way of summarizing a linear relationship.
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"predicted"
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Statisticians often write the word ____ in front of the y-variable in the equation of the regression line.
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least squares line
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Another name for the regression line is the ____ line.
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To make predictions about the values of y for a given x-value
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An important use of the regression line is to do what?
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predictor variable explanatory variable independent variable
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When writing a regression equation, what are names for the x-variable?
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predicted variable response variable dependent variable
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When writing a regression equation, what are names for the y-variable?
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A big effect
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What type of effect can outliers have on a regression line?
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Do regression and correlation with and without these points and comment on the differences
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When on has influential points in their data, how should regression and correlation be done?
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influential
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Since outliers can greatly affect the regression line they are also called ____ points
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extrapolation
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Attempting to use the regression equation to make predictions beyond the range of the data is called _____
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coefficient of determination
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The value that measures how much variation in the response variable is explained by the explanatory variable is called the ____.
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variance = s² = (?(x-x?)²/(n-1)
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Variance is another measure of variability and is used if the distribution is symmetric. What is the variance formula?
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r = (?ZxZy)/n-1
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The correlation coefficient (r) measures the strength of a linear association. What is its formula?
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z = (x-x?)/s
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A z-score converts observations into standard units. Its formula is?
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a = ? - bx?
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The formula for the intercept (a) of a regression line is?
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68% 95%
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What percentage of the observations will be within one standard deviation of the mean? Within two?
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IQR = Q? - Q?
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The interquartile range is the measurement of variability best used when the distribution is skewed. Its formula is?
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mean = x? = ?x/n
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The mean is the measure of center best used if the distribution is symmetric. Its formula is?
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"Predicted" y = a + bx
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The regression line summarizes the relationship of a distribution. The regression line formula is?
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Maximum - Minimum
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The range is a crude measure of variability. It's formula is?
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b = r(Sy/Sx)
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The formula for the slope (b) of a regression line is?
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Standard Deviation = s = ?(?(x-x?)²/(n-1)
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The standard deviation is the measure of variability best used if the distribution is symmetric. The formula for standard deviation is?
