Let's analyze the sales data Alan provided for each day of the week and calculate the different statistical measures: mean, median, and mode.
Here is the sales data:
- Monday: 5 sales
- Tuesday: 9 sales
- Wednesday: 4 sales
- Thursday: 9 sales
- Friday: 3 sales
### Calculating the Mean
The mean (or average) number of sales is calculated by summing the total number of sales and then dividing by the number of days.
[tex]\[ \text{Mean} = \frac{\text{Sum of Sales}}{\text{Number of Days}} \][/tex]
The total sales for the week:
[tex]\[ 5 + 9 + 4 + 9 + 3 = 30 \][/tex]
The number of days:
[tex]\[ 5 \][/tex]
Now, calculate the mean:
[tex]\[ \text{Mean} = \frac{30}{5} = 6 \][/tex]
So, the mean number of sales is 6.
### Calculating the Median
The median is the middle value in a list when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.
First, arrange the sales data in ascending order:
[tex]\[ 3, 4, 5, 9, 9 \][/tex]
Since there are 5 data points (an odd number), the median is the third number in this sorted list:
[tex]\[ \text{Median} = 5 \][/tex]
So, the median number of sales is 5.
### Calculating the Mode
The mode is the number that appears most frequently in the data set. If there is more than one such number, all of them are the mode.
Looking at the sales data:
[tex]\[ 5, 9, 4, 9, 3 \][/tex]
We see that the number 9 appears twice, while all other numbers appear only once. Thus, the mode is:
[tex]\[ \text{Mode} = 9 \][/tex]
So, the mode number of sales is 9.
### Conclusion
Based on Alan's weekly sales data for the given days:
- The mean number of sales is 6.
- The median number of sales is 5.
- The mode number of sales is 9.
Hence, Alan might be referring to the mode when he claims to have had about 9 sales per day, as the mode reflects the most frequently occurring number of sales in his data.
