Question

After a series of rainy days, a meteorologist wants to compare the average daily rainfall over the past week between two cities. The daily rainfall totals, in inches, for both cities are given below.

City A = 1.6, 3.8, 2.2, 0.4, 3.4, 2.6, 1.5
City B = 1.2, 4.5, 0.9, 3.6, 2.1, 1.1, 1.3

Which of the following statements are true regarding the data sets above?

I. The mean rainfall of city A is greater than the mean rainfall of city B.
II. The median rainfall of city B is half the median rainfall of city A.
III. The range of rainfall amounts for city A is greater than the range of rainfall amounts for city B.
IV. The median rainfall is less than the mean rainfall for both cities.

II and III

I and III

I and IV

II and IV

Answer 1

I and IV

Explanation:

In order to compare the two data sets with the given statements, find the mean, median, and range for each data set.

First, to compare the mean rainfall of the two cities, find the average of each city's inches of rainfall. To find the average, add up the data points and divide by the total number of points, which is 7.

Since the mean of city A is 2.21 and the mean of city B is 2.1, the mean rainfall of city A is greater than the mean rainfall of city B.

Next, determine the median rainfall for each city. To find the median of the data sets, list the data in order of least to greatest and find the middle term.

Hence, the median of city A is 2.2 and the median of city B is 1.3, so the median rainfall of city B is not half the median rainfall of city A.

In order to compare the ranges of rainfall, find the difference between the minimum and the maximum rainfall amounts for each city.

So, the range of rainfall amounts for city A is less than the range of rainfall amounts for city B.

Therefore, the statements which are true regarding the given data sets are I and IV.

Answer 2

I and IV

Explanation: