Question

name: alison
problem 1: a sociologist conducted a survey of 20 adults. she wants to report the frequency distribution of the ages of the survey respondents. the respondents were the following ages (in years):use 5 classes:
data: 52, 34, 32, 29, 63, 40, 46, 54, 36, 24, 19, 45, 20, 28, 29, 38, 33, 49, 37
data: 52, 34, 32, 29, 63, 40, 46, 54, 36, 24, 19, 45, 20, 28, 29, 38, 33, 49, 37 (round 5)
class interval | tally | frequency | relative frequency | class boundaries
19 - 23
24 - 28
29 - 33
34 - 38
39 - 44
problem 2: another sociologist conducted a survey of 25 adults. she collected the following data on their ages (in years):use 6 classes for this data.
data: 22, 41, 27, 53, 29, 34, 61, 45, 39, 23, 54, 31, 48, 55, 36, 44, 26, 40, 30, 58, 42, 47, 33, 43, 35
class interval | tally | frequency | relative frequency | class boundaries

Explanation:

Step1: Find range for Problem 1

For the first dataset with values 52, 34, 32, 29, 63, 40, 46, 54, 36, 24, 19, 45, 20, 28, 29, 38, 33, 49, 37. The range $R = 63 - 19=44$. Using 5 classes, the class - width $w=\frac{44}{5}=8.8$, we can round it up to 9.
The class intervals are: 19 - 27, 28 - 36, 37 - 45, 46 - 54, 55 - 63.

Tally and Frequency for Problem 1

• For the class interval 19 - 27: Tally: |||, Frequency: 3
• For the class interval 28 - 36: Tally: ||||||||, Frequency: 9
• For the class interval 37 - 45: Tally: |||||, Frequency: 5
• For the class interval 46 - 54: Tally: ||||, Frequency: 4
• For the class interval 55 - 63: Tally: |, Frequency: 1

Relative Frequency for Problem 1

The total frequency $n = 20$.

• For the class interval 19 - 27: Relative Frequency $=\frac{3}{20}=0.15$
• For the class interval 28 - 36: Relative Frequency $=\frac{9}{20}=0.45$
• For the class interval 37 - 45: Relative Frequency $=\frac{5}{20}=0.25$
• For the class interval 46 - 54: Relative Frequency $=\frac{4}{20}=0.2$
• For the class interval 55 - 63: Relative Frequency $=\frac{1}{20}=0.05$

Class Boundaries for Problem 1

• 19 - 27: Lower class boundary = 18.5, Upper class boundary = 27.5
• 28 - 36: Lower class boundary = 27.5, Upper class boundary = 36.5
• 37 - 45: Lower class boundary = 36.5, Upper class boundary = 45.5
• 46 - 54: Lower class boundary = 45.5, Upper class boundary = 54.5
• 55 - 63: Lower class boundary = 54.5, Upper class boundary = 63.5

Step2: Find range for Problem 2

For the second dataset with values 22, 41, 27, 53, 29, 34, 61, 45, 39, 23, 54, 31, 48, 55, 36, 44, 26, 40, 30, 58, 42, 47, 33, 43, 35. The range $R = 61 - 22 = 39$. Using 6 classes, the class - width $w=\frac{39}{6}=6.5$, we can round it up to 7.
The class intervals are: 22 - 28, 29 - 35, 36 - 42, 43 - 49, 50 - 56, 57 - 63.

Tally and Frequency for Problem 2

• For the class interval 22 - 28: Tally: ||||, Frequency: 4
• For the class interval 29 - 35: Tally: ||||||||, Frequency: 9
• For the class interval 36 - 42: Tally: |||||, Frequency: 5
• For the class interval 43 - 49: Tally: |||||, Frequency: 5
• For the class interval 50 - 56: Tally: |||, Frequency: 3
• For the class interval 57 - 63: Tally: |, Frequency: 1

Relative Frequency for Problem 2

The total frequency $n = 25$.

• For the class interval 22 - 28: Relative Frequency $=\frac{4}{25}=0.16$
• For the class interval 29 - 35: Relative Frequency $=\frac{9}{25}=0.36$
• For the class interval 36 - 42: Relative Frequency $=\frac{5}{25}=0.2$
• For the class interval 43 - 49: Relative Frequency $=\frac{5}{25}=0.2$
• For the class interval 50 - 56: Relative Frequency $=\frac{3}{25}=0.12$
• For the class interval 57 - 63: Relative Frequency $=\frac{1}{25}=0.04$

Class Boundaries for Problem 2

• 22 - 28: Lower class boundary = 21.5, Upper class boundary = 28.5
• 29 - 35: Lower class boundary = 28.5, Upper class boundary = 35.5
• 36 - 42: Lower class boundary = 35.5, Upper class boundary = 42.5
• 43 - 49: Lower class boundary = 42.5, Upper class boundary = 49.5
• 50 - 56: Lower class boundary = 49.5, Upper class boundary = 56.5
• 57 - 63: Lower class boundary = 56.5, Upper class boundary = 63.5

Answer:

Problem	Class Interval	Tally	Frequency	Relative Frequency	Class Boundaries
1	28 - 36										0.45	27.5 - 36.5
1	37 - 45							0.25	36.5 - 45.5
1	46 - 54						0.2	45.5 - 54.5
1	55 - 63			0.05	54.5 - 63.5
2	22 - 28						0.16	21.5 - 28.5
2	29 - 35										0.36	28.5 - 35.5
2	36 - 42							0.2	35.5 - 42.5
2	43 - 49							0.2	42.5 - 49.5
2	50 - 56					0.12	49.5 - 56.5
2	57 - 63			0.04	56.5 - 63.5