91Ó°ÊÓ

given,

A quantitative data set has been grouped by using limit grouping with equal-width classes of width 5 . The class limits are whole numbers.

a) If the grade 1 grade mark is $8$, we find the lower and upper limit given below:

The lower limit of the first class is,

$$\begin{gathered} Mark=\frac{Lowerlimitofthefirstclass+Upperlimitofthefirstclass}{2} \\ ⇒Upperlimitofthefirstclass=2Mark-Lowerlimitofthefirstclass \\ =2\left(8\right)-6=10 \end{gathered}$$

Therefore,
The lower limit of the first class is $6$.
The upper limit of the second class is$8$.

The lower limit of the second class is,

$$\begin{gathered} =Lowerlimitofthefirstclass+Classwidth \\ =6+5=11 \end{gathered}$$

The upper limit of the second Class is,

$$\begin{gathered} =Upperlimitofthefirstclass+Classwidth \\ =10+5=15 \end{gathered}$$

The class width is 5 .
The second class interval is $11-15$
Class mark is obtained by using the following formula:

$$\begin{gathered} Mark=\frac{Lowerlimitofthesecondclass+Upperlimitofthesecondclass}{2} \\ =\frac{11+15}{2}=13 \end{gathered}$$

Therefore, the class mark of the second class is 13.

The lower limit of the third class is,

$$\begin{gathered} =Lowerlimitofthesecondclass+Classwidth \\ =15+5=16 \end{gathered}$$

The upper limit of the third class is,

$$\begin{gathered} =Upperlimitofthesecondclass+Classwidth \\ =15+5=20 \end{gathered}$$

The class width is$5$.
The third class interval is $16-20$.

The lower limit of the fourth class is,

$$\begin{gathered} =Lowerlimitofthethirdclass+Classwidth \\ =16+5=21 \end{gathered}$$

The upper limit of the fourth class is,

$$\begin{gathered} =Upperlimitofthethirdclass+Classwidth \\ =20+5=25 \end{gathered}$$

The lower limit of the fifth class is,

$$\begin{gathered} =LowerlimitofthefourthclassClasswidth \\ =21+5=26 \end{gathered}$$

The upper limit of the fifth class is,