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2 years ago

You would like to build a relative frequency distribution for this data set to easily compare it to another class of students.

Mathematics

1 answer:

Dafna1 [17]2 years ago

8 0

The relative frequency for the third class, 60 - 69 is equal to 12%.

<h3>What is a class width?</h3>

In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table.

<h3>What is a frequency table?</h3>

A frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

<h3>How to calculate the relative frequency for the third class, 60 - 69?</h3>

First of all, we would determine the total number of frequency as follows:

Total frequency = 12 + 11 + 6 + 10 + 11

Total frequency = 50.

Mathematically, relative frequency can be calculated by using this formula:

Relative frequency = class frequency/total frequency × 100

Relative frequency = 6/50 × 100

Relative frequency = 0.12 × 100

Relative frequency = 12%.

Read more on frequency table here: brainly.com/question/20744563

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Complete Question:

You would like to build a relative frequency distribution for this data set to easily compare it to another class of students.

What is the relative frequency for the third class, 60 - 69?

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The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city

Tresset [83]

The quadratic regression equation for this data set is $\rm y=-0.143x^2+0.59x+2.82\\$ .

<h3>What is the general form of a quadratic equation?</h3>

The general form of the quadratic equation is given by;

$\rm ax^2+bx+c=0$

Where; a, b, and c are the constants.

x; 0 1 2 3 4 5

y; 2.82 3. 29 3. 46 3. 33 2. 88 2. 24

From the table when the value of x = 0 the value of y is 2.82.

Then,

$\rm y=ax^2+bx+c\\\\x=0\\\\2.82=a0^2+b(0)+c\\\\c=2.82$

From the table when the value of x = 3 the value of y is 3.33.

$\rm y=ax^2+bx+c\\\\x=3\\\\2.82=a(3)^2+b(3)+c\\\\9a+3b+2.82=2.82\\\\9a=-3b\\\\b=-3a\\\\$

From the table when the value of x = 5 the value of y is 2.24.

$\rm y=ax^2+bx+c\\\\x=3\\\\2.24=a(5)^2+(-3a)(5)+c\\\\25a-15a+2.82=2.24\\\\40a=2.24-2.82\\\\10a=-0.68\\\\a= \dfrac{-0.68}{10}\\\\a=-0.143$

And the value of b is;

$\rm b=3a\\\\b=3(-0.14)\\\\b=0.59$

Therefore,

The quadratic regression equation for this data set is;

$\rm y=ax^2+bx+c\\\\y=-0.143x^2+0.59x+2.82\\\\$

Hence, the quadratic regression equation for this data set is $\rm y=-0.143x^2+0.59x+2.82\\$ .

To know more about the Quadratic equation click the link given below.

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