Question

Comparing Measures of Center and Variability

This Week's High Temperatures (°F): 29, 38, 45, 31, 50, 58, 62
Last Week's High Temperatures (°F): mean 44, 31, 66, 32, 26, 58, 78, median, mode, range, mean absolute deviation

Which measures of center and variability for the temperatures were lower this week than last week? Check all that apply.

a. Mean
b. Median
c. Range
d. Mean Absolute Deviation

Answer 1

Upon calculating the mean, median, and range for this week's temperatures, we find that only the range is definitively lower this week (33) compared to last week (52). We cannot accurately compare the median or mean absolute deviation without additional information from last week.

Step-by-step explanation:

In order to determine which measures of center and variability for the temperatures were lower this week than last, we first need to calculate these measures for this week's temperatures.

• Mean: (29 + 38 + 45 + 31 + 50 + 58 + 62) / 7 = 44.7
• Median: The middle number when arranged in order is 45.
• Range: 62 - 29 = 33
• Mean Absolute Deviation: This requires us to find the absolute differences from the mean, add them together, and divide by the number of terms.

Now, comparing to last week's data:

- The mean is slightly higher this week.

- Without the exact median, we cannot conclude if it is lower or not.

- The range is definitely lower this week (33 vs. 78 - 26 = 52).

- Without all last week's data points, we cannot accurately compare the mean absolute deviation.

Thus, from the provided data, only the range is definitively lower this week than last week.