Explanation:
To identify any outliers in the distribution of file sizes, we can use a common method called the "1.5 times the interquartile range (IQR)" rule.
First, we need to find the median of the file sizes. Arranging the sizes in ascending order:
1.1, 1.3, 1.6, 1.9, 1.9, 2.1, 2.2, 2.5, 2.7, 3.0, 4.7, 5.0, 5.6, 6.2, 7.5, 13, 24, 44
We have 18 data points, so the median is the 9th value, which is 2.5.
Next, we calculate the quartiles. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half of the data.
Lower half of the data: 1.1, 1.3, 1.6, 1.9, 1.9, 2.1, 2.2, 2.5
Upper half of the data: 3.0, 4.7, 5.0, 5.6, 6.2, 7.5, 13, 24, 44
Median of the lower half (Q1): (1.9 + 2.1) / 2 = 2.0
Median of the upper half (Q3): (6.2 + 7.5) / 2 = 6.85
Now we can calculate the interquartile range (IQR), which is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 6.85 - 2.0 = 4.85
Finally, we apply the 1.5 times IQR rule to identify any outliers. According to this rule, any data point below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered an outlier.
Lower outlier threshold: Q1 - 1.5 * IQR = 2.0 - 1.5 * 4.85 = -4.275 (ignoring negative values)
Upper outlier threshold: Q3 + 1.5 * IQR = 6.85 + 1.5 * 4.85 = 14.025
Comparing the file sizes to the outlier thresholds, we find that the size of 44 MB is above the upper threshold. Therefore, 44 MB is considered an outlier in this distribution.
To summarize, the outlier in the distribution of file sizes is 44 MB.