Math Problem Statement
heckout times. The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are: 5.3 5.3 5.5 9.4 12.7 9.9 6.8 8.9 9.3 8.9 13.1 13.8 find the mean and standard deviation
Solution
To find the mean and standard deviation of the checkout times, we can follow these steps:
1. Calculate the Mean:
The mean (average) is the sum of all values divided by the number of values.
Given the checkout times:
Sum of the checkout times:
Number of customers = 12
So, the mean is:
2. Calculate the Standard Deviation:
The standard deviation measures how spread out the numbers are. First, we need to calculate the variance, and then take the square root of it.
Variance formula: Where:
- is each individual checkout time
- is the mean (9.0)
- is the number of data points (12)
Step-by-step:
- Subtract the mean from each value, square the result, and sum them up:
Now, sum up all the squared differences:
Variance:
Finally, take the square root to find the standard deviation:
Final Results:
- Mean = 9.0 minutes
- Standard Deviation ≈ 2.82 minutes
Would you like a more detailed breakdown, or any clarifications? Here are a few follow-up questions to dive deeper:
- How can the standard deviation help in understanding customer behavior during checkout?
- What is the importance of the mean in determining the efficiency of checkout times?
- How can we visualize the distribution of these checkout times?
- How would adding more customers affect the mean and standard deviation?
- What does a high standard deviation indicate in a set of data?
Tip: A small standard deviation indicates that the data points are close to the mean, while a large one suggests more variability.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Standard Deviation
Variance
Formulas
Mean = (Sum of all values) / (Number of values)
Variance = Sum of squared differences from the mean / Number of values
Standard Deviation = Square root of Variance
Theorems
Basic Properties of Mean and Standard Deviation
Suitable Grade Level
Grades 9-11
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