The amounts spent by 12 customers at a Burger King restaurant were as follows

Oct 13, 2025 by talynt.org 143 views

The amounts spent by 12 customers at a Burger King restaurant were as follows

Understanding the Problem and Calculating the Mean

The problem presents a set of 12 amounts spent by customers at a Burger King restaurant. To begin, we need to understand the concept of the mean, which is a measure of central tendency that represents the average value of a dataset. The mean is calculated by summing up all the values and then dividing by the total number of values.

To calculate the mean, we first need to add up all the amounts spent by the customers. The amounts are as follows: $11.01, $10.50, $5.70, $14.67, $9.50, $12.54, $8.90, $13.56, $11.23, $6.80, $3.00, and $10.55.

# Calculating the Sum of the Amounts Spent
## Step 1: Add up all the amounts spent by the customers
$11.01 + $10.50 = $21.51
$21.51 + $5.70 = $27.21
$27.21 + $14.67 = $41.88
$41.88 + $9.50 = $51.38
$51.38 + $12.54 = $63.92
$63.92 + $8.90 = $72.82
$72.82 + $13.56 = $86.38
$86.38 + $11.23 = $97.61
$97.61 + $6.80 = $104.41
$104.41 + $3.00 = $107.41
$107.41 + $10.55 = $117.96

The sum of the amounts spent by the customers is $117.96.

Calculating the Mean

To calculate the mean, we divide the sum of the amounts spent by the total number of customers, which is 12.

# Calculating the Mean
## Step 1: Divide the sum of the amounts spent by the total number of customers
$117.96 ÷ 12 = $9.83

The mean amount spent by the customers is $9.83.

Understanding the Problem and Calculating the Median

The median is another measure of central tendency that represents the middle value of a dataset when it is arranged in order. To calculate the median, we need to arrange the amounts spent by the customers in order from smallest to largest.

# Arranging the Amounts Spent in Order
## Step 1: Arrange the amounts spent by the customers in order from smallest to largest
$3.00, $5.70, $6.80, $8.90, $9.50, $10.50, $10.55, $11.01, $11.23, $12.54, $13.56, $14.67

The median is the middle value of the dataset, which is $9.50.

Understanding the Problem and Calculating the Mode

The mode is the value that appears most frequently in a dataset. To calculate the mode, we need to count the frequency of each value in the dataset.

# Counting the Frequency of Each Value
## Step 1: Count the frequency of each value in the dataset
$3.00: 1
$5.70: 1
$6.80: 1
$8.90: 1
$9.50: 1
$10.50: 1
$10.55: 1
$11.01: 1
$11.23: 1
$12.54: 1
$13.56: 1
$14.67: 1

There is no value that appears more than once in the dataset, so there is no mode.

Understanding the Problem and Calculating the Range

The range is the difference between the largest and smallest values in a dataset. To calculate the range, we need to find the largest and smallest values in the dataset.

# Finding the Largest and Smallest Values
## Step 1: Find the largest and smallest values in the dataset
Largest value: $14.67
Smallest value: $3.00

The range is the difference between the largest and smallest values, which is $14.67 - $3.00 = $11.67.

Understanding the Problem and Calculating the Variance

The variance is a measure of the spread of a dataset. To calculate the variance, we need to find the average of the squared differences between each value and the mean.

# Calculating the Variance
## Step 1: Calculate the squared differences between each value and the mean
($11.01 - $9.83)^2 = $1.18
($10.50 - $9.83)^2 = $0.69
($5.70 - $9.83)^2 = $16.13
($14.67 - $9.83)^2 = $29.13
($9.50 - $9.83)^2 = $0.09
($12.54 - $9.83)^2 = $6.31
($8.90 - $9.83)^2 = $1.93
($13.56 - $9.83)^2 = $14.73
($11.23 - $9.83)^2 = $2.40
($6.80 - $9.83)^2 = $12.03
($3.00 - $9.83)^2 = $34.83
($10.55 - $9.83)^2 = $0.72

The average of the squared differences is ($1.18 + $0.69 + $16.13 + $29.13 + $0.09 + $6.31 + $1.93 + $14.73 + $2.40 + $12.03 + $34.83 + $0.72) / 12 = $9.01.

The variance is the average of the squared differences, which is $9.01.

Understanding the Problem and Calculating the Standard Deviation

The standard deviation is the square root of the variance. To calculate the standard deviation, we need to find the square root of the variance.

# Calculating the Standard Deviation
## Step 1: Find the square root of the variance
√$9.01 = $3.00

The standard deviation is the square root of the variance, which is $3.00.

Conclusion

In this article, we have calculated the mean, median, mode, range, variance, and standard deviation of a dataset of 12 amounts spent by customers at a Burger King restaurant. The mean amount spent by the customers is $9.83, the median is $9.50, and there is no mode. The range is $11.67, the variance is $9.01, and the standard deviation is $3.00. These calculations provide a better understanding of the distribution of the amounts spent by the customers and can be used to make informed decisions about the business.
Frequently Asked Questions (FAQs) about the Amounts Spent by Customers at a Burger King Restaurant

Q: What is the mean amount spent by the customers at the Burger King restaurant? A: The mean amount spent by the customers at the Burger King restaurant is $9.83.

Q: What is the median amount spent by the customers at the Burger King restaurant? A: The median amount spent by the customers at the Burger King restaurant is $9.50.

Q: Is there a mode in the dataset of amounts spent by customers at the Burger King restaurant? A: No, there is no mode in the dataset of amounts spent by customers at the Burger King restaurant.

Q: What is the range of the amounts spent by customers at the Burger King restaurant? A: The range of the amounts spent by customers at the Burger King restaurant is $11.67.

Q: What is the variance of the amounts spent by customers at the Burger King restaurant? A: The variance of the amounts spent by customers at the Burger King restaurant is $9.01.

Q: What is the standard deviation of the amounts spent by customers at the Burger King restaurant? A: The standard deviation of the amounts spent by customers at the Burger King restaurant is $3.00.

Q: How can I use the calculations of mean, median, mode, range, variance, and standard deviation to make informed decisions about the business? A: The calculations of mean, median, mode, range, variance, and standard deviation can be used to make informed decisions about the business by providing a better understanding of the distribution of the amounts spent by customers. For example, the mean and median can be used to determine the average amount spent by customers, while the range and variance can be used to determine the spread of the amounts spent by customers. The standard deviation can be used to determine the variability of the amounts spent by customers.

Q: How can I apply the concepts of mean, median, mode, range, variance, and standard deviation to other business problems? A: The concepts of mean, median, mode, range, variance, and standard deviation can be applied to other business problems by using them to analyze and understand the distribution of data. For example, the mean and median can be used to determine the average price of a product, while the range and variance can be used to determine the spread of prices. The standard deviation can be used to determine the variability of prices.

Q: What are some common applications of the concepts of mean, median, mode, range, variance, and standard deviation in business? A: Some common applications of the concepts of mean, median, mode, range, variance, and standard deviation in business include:

Analyzing customer spending habits
Determining the average price of a product
Understanding the spread of prices
Determining the variability of prices
Making informed decisions about the business

Q: How can I use the concepts of mean, median, mode, range, variance, and standard deviation to improve customer satisfaction? A: The concepts of mean, median, mode, range, variance, and standard deviation can be used to improve customer satisfaction by providing a better understanding of the distribution of customer spending habits. For example, the mean and median can be used to determine the average amount spent by customers, while the range and variance can be used to determine the spread of amounts spent by customers. The standard deviation can be used to determine the variability of amounts spent by customers.

Q: How can I use the concepts of mean, median, mode, range, variance, and standard deviation to improve business operations? A: The concepts of mean, median, mode, range, variance, and standard deviation can be used to improve business operations by providing a better understanding of the distribution of data. For example, the mean and median can be used to determine the average price of a product, while the range and variance can be used to determine the spread of prices. The standard deviation can be used to determine the variability of prices.

Conclusion

In this article, we have answered some frequently asked questions about the amounts spent by customers at a Burger King restaurant. We have discussed the mean, median, mode, range, variance, and standard deviation of the dataset and provided examples of how these calculations can be used to make informed decisions about the business. We have also discussed some common applications of the concepts of mean, median, mode, range, variance, and standard deviation in business and provided examples of how these concepts can be used to improve customer satisfaction and business operations.