Construct the frequency distribution for​ drive-through service times for Burger King lunches using the accompanying data set. Times begin when a vehicle stops at the order window and end when the vehicle leaves the pickup window. Lunch times were measured between​ 11:00 AM and​ 2:00 PM. Begin with a lower class limit of 70 seconds and use a class width of 40 seconds.
Construct the frequency distribution.
Service Time​ (seconds)
Frequency
70dash
​(Type whole​ numbers.)
Drive-Through Service Times
116
131
147
120
126
136
77
136
133
146
138
110
149
148
110
208
120
105
79
120
91
145
159
109
78
224
198
137
142
76
166
195
253
231
259
192
128
106
84
153
151
145
171
160
124

To construct the frequency distribution for the given drive-through service times, we will follow these steps:

1. **Determine the Class Limits**:
   - **Lower Class Limit**: 70 seconds
   - **Class Width**: 40 seconds

   We will calculate the class limits by adding the class width to each previous class's lower limit.

2. **Determine the Class Boundaries**:
   - For each class, the upper class limit will be 1 less than the next class's lower limit.

3. **Tally the Frequencies**:
   - Count how many service times fall within each class.

### Step 1: Define Class Limits
- **Class 1**: 70 to 109 seconds
- **Class 2**: 110 to 149 seconds
- **Class 3**: 150 to 189 seconds
- **Class 4**: 190 to 229 seconds
- **Class 5**: 230 to 269 seconds

### Step 2: Tally the Frequencies
Now, let's count the number of data points within each class.

- **Class 1** (70 to 109 seconds): 77, 78, 79, 84, 91, 105, 106, 109 -> 8 data points
- **Class 2** (110 to 149 seconds): 110, 110, 116, 120, 120, 120, 124, 126, 128, 131, 133, 136, 136, 137, 138, 142, 145, 145, 146, 147, 148, 149 -> 22 data points
- **Class 3** (150 to 189 seconds): 151, 153, 159, 160, 166, 171 -> 6 data points
- **Class 4** (190 to 229 seconds): 192, 195, 198, 208 -> 4 data points
- **Class 5** (230 to 269 seconds): 224, 231, 253, 259 -> 4 data points

### Step 3: Construct the Frequency Distribution Table
Here is the frequency distribution:

| Service Time (seconds) | Frequency |
|------------------------|-----------|
| 70 - 109               | 8         |
| 110 - 149              | 22        |
| 150 - 189              | 6         |
| 190 - 229              | 4         |
| 230 - 269              | 4         |

Would you like to see more details on how to interpret this distribution? Do you have any other questions?

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Here are five related questions that expand on this concept:
1. How would you calculate the relative frequency for each class?
2. What is the cumulative frequency distribution for the service times?
3. How can you use this frequency distribution to calculate the mean service time?
4. How would changing the class width affect the distribution?
5. What is the standard deviation of the service times based on this distribution?

**Tip:** When constructing histograms, always ensure that the class widths are consistent to accurately represent the data.

Learn how to construct a frequency distribution for Burger King lunch drive-through service times from 11:00 AM to 2:00 PM. Class intervals are determined using a lower class limit of 70 seconds and a class width of 40 seconds. This problem involves analyzing service time data and organizing it into meaningful intervals.

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