Representing Data with Number Line Plots - Statistics
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What is a dot plot (line plot) used for when representing numerical data on a number line?
What is a dot plot (line plot) used for when representing numerical data on a number line?
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A plot using dots above values to show frequencies on a number line. Shows frequency distribution of individual values visually.
A plot using dots above values to show frequencies on a number line. Shows frequency distribution of individual values visually.
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Choose the correct statement: In a histogram, do bars touch or have gaps for continuous data?
Choose the correct statement: In a histogram, do bars touch or have gaps for continuous data?
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Bars touch (no gaps) to represent continuous intervals. Adjacent bars show data is continuous, not discrete categories.
Bars touch (no gaps) to represent continuous intervals. Adjacent bars show data is continuous, not discrete categories.
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Identify the frequency: Values $3,4,4,5,5,5$ are plotted; how many dots are above $5$?
Identify the frequency: Values $3,4,4,5,5,5$ are plotted; how many dots are above $5$?
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$3$. Count occurrences: 5 appears three times in the list.
$3$. Count occurrences: 5 appears three times in the list.
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Identify the outlier cutoff: If $Q_3 = 18$ and $IQR = 4$, what is the upper fence?
Identify the outlier cutoff: If $Q_3 = 18$ and $IQR = 4$, what is the upper fence?
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$Q_3 + 1.5(IQR) = 18 + 6 = 24$. Upper fence = $Q_3 + 1.5 imes 4 = 18 + 6 = 24$.
$Q_3 + 1.5(IQR) = 18 + 6 = 24$. Upper fence = $Q_3 + 1.5 imes 4 = 18 + 6 = 24$.
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Identify the outlier cutoff: If $Q_1 = 10$ and $IQR = 6$, what is the lower fence?
Identify the outlier cutoff: If $Q_1 = 10$ and $IQR = 6$, what is the lower fence?
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$Q_1 - 1.5(IQR) = 10 - 9 = 1$. Lower fence = $Q_1 - 1.5 imes 6 = 10 - 9 = 1$.
$Q_1 - 1.5(IQR) = 10 - 9 = 1$. Lower fence = $Q_1 - 1.5 imes 6 = 10 - 9 = 1$.
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Find the $IQR$: If $Q_1 = 12$ and $Q_3 = 20$, what is $IQR$?
Find the $IQR$: If $Q_1 = 12$ and $Q_3 = 20$, what is $IQR$?
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$8$. $IQR = Q_3 - Q_1 = 20 - 12 = 8$.
$8$. $IQR = Q_3 - Q_1 = 20 - 12 = 8$.
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Which plot type is best for comparing medians and $IQR$ across groups quickly?
Which plot type is best for comparing medians and $IQR$ across groups quickly?
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Box plot. Compact display emphasizes quartiles for group comparisons.
Box plot. Compact display emphasizes quartiles for group comparisons.
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Which plot type is usually best for large quantitative data sets to show overall shape?
Which plot type is usually best for large quantitative data sets to show overall shape?
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Histogram. Bins summarize patterns in large continuous datasets.
Histogram. Bins summarize patterns in large continuous datasets.
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Which plot type is usually best for very small data sets where individual values matter most?
Which plot type is usually best for very small data sets where individual values matter most?
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Dot plot. Shows each value clearly when n is small.
Dot plot. Shows each value clearly when n is small.
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What do the whiskers represent in a modified box plot (with outliers shown separately)?
What do the whiskers represent in a modified box plot (with outliers shown separately)?
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The smallest and largest non-outlier values (within $1.5(IQR)$). Whiskers extend to most extreme non-outlier values.
The smallest and largest non-outlier values (within $1.5(IQR)$). Whiskers extend to most extreme non-outlier values.
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Identify the median location: In a box plot, what does the line inside the box represent?
Identify the median location: In a box plot, what does the line inside the box represent?
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The median (the $50$th percentile) of the data. Divides data into two equal halves by count.
The median (the $50$th percentile) of the data. Divides data into two equal halves by count.
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What is the standard outlier rule using the $IQR$?
What is the standard outlier rule using the $IQR$?
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Outliers are $< Q_1 - 1.5(IQR)$ or $> Q_3 + 1.5(IQR)$. Values beyond 1.5 IQRs from quartiles are potential outliers.
Outliers are $< Q_1 - 1.5(IQR)$ or $> Q_3 + 1.5(IQR)$. Values beyond 1.5 IQRs from quartiles are potential outliers.
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What is the interquartile range in terms of quartiles?
What is the interquartile range in terms of quartiles?
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$IQR = Q_3 - Q_1$. Measures middle 50% spread between 25th and 75th percentiles.
$IQR = Q_3 - Q_1$. Measures middle 50% spread between 25th and 75th percentiles.
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What is a box plot (box-and-whisker plot) designed to display for a data set?
What is a box plot (box-and-whisker plot) designed to display for a data set?
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The five-number summary: min, $Q_1$, median, $Q_3$, max. Visualizes spread and center using key percentiles.
The five-number summary: min, $Q_1$, median, $Q_3$, max. Visualizes spread and center using key percentiles.
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What does the area of a bar represent in a density histogram?
What does the area of a bar represent in a density histogram?
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The relative frequency (proportion) in that bin. Area = relative frequency when total area equals 1.
The relative frequency (proportion) in that bin. Area = relative frequency when total area equals 1.
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What does each dot represent in a dot plot when no key or scale change is given?
What does each dot represent in a dot plot when no key or scale change is given?
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One data value (one observation) at that number line position. Standard convention: one dot = one data point unless specified.
One data value (one observation) at that number line position. Standard convention: one dot = one data point unless specified.
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What is the main purpose of a histogram when representing quantitative data?
What is the main purpose of a histogram when representing quantitative data?
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To show frequencies of data grouped into equal-width intervals (bins). Bins group continuous data to visualize distribution shape.
To show frequencies of data grouped into equal-width intervals (bins). Bins group continuous data to visualize distribution shape.
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What does the height of a bar represent in a frequency histogram?
What does the height of a bar represent in a frequency histogram?
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The number of data values in that bin (the frequency). Height shows count of values falling within that bin's range.
The number of data values in that bin (the frequency). Height shows count of values falling within that bin's range.
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What must be true about bin widths in a typical histogram used for comparison?
What must be true about bin widths in a typical histogram used for comparison?
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Bin widths should be equal so bar heights compare frequencies fairly. Equal widths ensure visual comparison of frequencies is valid.
Bin widths should be equal so bar heights compare frequencies fairly. Equal widths ensure visual comparison of frequencies is valid.
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What is a bin (class interval) in a histogram?
What is a bin (class interval) in a histogram?
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A numerical interval that groups data values for counting frequency. Groups consecutive values to count occurrences in ranges.
A numerical interval that groups data values for counting frequency. Groups consecutive values to count occurrences in ranges.
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What is a histogram used to represent for quantitative data?
What is a histogram used to represent for quantitative data?
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Frequencies of data values grouped into equal-width intervals (bins). Groups continuous data into bins to show distribution patterns.
Frequencies of data values grouped into equal-width intervals (bins). Groups continuous data into bins to show distribution patterns.
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What does stacking dots at the same position mean in a dot plot?
What does stacking dots at the same position mean in a dot plot?
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Multiple data points have the same value (higher frequency). Dots stack vertically when values repeat, showing frequency visually.
Multiple data points have the same value (higher frequency). Dots stack vertically when values repeat, showing frequency visually.
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What is a dot plot (line plot) used to represent on a number line?
What is a dot plot (line plot) used to represent on a number line?
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A data set by placing one dot above each value on a number line. Each value gets one dot positioned at its location on the number line.
A data set by placing one dot above each value on a number line. Each value gets one dot positioned at its location on the number line.
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Identify the plot type that best shows overall shape for large data sets.
Identify the plot type that best shows overall shape for large data sets.
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Histogram. Bins group many values to reveal distribution patterns.
Histogram. Bins group many values to reveal distribution patterns.
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Identify the plot type that best compares medians and IQRs across groups.
Identify the plot type that best compares medians and IQRs across groups.
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Box plot. Displays five-number summaries side-by-side for comparison.
Box plot. Displays five-number summaries side-by-side for comparison.
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What percentile corresponds to $Q_1$ in a box plot?
What percentile corresponds to $Q_1$ in a box plot?
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The $25$th percentile. One-quarter of data values fall below this point.
The $25$th percentile. One-quarter of data values fall below this point.
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Identify the plot type that best shows individual repeated values clearly.
Identify the plot type that best shows individual repeated values clearly.
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Dot plot. Shows exact values and frequencies with stacked dots.
Dot plot. Shows exact values and frequencies with stacked dots.
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What is a box plot (box-and-whisker plot) designed to display?
What is a box plot (box-and-whisker plot) designed to display?
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The five-number summary: min, $Q_1$, median, $Q_3$, max. Summarizes data spread using five key positional values.
The five-number summary: min, $Q_1$, median, $Q_3$, max. Summarizes data spread using five key positional values.
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Identify the bin frequency if a histogram bar for $[10,15)$ has height $7$.
Identify the bin frequency if a histogram bar for $[10,15)$ has height $7$.
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$7$ data values. Height directly represents count of values in that interval.
$7$ data values. Height directly represents count of values in that interval.
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What does the median line inside a box plot represent?
What does the median line inside a box plot represent?
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The $50$th percentile of the data (middle value). Divides data in half: 50% above and 50% below this value.
The $50$th percentile of the data (middle value). Divides data in half: 50% above and 50% below this value.
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