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. (D)</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. (B)</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. (C)</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. (A)</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. (C)</p> Signup and view all the answers

What is the formula for calculating the relative frequency?

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

What is the purpose of the cumulative frequency table?

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

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

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

What is the unit of the standard deviation?

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

What is the purpose of the ogive?

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

What is the formula for calculating the cumulative frequency?

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

What is the definition of the variance?

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

What is the property of the standard deviation?

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

What is the purpose of the histogram?

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

What is the formula for calculating the percentile?

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

What is the formula to calculate the standard deviation?

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

What does a small standard deviation indicate?

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

What is a characteristic of a symmetric distribution?

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

What is a characteristic of a right skewed distribution?

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

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

<p>$IQR = Q3 - Q1$ (A)</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 $Q3 + 1.5 imes IQR$ (C)</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 (B)</p> Signup and view all the answers

What is the purpose of a scatter plot?

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

What is the purpose of calculating the five number summary?

<p>To identify outliers in a dataset (C)</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 (C)</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 (A)</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 (D)</p> Signup and view all the answers

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

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

Why are histograms commonly used in statistics?

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

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

<p>Calculate the median (D)</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. (D)</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. (C)</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. (D)</p> Signup and view all the answers

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

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

What is the formula for calculating the standard deviation?

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

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

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

What is a common characteristic of a symmetric distribution?

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

What does a scatter plot typically show?

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

What is the purpose of the five number summary?

<p>To create a box-and-whisker plot. (D)</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 (B)</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 (C)</p> Signup and view all the answers

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

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

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

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

What is the characteristic of a right-skewed distribution?

<p>The mean is greater than the median (D)</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 (C)</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 (C)</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 (D)</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 (C)</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 (B)</p> Signup and view all the answers

What is the purpose of drawing a histogram?

<p>To visualize the frequency distribution of a dataset (C)</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 (D)</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 (B)</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 (B)</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 (C)</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) (C)</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 (A)</p> Signup and view all the answers

What is the property of the variance of a dataset?

<p>It is always positive (B)</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 (D)</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 (B)</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 (B)</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 (A)</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 (C)</p> Signup and view all the answers

What is the purpose of constructing a frequency polygon?

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

What does the standard deviation measure in a dataset?

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

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

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

What is a characteristic of a right skewed distribution?

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

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

<p>Q3 - Q1 (A)</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 (B)</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 (A)</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 (B)</p> Signup and view all the answers

What is the purpose of a scatter plot?

<p>To show the correlation between two variables (D)</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 (C)</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 (A)</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 (B)</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 (D)</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 (A)</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 (B)</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 (C)</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 (A)</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 (C)</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 (D)</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 (C)</p> Signup and view all the answers

What is the purpose of calculating the cumulative frequency?

<p>To construct an ogive plot (D)</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) (B)</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 (D)</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 (D)</p> Signup and view all the answers

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

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

What is the purpose of an ogive plot?

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

What is the property of the variance of a dataset?

<p>It is always positive (A)</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 (C)</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 (C)</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 (C)</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 (A)</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 (A)</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 (D)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

What is the purpose of a scatter plot?

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

What is the formula for calculating the standard deviation?

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

What is the characteristic of a left skewed distribution?

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

What is the purpose of a scatter plot?

<p>To show the relationship between two variables (D)</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) (D)</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 (B)</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. (A)</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 (C)</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 (B)</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 (D)</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 (D)</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 (C)</p> Signup and view all the answers

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

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

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