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Questions and Answers
What is the range of the masses of the pineapples?
What is the range of the masses of the pineapples?
500 g
What is the formula to find the range of the masses of the pineapples?
What is the formula to find the range of the masses of the pineapples?
Midpoint of the highest class – midpoint of the lowest class
How many pineapples have a mass between 500 g and 599 g?
How many pineapples have a mass between 500 g and 599 g?
12
What is the cumulative frequency of pineapples with a mass less than or equal to 699 g?
What is the cumulative frequency of pineapples with a mass less than or equal to 699 g?
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How many pineapples have a mass greater than 800 g?
How many pineapples have a mass greater than 800 g?
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What is the interquartile range (IQR) of the masses of the pineapples?
What is the interquartile range (IQR) of the masses of the pineapples?
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How can the interquartile range of a set of grouped data be determined from an ogive?
How can the interquartile range of a set of grouped data be determined from an ogive?
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What is the midpoint of the class 400 – 499?
What is the midpoint of the class 400 – 499?
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What is the midpoint of the class 900 – 999?
What is the midpoint of the class 900 – 999?
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How many pineapples have a mass less than or equal to 599 g?
How many pineapples have a mass less than or equal to 599 g?
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Study Notes
Constructing a Frequency Table
- To construct a frequency table, first find the largest and smallest data values.
- Calculate the size of each class interval by dividing the range of data values by the number of classes.
- Determine the class intervals using the size of each class interval.
- Create the frequency table with columns for height (or other variable), frequency, lower limit, upper limit, midpoint, lower boundary, and upper boundary.
Calculating Midpoint, Lower Boundary, and Upper Boundary
- Midpoint = (lower limit + upper limit) / 2
- Lower boundary = lower limit - 0.5
- Upper boundary = upper limit + 0.5
Measures of Dispersion for Grouped Data
- Dispersion can be calculated using two methods.
- To compare the dispersions of two groups, calculate the range or interquartile range for each group.
Traffic Flow Survey
- The diagram shows the survey results of traffic flow in two different locations.
- The distribution shapes in both locations can be determined by examining the graph.
- The dispersions of car speeds in both locations can be compared by calculating the range or interquartile range.
Constructing an Ogive
- An ogive is a cumulative frequency graph.
- To construct an ogive, first create a frequency table with cumulative frequencies.
- Plot the cumulative frequencies against the upper boundaries of the class intervals.
Calculating Quartiles from an Ogive
- To find the first quartile (Q1), draw a horizontal line from the axis of cumulative frequency at 25% until it intersects the ogive, then draw a vertical line down to find the value of Q1.
- Repeat the process to find the second quartile (Q2) and third quartile (Q3).
- Interquartile range = Q3 - Q1.
Calculating Range
- Range = midpoint of the highest class - midpoint of the lowest class.
- Range can be used to measure the dispersion of a set of grouped data.
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Description
Construct a frequency table based on raw data, including finding the lower limit, upper limit, midpoint, lower boundary, and upper boundary. Learn how to organize data into classes and calculate class intervals.
