The numbers of visitors every hour in a shop from 1 p.m. to 8 p.m. on Monday were recorded as 7, 10, 15, 22, 6, 4 and 13. The arithmetic mean of visitors is:
11
Understanding the Arithmetic Mean of Visitor Numbers
This solution explains how to calculate the arithmetic mean (average) for the given hourly visitor numbers to a shop.
Visitor Data Recorded
The number of visitors recorded every hour from 1 p.m. to 8 p.m. on a Monday are provided as a dataset. The specific numbers are:
- 7
- 10
- 15
- 22
- 6
- 4
- 13
There are a total of 7 data points in this set, representing the visitor count for 7 different hours.
Arithmetic Mean Formula and Calculation
The arithmetic mean, often called the average, is calculated by summing up all the values in a dataset and then dividing by the total count of values in that dataset.
The formula for the arithmetic mean is:
$$ \text{Arithmetic Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} $$Let's apply this formula to the visitor data:
Step 1: Sum the observations
Add all the recorded visitor numbers together:
$$ 7 + 10 + 15 + 22 + 6 + 4 + 13 = 77 $$Step 2: Count the number of observations
Count how many numbers are in the dataset. In this case, there are 7 hourly records.
Step 3: Divide the sum by the count
Now, divide the total sum (77) by the number of observations (7):
$$ \text{Mean} = \frac{77}{7} $$ $$ \text{Mean} = 11 $$Conclusion: The Mean Number of Visitors
The calculation shows that the arithmetic mean of the visitors recorded between 1 p.m. and 8 p.m. is 11.
Comparing this result with the given options, the arithmetic mean of the visitors is 11.
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