Suppose that you have bivariate data for a sample of a population.

a. How would you decide whether an association exists between the two variables under consideration?

b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.

A quantitative data set has been grouped by using limit grouping with equal-width classes.

The lower limit of the first class is 3 .

The upper limit of the first class is 8.

The class width is 6 .

(a)

The class mark for the second class is as follows:

The second class's lower limit is

= First-class lower limit + Class width

=3+6

=9

The second class's top limit is

= First-class upper limit + Class width

=8+6

=14

The breadth of the class is 6.

9-14 is the second class interval.

The following formula is used to calculate the class mark:

$$\begin{gathered} Mark=\frac{Lowerlimitofthesecondclass+Upperlimitofthesecondclass}{2} \\ =\frac{9+14}{2} \\ =11.5 \end{gathered}$$

As a result, the second-class class mark is 11.5.

(b)

The third class intervals are shown below.

The third class's bottom limit is

$$\begin{gathered} =Thelowerlimitofthesecondclass+theclasswidth. \\ =9+6 \\ =15 \end{gathered}$$

The third class's top maximum is

$$\begin{gathered} =Thesecond-classupperlimit+Classwidth \\ =14+6 \\ =20 \end{gathered}$$

The breadth of the class is 6.

The third class interval costs between 15 and 20.

(c)

The fourth class intervals are shown below.

The fourth class's lower limit is

$$\begin{gathered} =Lowerlimitofthethirdclass+Classwidth \\ =15+6 \\ =21 \end{gathered}$$

The fourth class's upper limit is

$$\begin{gathered} =thethirdclass\text{'}supperlimit+theclass\text{'}swidth \\ =20+6 \\ =26. \end{gathered}$$

The breadth of the class is six.

21 - 26 is the fourth class interval.

As a result, the observation 23 is included in the fourth class intervals.