Consider a ${\chi }^2$-curve with 17 degrees of freedom. Use Table V to determine

a.$x_{0.10-}^2$

b. $x_{0.01}^2.$

c. the $x^2$-value that has area 0.05 to its right.

Limit grouping with equal-width 5 was used to group a quantitative data collection.

a)

If the first-class mark is 8, we may calculate the lower and higher limits as follows:

The first class's lowest limit is

$$\begin{gathered} =1+Classwidth \\ =1+5 \\ =6 \end{gathered}$$

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

Therefore,

The first class has a lower limit of 6.

The second class has a maximum of 10 students.

b)

The class mark for the second class is as follows.

The second class's lower limit is

$$\begin{gathered} =thefirstclass\text{'}slowerlimit+classwidth \\ =6+5 \\ =11 \end{gathered}$$

The second class's maximum limit is

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

The breadth of the class is 5.

11-15 is the second class interval.

The following formula is used to calculate the class mark:

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

As a result, the second-class class mark is 13.

c)

The third class intervals are shown below.

The third class's lowest limit is

$$\begin{gathered} =Lowerlimitofthesecondclass+Classwidth \\ =11+5 \\ =16 \end{gathered}$$

The third class's top maximum is

$$\begin{gathered} =Second-classupperlimit+Classwidth \\ =15+5 \\ =20 \end{gathered}$$

The breadth of the class is 5.

The third class interval is between 16 and 20.

d)

The fourth class intervals are shown below.

The fourth class's lower limit is

$$\begin{gathered} =thethirdclass\text{'}slowerlimit+theclass\text{'}swidth. \\ =16+5 \\ =21 \end{gathered}$$

The fourth class's upper limit is

$$\begin{gathered} =thethirdclass\text{'}supperlimit+theclass\text{'}swidth \\ =20+5 \\ =25. \end{gathered}$$

The fifth-class intervals are listed below.

The fifth class's lower limit is

$$\begin{gathered} =thefourthclass\text{'}slowerlimit+theclass\text{'}swidth \\ =21+5 \\ =26. \end{gathered}$$

The fifth class's top maximum is

$$\begin{gathered} =Upperlimitofthefourthclass+Classwidth \\ =25+5 \\ =30 \end{gathered}$$

The fifth-class interval is between 26 and 30.

As a result, the observation 28 is included in the fifth class intervals.