Question

carpool
carpool
carpool
private
private
private
public
private
private
other
other
carpool
other
carpool
private
other
private
other
public
other
a) since data were collected for ? select an answer variable(s), the correct graph to make is a select an answer .
b) complete the frequency/relative frequency table.
transportation type | frequency | relative frequency
carpool | |
private | |
public | |
other | |
c) which of the following is the correct bar chart for the given data?

Explanation:

Part (a)

Step1: Identify Variable Type

The data is about transportation type (Carpool, Private, Public, Other), which is a single categorical variable. For a single categorical variable, a bar graph (or bar chart) is appropriate. So we have one variable (categorical), and the correct graph is a bar graph.

Step1: Count Frequencies

• Carpool: Let's count the number of times "Carpool" appears. Looking at the list: 1st, 2nd, 3rd, 12th, 14th. So that's \(5\) times.
• Private: Count "Private": 4th, 5th, 6th, 8th, 9th, 15th, 16th. Wait, let's list all: 4 (Private), 5 (Private), 6 (Private), 8 (Private), 9 (Private), 15 (Private), 16 (Private). Wait, original list:

1. Carpool
2. Carpool
3. Carpool
4. Private
5. Private
6. Private
7. Public
8. Private
9. Private
10. Other
11. Other
12. Carpool
13. Other
14. Carpool
15. Private
16. Other
17. Private
18. Other
19. Public
20. Other

Wait, let's recount properly:

• Carpool: positions 1,2,3,12,14 → \(5\)
• Private: positions 4,5,6,8,9,15,17 → Let's count: 4 (1),5(2),6(3),8(4),9(5),15(6),17(7) → \(7\)
• Public: positions 7,19 → \(2\)
• Other: positions 10,11,13,16,18,20 → Let's count: 10(1),11(2),13(3),16(4),18(5),20(6) → \(6\)

Total data points: \(5 + 7 + 2 + 6 = 20\), which matches the number of entries (20).

Step2: Calculate Relative Frequencies

Relative Frequency = \(\frac{\text{Frequency}}{\text{Total Number of Data Points}}\) (Total = 20)

• Carpool: \(\frac{5}{20} = 0.25\)
• Private: \(\frac{7}{20} = 0.35\)
• Public: \(\frac{2}{20} = 0.1\)
• Other: \(\frac{6}{20} = 0.3\)

To determine the correct bar chart, we look at the frequencies: Carpool (5), Private (7), Public (2), Other (6). So the bar heights should correspond to these frequencies. The bar for "Private" should be the tallest (height 7), then "Other" (6), then "Carpool" (5), then "Public" (2). We would identify the bar graph where the bars have these relative heights (or counts). Since we don't have the options listed here, but the process is to check which bar chart has bars with heights 5,7,2,6 for Carpool, Private, Public, Other respectively.

Answer:

Since data were collected for \(\boldsymbol{1}\) (one) categorical variable(s), the correct graph to make is a \(\boldsymbol{\text{Bar Graph}}\).

Part (b)