Gr 11 Math Ch 11 SUM: Statistics

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?

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

What is the first step in drawing a frequency polygon?

Start by drawing a histogram for the data. Signup and view all the answers

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

A point. Signup and view all the answers

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

Relative frequency. Signup and view all the answers

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

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

What is the formula for calculating the relative frequency?

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

What is the purpose of the cumulative frequency table?

To construct the ogive Signup and view all the answers

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

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

What is the unit of the standard deviation?

Same as the original data Signup and view all the answers

What is the purpose of the ogive?

To find the quartiles of the data Signup and view all the answers

What is the formula for calculating the cumulative frequency?

Sum of all previous frequencies + Current frequency Signup and view all the answers

What is the definition of the variance?

The average of the squared differences from the mean Signup and view all the answers

What is the property of the standard deviation?

It is always a positive number Signup and view all the answers

What is the purpose of the histogram?

To visualize the distribution of the data Signup and view all the answers

What is the formula for calculating the percentile?

k/100 × N Signup and view all the answers

What is the formula to calculate the standard deviation?

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

What does a small standard deviation indicate?

Data values are close to the mean Signup and view all the answers

What is a characteristic of a symmetric distribution?

The mean is approximately equal to the median Signup and view all the answers

What is a characteristic of a right skewed distribution?

The mean is greater than the median Signup and view all the answers

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

$IQR = Q3 - Q1$ Signup and view all the answers

How do you identify an outlier in a dataset?

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

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

The median is always at the center of the plot Signup and view all the answers

What is the purpose of a scatter plot?

To show the relationship between two variables Signup and view all the answers

What is an outlier in a dataset?

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

What is the purpose of calculating the five number summary?

To identify outliers in a dataset Signup and view all the answers

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

To ensure equal width intervals Signup and view all the answers

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

There are gaps between the bars Signup and view all the answers

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

It is easier to read Signup and view all the answers

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

A point representing the frequency Signup and view all the answers

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

The presence of gaps between bars Signup and view all the answers

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

The heights of students in a class Signup and view all the answers

Why are histograms commonly used in statistics?

To visualize and understand the distribution of data Signup and view all the answers

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

Calculate the median Signup and view all the answers

What does a large standard deviation indicate about the data?

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

What is a common characteristic of a right skewed distribution?

The mean is greater than the median. Signup and view all the answers

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

Using the five number summary and interquartile range. Signup and view all the answers

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

To identify outliers in a dataset. Signup and view all the answers

What is a common characteristic of a left skewed distribution?

The mean is less than the median. Signup and view all the answers

What is the formula for calculating the standard deviation?

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

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

To create boundaries for outliers. Signup and view all the answers

What is a common characteristic of a symmetric distribution?

The left and right tails are balanced. Signup and view all the answers

What does a scatter plot typically show?

The relationships between two variables. Signup and view all the answers

What is the purpose of the five number summary?

To create a box-and-whisker plot. Signup and view all the answers

What is the main purpose of an ogive plot?

To calculate the cumulative frequency of a dataset Signup and view all the answers

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

The median and mean are equal Signup and view all the answers

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

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

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

To identify the most frequently occurring value in a dataset Signup and view all the answers

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

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

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

To represent the midpoint of each class interval Signup and view all the answers

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

The variance is the square of the standard deviation Signup and view all the answers

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

To find the class interval where the median falls Signup and view all the answers

What is the characteristic of a right-skewed distribution?

The mean is greater than the median Signup and view all the answers

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

To find percentiles, including the median Signup and view all the answers

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

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

How do you draw a frequency polygon from a histogram?

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

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

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

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

Relative frequency Signup and view all the answers

What is the purpose of drawing a histogram?

To visualize the frequency distribution of a dataset Signup and view all the answers

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

A point corresponding to the frequency of the class interval Signup and view all the answers

What is the primary use of a histogram in statistics?

To visualize the frequency distribution of a dataset 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?

A frequency polygon Signup and view all the answers

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

To compare the frequency of different events in a dataset Signup and view all the answers

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

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

What is the purpose of an ogive plot?

To identify the median and quartiles of a dataset Signup and view all the answers

What is the property of the variance of a dataset?

It is always positive Signup and view all the answers

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

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

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

To identify the middle value of a dataset Signup and view all the answers

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

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

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

The data points are close to the mean Signup and view all the answers

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

To identify the median and interquartile range of a dataset Signup and view all the answers

What is the purpose of constructing a frequency polygon?

To visualize the distribution of a dataset Signup and view all the answers

What does the standard deviation measure in a dataset?

The amount of variability in the data Signup and view all the answers

What is an outlier in a dataset?

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

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

To identify outliers in a dataset Signup and view all the answers

What is a characteristic of a right skewed distribution?

The mean is greater than the median Signup and view all the answers

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

Q3 - Q1 Signup and view all the answers

What does a small standard deviation indicate about the data?

The data values are close to the mean Signup and view all the answers

What is the purpose of the five number summary?

To summarize the basic features of a dataset Signup and view all the answers

What is a common characteristic of a left skewed distribution?

The mean is less than the median Signup and view all the answers

What is the purpose of a scatter plot?

To show the correlation between two variables Signup and view all the answers

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

Q1 ± 1.5 × IQR Signup and view all the answers

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

To divide the data into equal length intervals Signup and view all the answers

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

The way the frequencies are represented Signup and view all the answers

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

Relative frequency Signup and view all the answers

Why are histograms and frequency polygons used in statistics?

To visualize the frequency distribution of the data Signup and view all the answers

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

It provides a clearer picture of the underlying distribution Signup and view all the answers

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

To plot the points on the horizontal axis Signup and view all the answers

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

There are no gaps between the bars Signup and view all the answers

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

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

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

To show the proportion of data points in each class Signup and view all the answers

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

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

What is the purpose of calculating the cumulative frequency?

To construct an ogive plot Signup and view all the answers

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

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

What does a small standard deviation indicate about the data?

The data is closely clustered around the mean Signup and view all the answers

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

To construct a box-and-whisker plot Signup and view all the answers

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

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

What is the purpose of an ogive plot?

To find the median of the dataset Signup and view all the answers

What is the property of the variance of a dataset?

It is always positive Signup and view all the answers

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

To measure the spread of the data Signup and view all the answers

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

Data values have a high degree of variability Signup and view all the answers

What is the primary purpose of calculating the standard deviation?

To measure the spread or dispersion of a dataset Signup and view all the answers

What is the characteristic of a right skewed distribution?

The right tail is longer than the left tail Signup and view all the answers

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

To calculate the boundaries for outliers Signup and view all the answers

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

It displays the five number summary of a dataset Signup and view all the answers

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

Data values are closely clustered around the mean Signup and view all the answers

What is the purpose of calculating the five number summary?

To summarize the distribution of a dataset Signup and view all the answers

What is the characteristic of a left skewed distribution?

The left tail is longer than the right tail Signup and view all the answers

What is the purpose of a scatter plot?

To show the relationship between two variables Signup and view all the answers

What is the formula for calculating the standard deviation?

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

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

To accurately represent the frequency distribution of the data Signup and view all the answers

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

The method of plotting the data Signup and view all the answers

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

To plot the points on the graph Signup and view all the answers

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

Relative frequency Signup and view all the answers

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

It provides a clearer representation of the data distribution Signup and view all the answers

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

To represent the class intervals of the data Signup and view all the answers

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

The absence of gaps between the bars Signup and view all the answers

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

To represent the frequency of the data Signup and view all the answers

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

To measure the spread of the data from the mean Signup and view all the answers

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

The data values are close to the mean Signup and view all the answers

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

The mean is greater than the median Signup and view all the answers

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

To identify the outliers in the dataset Signup and view all the answers

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

Q1 - 1.5 × IQR Signup and view all the answers

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

To identify the outliers in the dataset Signup and view all the answers

What is the characteristic of a left skewed distribution?

The mean is less than the median Signup and view all the answers

What is the purpose of a scatter plot?

To show the relationship between two variables Signup and view all the answers

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

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

What is the purpose of calculating the five number summary?

To summarize the distribution of the data Signup and view all the answers

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

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. Signup and view all the answers

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

Relative Frequency = Frequency / Total number of observations 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?

To find the median and quartiles of a dataset Signup and view all the answers

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

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

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

It has the same units as the original data Signup and view all the answers

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

To group the data into equal-sized intervals Signup and view all the answers

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

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

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

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

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

To find the median and quartiles of a dataset Signup and view all the answers

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

It has squared units Signup and view all the answers

Gr 11 Math Ch 11 SUM: Statistics

Questions and Answers

What is a histogram?

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

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

What is a key characteristic of a frequency polygon?

What is the first step in drawing a frequency polygon?

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

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

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

What is the formula for calculating the relative frequency?

What is the purpose of the cumulative frequency table?

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

What is the unit of the standard deviation?

What is the purpose of the ogive?

What is the formula for calculating the cumulative frequency?

What is the definition of the variance?

What is the property of the standard deviation?

What is the purpose of the histogram?

What is the formula for calculating the percentile?

What is the formula to calculate the standard deviation?

What does a small standard deviation indicate?

What is a characteristic of a symmetric distribution?

What is a characteristic of a right skewed distribution?

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

How do you identify an outlier in a dataset?

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

What is the purpose of a scatter plot?

What is an outlier in a dataset?

What is the purpose of calculating the five number summary?

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

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

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

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

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

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

Why are histograms commonly used in statistics?

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

What does a large standard deviation indicate about the data?

What is a common characteristic of a right skewed distribution?

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

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

What is a common characteristic of a left skewed distribution?

What is the formula for calculating the standard deviation?

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

What is a common characteristic of a symmetric distribution?

What does a scatter plot typically show?

What is the purpose of the five number summary?

What is the main purpose of an ogive plot?

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

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

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

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

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

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

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

What is the characteristic of a right-skewed distribution?

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

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

How do you draw a frequency polygon from a histogram?

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

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

What is the purpose of drawing a histogram?

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

What is the primary use of a histogram in statistics?

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

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

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

What is the purpose of an ogive plot?

What is the property of the variance of a dataset?

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

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

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

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

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

What is the purpose of constructing a frequency polygon?

What does the standard deviation measure in a dataset?

What is an outlier in a dataset?

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

What is a characteristic of a right skewed distribution?