Question

using measures of center and variability to compare data tutorial level 6
which measure of center more accurately represents how
long it takes a phone with com - com service to download a
file.
com - com:
5.3, 5.7, 6.1, 6.5, 6.9, 7.2, 7.7, 8.8, 8.9, 8.9, 9.0, 9.1, 9.4, 9.5, 45
10 mb download times

of locations

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

Explanation:

Step1: Identify outlier in data

The value 45 is an extreme outlier, far from other data points (all others are between 5.3 and 9.5).

Step2: Analyze mean sensitivity to outliers

Calculate the mean:
$$\text{Mean} = \frac{5.3 + 5.7 + 6.1 + 6.5 + 6.9 + 7.2 + 7.7 + 8.8 + 8.9 + 8.9 + 9.0 + 9.1 + 9.4 + 9.5 + 45}{15}$$
$$= \frac{152.0}{15} \approx 10.13$$
This mean is pulled upward by the outlier, not representative of typical values.

Step3: Analyze median resistance to outliers

Arrange data, find the 8th value (middle of 15 points):
Sorted data: 5.3, 5.7, 6.1, 6.5, 6.9, 7.2, 7.7, 8.8, 8.9, 8.9, 9.0, 9.1, 9.4, 9.5, 45
Median = 8.8, which reflects the typical cluster of values.

Answer:

The median (8.8 seconds) more accurately represents the typical download time, as the mean is skewed upward by the outlier value of 45 seconds.