Grade 9 Math: Density Graphs
Explore density graphs, their interpretation, and how to calculate density from given data, suitable for Grade 9 mathematics students.
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Density Graphs Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
Understanding Density Graphs
A density graph (or probability density function) illustrates the likelihood of a variable taking on a given value. The area under the curve represents probability, and the total area under the entire curve is always equal to 1.
1. What does the area under a density graph represent?
2. Which of the following statements is true about the total area under any probability density curve?
It is always greater than 1.
It is always less than 1.
It is always equal to 1.
It varies depending on the data.
3. The following density graph represents the distribution of heights (in cm) of a group of students. Use the graph to answer the questions below.
a) What height range has the highest density of students?
b) Roughly what is the density at 160 cm?
c) Describe the overall shape of the distribution. Is it symmetric, skewed left, or skewed right?
4. Complete the following sentences regarding density calculations.
a) Density is calculated by dividing by .
b) If a substance has a mass of 50 grams and a volume of 10 cm³, its density is .
5. A factory produces cylindrical metal rods. The lengths of these rods are found to follow a distribution that can be represented by a density curve. If the mean length is 20 cm and the standard deviation is 2 cm, how would you expect the density curve to look?
6. Explain why a density curve can never dip below the x-axis.
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