Gr 11 Math Ch 11 SUM: Statistics
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Questions and Answers

What is a histogram?

  • A graphical representation of the relative frequency of a set of continuous or discrete data.
  • A graphical representation of the frequency distribution of a set of continuous or discrete data. (correct)
  • A graphical representation of the mode of a set of continuous or discrete data.
  • A graphical representation of the median of a set of continuous or discrete data.

    • What do the heights of the bars in a histogram represent?

  • The median of the data in each class interval.
  • The mode of the data in each class interval.
  • The frequency of data in each class interval. (correct)
  • The relative frequency of data in each class interval.

    • What is the purpose of determining class intervals when drawing a histogram?

  • To find the relative frequency of the data.
  • To divide the data into equal length intervals. (correct)
  • To find the median of the data.
  • To find the mode of the data.

    • What is a key characteristic of a frequency polygon?

    <p>It uses points connected by straight lines to represent the frequencies of different class intervals.</p> Signup and view all the answers

    What is the first step in drawing a frequency polygon?

    <p>Start by drawing a histogram for the data.</p> Signup and view all the answers

    What is plotted at the midpoint of each class interval on the horizontal axis in a frequency polygon?

    <p>A point.</p> Signup and view all the answers

    What is the ratio of the frequency of an event to the total number of observations?

    <p>Relative frequency.</p> Signup and view all the answers

    What is the main difference between a histogram and a bar graph?

    <p>A histogram does not have gaps between the bars, while a bar graph does.</p> Signup and view all the answers

    What is the formula for calculating the relative frequency?

    <p>Frequency/Total number of observations</p> Signup and view all the answers

    What is the purpose of the cumulative frequency table?

    <p>To construct the ogive</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>∑(xi - x̄)² / n</p> Signup and view all the answers

    What is the unit of the standard deviation?

    <p>Same as the original data</p> Signup and view all the answers

    What is the purpose of the ogive?

    <p>To find the quartiles of the data</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency?

    <p>Sum of all previous frequencies + Current frequency</p> Signup and view all the answers

    What is the definition of the variance?

    <p>The average of the squared differences from the mean</p> Signup and view all the answers

    What is the property of the standard deviation?

    <p>It is always a positive number</p> Signup and view all the answers

    What is the purpose of the histogram?

    <p>To visualize the distribution of the data</p> Signup and view all the answers

    What is the formula for calculating the percentile?

    <p>k/100 × N</p> Signup and view all the answers

    What is the formula to calculate the standard deviation?

    <p>$\sigma = \sqrt{rac{\sum_{i=1}^{n} (x_i - ar{x})^2}{n}}$</p> Signup and view all the answers

    What does a small standard deviation indicate?

    <p>Data values are close to the mean</p> Signup and view all the answers

    What is a characteristic of a symmetric distribution?

    <p>The mean is approximately equal to the median</p> Signup and view all the answers

    What is a characteristic of a right skewed distribution?

    <p>The mean is greater than the median</p> Signup and view all the answers

    What is the formula to calculate the interquartile range (IQR)?

    <p>$IQR = Q3 - Q1$</p> Signup and view all the answers

    How do you identify an outlier in a dataset?

    <p>If the data point is outside the boundaries of $Q1 - 1.5 imes IQR$ and $Q3 + 1.5 imes IQR$</p> Signup and view all the answers

    What is a characteristic of a box-and-whisker plot?

    <p>The median is always at the center of the plot</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show the relationship between two variables</p> Signup and view all the answers

    What is an outlier in a dataset?

    <p>A data point that is far away from the central cluster of data points</p> Signup and view all the answers

    What is the purpose of calculating the five number summary?

    <p>To identify outliers in a dataset</p> Signup and view all the answers

    What is the primary purpose of using class intervals when creating a histogram?

    <p>To ensure equal width intervals</p> Signup and view all the answers

    Which of the following is NOT a characteristic of a histogram?

    <p>There are gaps between the bars</p> Signup and view all the answers

    What is the main advantage of using a frequency polygon over a histogram?

    <p>It is easier to read</p> Signup and view all the answers

    When drawing a frequency polygon, what is plotted at each midpoint?

    <p>A point representing the frequency</p> Signup and view all the answers

    What is the main difference between a histogram and a bar graph?

    <p>The presence of gaps between bars</p> Signup and view all the answers

    Which of the following is an example of a continuous data set?

    <p>The heights of students in a class</p> Signup and view all the answers

    Why are histograms commonly used in statistics?

    <p>To visualize and understand the distribution of data</p> Signup and view all the answers

    Which of the following is NOT a step in drawing a histogram?

    <p>Calculate the median</p> Signup and view all the answers

    What does a large standard deviation indicate about the data?

    <p>Data values are spread out over a larger range.</p> Signup and view all the answers

    What is a common characteristic of a right skewed distribution?

    <p>The mean is greater than the median.</p> Signup and view all the answers

    How do you calculate the boundaries for outliers in a dataset?

    <p>Using the five number summary and interquartile range.</p> Signup and view all the answers

    What is the purpose of a box-and-whisker diagram?

    <p>To identify outliers in a dataset.</p> Signup and view all the answers

    What is a common characteristic of a left skewed distribution?

    <p>The mean is less than the median.</p> Signup and view all the answers

    What is the formula for calculating the standard deviation?

    <p>$\sigma = \sqrt{rac{\sum_{i=1}^{n} (x_i - ar{x})^2}{n}}$</p> Signup and view all the answers

    What is the purpose of the interquartile range in identifying outliers?

    <p>To create boundaries for outliers.</p> Signup and view all the answers

    What is a common characteristic of a symmetric distribution?

    <p>The left and right tails are balanced.</p> Signup and view all the answers

    What does a scatter plot typically show?

    <p>The relationships between two variables.</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To create a box-and-whisker plot.</p> Signup and view all the answers

    What is the main purpose of an ogive plot?

    <p>To calculate the cumulative frequency of a dataset</p> Signup and view all the answers

    Which of the following is a characteristic of a symmetric distribution?

    <p>The median and mean are equal</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>$\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}$</p> Signup and view all the answers

    What is the purpose of calculating the mode of a dataset?

    <p>To identify the most frequently occurring value in a dataset</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>$\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}}$</p> Signup and view all the answers

    What is the purpose of the class mark in a histogram?

    <p>To represent the midpoint of each class interval</p> Signup and view all the answers

    What is the relationship between the variance and standard deviation of a dataset?

    <p>The variance is the square of the standard deviation</p> Signup and view all the answers

    What is the purpose of the median class in a histogram?

    <p>To find the class interval where the median falls</p> Signup and view all the answers

    What is the characteristic of a right-skewed distribution?

    <p>The mean is greater than the median</p> Signup and view all the answers

    What is the purpose of calculating the cumulative frequency of a dataset?

    <p>To find percentiles, including the median</p> Signup and view all the answers

    What is the purpose of using class intervals when drawing a histogram?

    <p>To group data into equal length intervals for easy visualization</p> Signup and view all the answers

    How do you draw a frequency polygon from a histogram?

    <p>By plotting points at the midpoint of each class interval and connecting them with straight lines</p> Signup and view all the answers

    What is the main difference between a histogram and a bar graph?

    <p>A bar graph has gaps between the bars, while a histogram does not</p> Signup and view all the answers

    What is the ratio of the frequency of an event to the total number of observations called?

    <p>Relative frequency</p> Signup and view all the answers

    What is the purpose of drawing a histogram?

    <p>To visualize the frequency distribution of a dataset</p> Signup and view all the answers

    What is plotted at the midpoint of each class interval on the horizontal axis in a frequency polygon?

    <p>A point corresponding to the frequency of the class interval</p> Signup and view all the answers

    What is the primary use of a histogram in statistics?

    <p>To visualize the frequency distribution of a dataset</p> Signup and view all the answers

    What is the result of connecting points plotted at the midpoint of each class interval in a frequency polygon?

    <p>A frequency polygon</p> Signup and view all the answers

    What is the purpose of calculating the relative frequency in a dataset?

    <p>To compare the frequency of different events in a dataset</p> Signup and view all the answers

    What is the formula for calculating the cumulative frequency up to the i-th interval?

    <p>CF_i = ∑_(j=1)^i (f_j)</p> Signup and view all the answers

    What is the purpose of an ogive plot?

    <p>To identify the median and quartiles of a dataset</p> Signup and view all the answers

    What is the property of the variance of a dataset?

    <p>It is always positive</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>σ = (∑_(i=1)^n (x_i - x̄)^2) / n</p> Signup and view all the answers

    What is the purpose of calculating the median of a dataset?

    <p>To identify the middle value of a dataset</p> Signup and view all the answers

    What is the formula for calculating the k-th percentile of a dataset?

    <p>P_k = (k / 100) × N</p> Signup and view all the answers

    What is the characteristic of a dataset with a small standard deviation?

    <p>The data points are close to the mean</p> Signup and view all the answers

    What is the purpose of calculating the quartiles of a dataset?

    <p>To identify the median and interquartile range of a dataset</p> Signup and view all the answers

    What is the purpose of constructing a frequency polygon?

    <p>To visualize the distribution of a dataset</p> Signup and view all the answers

    What does the standard deviation measure in a dataset?

    <p>The amount of variability in the data</p> Signup and view all the answers

    What is an outlier in a dataset?

    <p>A data value that is far away from the central cluster of data points</p> Signup and view all the answers

    What is the purpose of a box-and-whisker plot?

    <p>To identify outliers in a dataset</p> Signup and view all the answers

    What is a characteristic of a right skewed distribution?

    <p>The mean is greater than the median</p> Signup and view all the answers

    What is the formula to calculate the interquartile range (IQR)?

    <p>Q3 - Q1</p> Signup and view all the answers

    What does a small standard deviation indicate about the data?

    <p>The data values are close to the mean</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To summarize the basic features of a dataset</p> Signup and view all the answers

    What is a common characteristic of a left skewed distribution?

    <p>The mean is less than the median</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show the correlation between two variables</p> Signup and view all the answers

    What is the formula to calculate the boundaries for outliers in a dataset?

    <p>Q1 ± 1.5 × IQR</p> Signup and view all the answers

    What is the primary purpose of using class intervals when creating a histogram?

    <p>To divide the data into equal length intervals</p> Signup and view all the answers

    What is the key difference between a histogram and a frequency polygon?

    <p>The way the frequencies are represented</p> Signup and view all the answers

    What is the ratio of the frequency of an event to the total number of observations?

    <p>Relative frequency</p> Signup and view all the answers

    Why are histograms and frequency polygons used in statistics?

    <p>To visualize the frequency distribution of the data</p> Signup and view all the answers

    What is the main advantage of using a frequency polygon over a histogram?

    <p>It provides a clearer picture of the underlying distribution</p> Signup and view all the answers

    What is the purpose of finding the midpoint of each class interval when drawing a frequency polygon?

    <p>To plot the points on the horizontal axis</p> Signup and view all the answers

    What is a characteristic of a histogram that is not present in a bar graph?

    <p>There are no gaps between the bars</p> Signup and view all the answers

    What is the main difference between a histogram and a frequency polygon in terms of their applications?

    <p>Histograms are used for exploratory data analysis, while frequency polygons are used for inferential statistics</p> Signup and view all the answers

    What is the primary purpose of using relative frequency in a histogram?

    <p>To show the proportion of data points in each class</p> Signup and view all the answers

    What is the main difference between a histogram and a frequency polygon?

    <p>A histogram is used for continuous data, while a frequency polygon is used for discrete data</p> Signup and view all the answers

    What is the purpose of calculating the cumulative frequency?

    <p>To construct an ogive plot</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>σ = √(Σ(x - μ)^2 / n)</p> Signup and view all the answers

    What does a small standard deviation indicate about the data?

    <p>The data is closely clustered around the mean</p> Signup and view all the answers

    What is the purpose of calculating the quartiles of a dataset?

    <p>To construct a box-and-whisker plot</p> Signup and view all the answers

    What is the formula for calculating the percentile of a dataset?

    <p>P_k = (k/100) × N</p> Signup and view all the answers

    What is the purpose of an ogive plot?

    <p>To find the median of the dataset</p> Signup and view all the answers

    What is the property of the variance of a dataset?

    <p>It is always positive</p> Signup and view all the answers

    What is the purpose of calculating the variance of a dataset?

    <p>To measure the spread of the data</p> Signup and view all the answers

    What is the implication of a large standard deviation in a dataset?

    <p>Data values have a high degree of variability</p> Signup and view all the answers

    What is the primary purpose of calculating the standard deviation?

    <p>To measure the spread or dispersion of a dataset</p> Signup and view all the answers

    What is the characteristic of a right skewed distribution?

    <p>The right tail is longer than the left tail</p> Signup and view all the answers

    What is the purpose of the interquartile range (IQR) in identifying outliers?

    <p>To calculate the boundaries for outliers</p> Signup and view all the answers

    What is the characteristic of a box-and-whisker plot?

    <p>It displays the five number summary of a dataset</p> Signup and view all the answers

    What is the implication of a small standard deviation in a dataset?

    <p>Data values are closely clustered around the mean</p> Signup and view all the answers

    What is the purpose of calculating the five number summary?

    <p>To summarize the distribution of a dataset</p> Signup and view all the answers

    What is the characteristic of a left skewed distribution?

    <p>The left tail is longer than the right tail</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show the relationship between two variables</p> Signup and view all the answers

    What is the formula for calculating the standard deviation?

    <p>σ = √((Σ(xi - x̄)^2)/n)</p> Signup and view all the answers

    What is the primary purpose of using class intervals when creating a histogram?

    <p>To accurately represent the frequency distribution of the data</p> Signup and view all the answers

    What is the key difference between a histogram and a frequency polygon?

    <p>The method of plotting the data</p> Signup and view all the answers

    What is the purpose of finding the midpoint of each class interval when drawing a frequency polygon?

    <p>To plot the points on the graph</p> Signup and view all the answers

    What is the ratio of the frequency of an event to the total number of observations?

    <p>Relative frequency</p> Signup and view all the answers

    What is the advantage of using a frequency polygon over a histogram?

    <p>It provides a clearer representation of the data distribution</p> Signup and view all the answers

    What is the purpose of the horizontal axis in a histogram?

    <p>To represent the class intervals of the data</p> Signup and view all the answers

    What is the characteristic of a histogram that distinguishes it from a bar graph?

    <p>The absence of gaps between the bars</p> Signup and view all the answers

    What is the purpose of the vertical axis in a histogram?

    <p>To represent the frequency of the data</p> Signup and view all the answers

    What is the primary purpose of calculating the standard deviation in a dataset?

    <p>To measure the spread of the data from the mean</p> Signup and view all the answers

    What is the characteristic of a dataset with a small standard deviation?

    <p>The data values are close to the mean</p> Signup and view all the answers

    Which of the following is a characteristic of a right skewed distribution?

    <p>The mean is greater than the median</p> Signup and view all the answers

    What is the purpose of calculating the interquartile range (IQR)?

    <p>To identify the outliers in the dataset</p> Signup and view all the answers

    What is the formula for calculating the lower boundary for outliers in a dataset?

    <p>Q1 - 1.5 × IQR</p> Signup and view all the answers

    What is the primary purpose of a box-and-whisker diagram?

    <p>To identify the outliers in the dataset</p> Signup and view all the answers

    What is the characteristic of a left skewed distribution?

    <p>The mean is less than the median</p> Signup and view all the answers

    What is the purpose of a scatter plot?

    <p>To show the relationship between two variables</p> Signup and view all the answers

    What is the formula for calculating the standard deviation of a dataset?

    <p>√(Σ(xi - x̄)^2 / n)</p> Signup and view all the answers

    What is the purpose of calculating the five number summary?

    <p>To summarize the distribution of the data</p> Signup and view all the answers

    What is the main difference between a histogram and a frequency polygon?

    <p>A histogram is used to display the frequency of each class interval, while a frequency polygon is used to display the cumulative frequency of each class interval.</p> Signup and view all the answers

    What is the formula for calculating the relative frequency of a class interval?

    <p>Relative Frequency = Frequency / Total number of observations</p> Signup and view all the answers

    What is the purpose of plotting the cumulative frequency against the upper limits of the class intervals in an ogive?

    <p>To find the median and quartiles of a dataset</p> Signup and view all the answers

    What is the formula for calculating the variance of a dataset?

    <p>Variance = (Sum of squared deviations from the mean) / n</p> Signup and view all the answers

    What is the property of the standard deviation that makes it a useful measure of spread?

    <p>It has the same units as the original data</p> Signup and view all the answers

    What is the purpose of using class intervals when creating a histogram?

    <p>To group the data into equal-sized intervals</p> Signup and view all the answers

    What is the formula for calculating the percentile of a dataset?

    <p>P_k = (k/100) * N</p> Signup and view all the answers

    What is the main difference between the variance and standard deviation?

    <p>The variance is a squared measure, while the standard deviation is a non-squared measure</p> Signup and view all the answers

    What is the purpose of calculating the cumulative frequency of a dataset?

    <p>To find the median and quartiles of a dataset</p> Signup and view all the answers

    What is the property of the variance that makes it a useful measure of spread?

    <p>It has squared units</p> Signup and view all the answers

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