Question

the data to the right represent the number of customers waiting for a table at 6:00 p.m. for 40 consecutive saturdays at bobak’s restaurant. complete parts (a) through (h) below.

(b) construct a frequency distribution of the data.

number of customers
1–3
4–6
7–9
10–12
13–15

frequency

(c) construct a relative frequency distribution of the data.

number of customers
1–3

relative frequency

Explanation:

Step1: List all data points

Data set: 12,12,5,8,11,8,6,5,13,13,6,11,5,12,9,10,12,14,8,3,9,9,10,12,14,15,13,6,12,9,9,12,9,11,10,12,7,9,11,10

Step2: Tally frequencies for 1-3

Count values in [1,3]: only 3 → Frequency = 1

Step3: Tally frequencies for 4-6

Count values in [4,6]: 5,6,5,6,5,6 → Frequency = 6

Step4: Tally frequencies for 7-9

Count values in [7,9]: 8,8,9,8,9,9,9,9,7,9 → Frequency = 10

Step5: Tally frequencies for 10-12

Count values in [10,12]: 12,12,11,12,10,12,10,12,12,12,10,12,11,10,11 → Frequency = 19

Step6: Tally frequencies for 13-15

Count values in [13,15]: 13,13,14,14,15,13 → Frequency = 4

Step7: Calculate relative frequencies

Relative frequency = $\frac{\text{Frequency}}{40}$

• 1-3: $\frac{1}{40}=0.025$
• 4-6: $\frac{6}{40}=0.15$
• 7-9: $\frac{10}{40}=0.25$
• 10-12: $\frac{19}{40}=0.475$
• 13-15: $\frac{4}{40}=0.1$

Answer:

Part (b) Frequency Distribution

Number of Customers	Frequency
4-6	6
7-9	10
10-12	19
13-15	4

Part (c) Relative Frequency Distribution

Number of Customers	Relative Frequency
4-6	0.15
7-9	0.25
10-12	0.475
13-15	0.1