Find the mode of the given data (correct to two places of decimal).

Class interval	0-6	6-12	12-18	18-24	24-30
Frequency	8	7	5	9	4

The correct answer is 20.67.

Step-by-step Explanation:

1. Identify the Modal Class:

The mode of grouped data lies in the class interval with the highest frequency.

Looking at the given frequency distribution:

• Class interval 0-6 has frequency 8

• Class interval 6-12 has frequency 7

• Class interval 12-18 has frequency 5

• Class interval 18-24 has frequency 9

• Class interval 24-30 has frequency 4

The maximum frequency is 9, which corresponds to the class interval 18-24. Therefore, the modal class is 18-24.

2. Formula for Mode of Grouped Data:

The formula to calculate the mode for grouped data is:

$\text{Mode}=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

Where:

• L = Lower limit of the modal class = 18

• f₁ = Frequency of the modal class = 9

• f₀ = Frequency of the class preceding the modal class = 5

• f₂ = Frequency of the class succeeding the modal class = 4

• h = Width of the class interval = 24 - 18 = 6

3. Calculation:

Substitute these values into the mode formula:

$\text{Mode}=18+\left(\frac{9-5}{2\left(9\right)-5-4}\right)\times 6$

Simplify the terms inside the fraction:

$\text{Mode}=18+\left(\frac{4}{18-9}\right)\times 6$

$\text{Mode}=18+\left(\frac{4}{9}\right)\times 6$

$\text{Mode}=18+\frac{24}{9}$

$\text{Mode}=18+\frac{8}{3}$

$\text{Mode}=18+\mathrm{2.6667...}$

$\text{Mode}\approx 20.67$

Thus, the mode of the given data correct to two decimal places is 20.67.