The problem has two parts. Part 1: Complete the missing values in the given table, which represents the age distribution of students. The table has columns for Age(years), Frequency, Cumulative Frequency, and Relative Frequency. Part 2: Identify the features of a bar graph from the given statements.

1. Problem Description

The problem has two parts.

Part 1: Complete the missing values in the given table, which represents the age distribution of students. The table has columns for Age(years), Frequency, Cumulative Frequency, and Relative Frequency.

Part 2: Identify the features of a bar graph from the given statements.

2. Solution Steps

Part 1: Completing the Table

First, calculate the total frequency which is given as

2

5. We have the frequencies for the intervals 10-15, 16-21, and 44-

6

0. Let the frequency for 22-32 be $f_1$ and for 33-43 be $f_2$.

The sum of all frequencies must be 25:

$2 + 4 + f_1 + f_2 + 5 = 25$

$11 + f_1 + f_2 = 25$

$f_1 + f_2 = 14$

We are given that the relative frequency for the age group 22-32 is 0.

3

2. The relative frequency is calculated as the frequency of the interval divided by the total frequency.

$Relative\,Frequency = \frac{Frequency}{Total\,Frequency}$

$0.32 = \frac{f_1}{25}$

$f_1 = 0.32 * 25 = 8$

Substituting $f_1=8$ in the equation $f_1 + f_2 = 14$, we have:

$8 + f_2 = 14$

$f_2 = 6$

Now, calculate the cumulative frequencies.

For 10-15: Cumulative frequency = 2

For 16-21: Cumulative frequency = 2 + 4 = 6

For 22-32: Cumulative frequency = 6 + 8 = 14

For 33-43: Cumulative frequency = 14 + 6 = 20

For 44-60: Cumulative frequency = 20 + 5 = 25

Relative frequencies are calculated as Frequency/Total Frequency.

For 10-15: Relative frequency = 2/25 = 0.08

For 16-21: Relative frequency = 4/25 = 0.16

For 22-32: Relative frequency = 8/25 = 0.32 (Given)

For 33-43: Relative frequency = 6/25 = 0.24

For 44-60: Relative frequency = 5/25 = 0.20

Completed Table:

Age(years) | Frequency | Cumulative Frequency | Relative Frequency

------- | -------- | -------- | --------

10-15 | 2 | 2 | 0.08

16-21 | 4 | 6 | 0.16

22-32 | 8 | 14 | 0.32

33-43 | 6 | 20 | 0.24

44-60 | 5 | 25 | 0.20

Part 2: Features of a Bar Graph

I. This representation displays data in bars of equal size and spacing. (True)

II. Frequencies/relative frequencies represent height of bars. (True)

III. Bars are arranged in decreasing order of frequency or relative frequency. (False, this is not always the case).

Therefore, only statements I and II are true.

3. Final Answer

The completed table is:

Age(years) | Frequency | Cumulative Frequency | Relative Frequency

------- | -------- | -------- | --------

10-15 | 2 | 2 | 0.08

16-21 | 4 | 6 | 0.16

22-32 | 8 | 14 | 0.32

33-43 | 6 | 20 | 0.24

44-60 | 5 | 25 | 0.20

The answer to question 13 is: D. None of the above, as statements I and II are true while statement III is false. However, if the options meant to refer to which statements must be true of all bar charts, then option D is incorrect. Option A is also incorrect because statement III is not always true. Hence, since only options A, B, C, D are provided we will assume the question is asking which statement is individually true. Hence, option A would be selected because this answer could be rephrased to say: "Statement 1 AND Statement 2 only". There is no third statement provided in this question, hence it is impossible for statement III to be correct. However, if the question is asking which statements are always true of a bar chart, the answer is D. Since the relative frequencies do not appear to be arranged in any specific order, this could be the correct answer.

Considering that the preamble tells us the frequency table deals with the distribution of ages, and that it is a table, it is likely the questions intends to ask "what must be true" and hence option D, none of the above, is the correct answer.

There are two possible options. Either D is the correct option because it requires all three to be true (which it is not), or this question is asking for each independent statement to be true (in which case, A would be correct, if it implied "Only I and II are true"). Based on the preamble for creating the table, I believe that Option D is the correct answer.

Final Answer: The final answer is D.