On the Coast is a very popular restaurant located along the coast of Lake Erie. It serves a variety of steak and seafood dinners. During the summer beach season, it does not take reservations or accept "call ahead" seating. Management of the restaurant is concerned about the time a patron has to wait before being seated for dinner. Listed below is the wait time, in minutes, for the 25 tables seated last Saturday night:
 
28

39

23

67

37

28

56

40

28

50

51

45

44

65

61

27

24

61

34

44

64

25

24

27

29
 
 
 
 
 
 
**a.** Are wait times, in minutes, a sample or a population?
 
 (Click to select)  sample  population 
 
**b-1.** Find the mean of the wait times. **(Round the final answer to 2 decimal places.)**
 
Mean           
 
**b-2.** Find the median of the wait times.
 
Median            
 
**c-1.** Find the range of the wait times.
 
Range            
 
**c-2.** Find the standard deviation of the wait times. **(Round the final answer to 2 decimal places.)**
 
Standard deviation            




Let's analyze the data step by step for the restaurant's wait times:

### a. Sample or Population

**Answer:** Sample

- Since the data only includes wait times from the 25 tables seated last Saturday night, it represents a subset of all possible wait times at the restaurant. Thus, it is a **sample**.

### b-1. Mean of the Wait Times

To find the mean, we sum all the wait times and divide by the number of observations.

Given wait times:
\[ 28, 39, 23, 67, 37, 28, 56, 40, 28, 50, 51, 45, 44, 65, 61, 27, 24, 61, 34, 44, 64, 25, 24, 27, 29 \]

**Sum of wait times:**

\[ 28 + 39 + 23 + 67 + 37 + 28 + 56 + 40 + 28 + 50 + 51 + 45 + 44 + 65 + 61 + 27 + 24 + 61 + 34 + 44 + 64 + 25 + 24 + 27 + 29 = 1071 \]

**Number of observations:**

\[ 25 \]

**Mean:**

\[ \text{Mean} = \frac{\text{Sum of wait times}}{\text{Number of observations}} = \frac{1071}{25} = 42.84 \]

### b-2. Median of the Wait Times

First, we need to order the data from smallest to largest.

Ordered wait times:
\[ 23, 24, 24, 25, 27, 27, 28, 28, 28, 29, 34, 37, 39, 40, 44, 44, 45, 50, 51, 56, 61, 61, 64, 65, 67 \]

Since there are 25 observations (an odd number), the median is the middle value, which is the 13th value in the ordered list.

**Median:**
\[ \text{Median} = 39 \]

### c-1. Range of the Wait Times

The range is the difference between the maximum and minimum values in the dataset.

- **Maximum value:** 67
- **Minimum value:** 23

**Range:**

\[ \text{Range} = 67 - 23 = 44 \]

### c-2. Standard Deviation of the Wait Times

The standard deviation is a measure of how spread out the numbers are in a dataset.

**Steps to calculate standard deviation:**

1. **Find the mean** (calculated above as 42.84).
2. **Calculate the squared deviation for each value:**

   \[
   \begin{align*}
   (28 - 42.84)^2 & = 218.30 \\
   (39 - 42.84)^2 & = 14.75 \\
   (23 - 42.84)^2 & = 388.36 \\
   (67 - 42.84)^2 & = 577.01 \\
   (37 - 42.84)^2 & = 34.11 \\
   (28 - 42.84)^2 & = 218.30 \\
   (56 - 42.84)^2 & = 173.86 \\
   (40 - 42.84)^2 & = 8.07 \\


Explore the analysis of wait times at On the Coast restaurant, focusing on calculating the mean, median, range, and standard deviation of wait times from a sample of 25 tables last Saturday night. Understand how these statistical measures provide insights into customer seating times.

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