To determine which statistics are most affected by the least number of ice cream cones sold, we need to look at the mean, median, mode, and the least number of cones sold from the Stem-and-Leaf Plot data.
#### Data Interpretation:
The Stem-and-Leaf Plot provides the following data:
- 44 (from stem 4 and leaf 4)
- 70, 70, 70, 75, 79 (from stem 7 and leaves 0, 0, 0, 5, 9)
- 81, 86 (from stem 8 and leaves 1, 6)
Thus, the data set is: 44, 70, 70, 70, 75, 79, 81, 86.
#### Calculating the Statistics:
1. Mean:
The mean is the average of all the data points.
[tex]\[
\text{Mean} = \frac{44 + 70 + 70 + 70 + 75 + 79 + 81 + 86}{8} = 71.875
\][/tex]
2. Median:
To find the median, we need the middle value(s) of the sorted data set.
[tex]\[
\text{Sorted data set: } [44, 70, 70, 70, 75, 79, 81, 86]
\][/tex]
Since there are 8 data points (an even number), the median is the average of the 4th and 5th values:
[tex]\[
\text{Median} = \frac{70 + 75}{2} = 72.5
\][/tex]
3. Mode:
The mode is the most frequently occurring value in the data set. In this case, 70 appears three times:
[tex]\[
\text{Mode} = 70
\][/tex]
4. Least Number of Cones Sold:
The smallest value in the data set is:
[tex]\[
\text{Least number} = 44
\][/tex]
#### Analysis:
- Mean is affected by all data points in the set, including the smallest value. Since it aggregates the total sum of all data points, the least number (44 in this case) significantly pulls the average down.
- Median is affected less by extreme values, as it is a measure of the middle of the data set. Adding or removing an extreme low value has less of an effect since the median looks at the middle pair of numbers.
- Mode is not affected by single extreme values at all, as it only depends on the frequency of a given number in the data set.
Given this:
Answer: A) the mean
