Question

the following data represent the exchange rates for currency a in terms of currency b for 14 months. complete parts a through e below.

0.67, 0.73, 0.91, 1.13, 1.44, 0.95, 0.77
0.59, 1.53, 0.59, 0.55, 0.85, 1.40, 0.90

(round to the nearest cent as needed.)

c.) determine the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the mode(s) is/are \\$ 0.59
(type an integer or a decimal. use a comma to separate answers as needed.)
b. there is no mode for this data set.

d.) which of the three measurements would best describe the central tendency of this data?

a. the mode is the better indicator of the central tendency of the exchange rate since this data is categorical.
b. the median would be a better indicator of the central tendency of the exchange rate since there appear to be outliers.
c. both the mean and the median are accurate indicators of the central tendency of the exchange rate since there do not appear to be any outliers.
d. the mean would be a better indicator of the central tendency of the exchange rate since there appear to be outliers.

Explanation:

⚡ Using what you learned: comparing measures of center & spread

Step 1: Analyze the dataset for outliers

To determine which measure of central tendency is best, we look at the distribution of the 14 exchange rates:

$$ 0.55, 0.59, 0.59, 0.67, 0.73, 0.77, 0.85, 0.90, 0.91, 0.95, 1.13, 1.40, 1.44, 1.53 $$

The values are relatively spread out continuously from \(0.55\) to \(1.53\) without any extreme, isolated values (outliers) that would heavily distort the mean.

Step 2: Evaluate the options

• Option A is incorrect because the data is quantitative (numerical), not categorical.
• Option B and D are incorrect because there are no extreme outliers in this dataset to warrant avoiding the mean.
• Option C is correct because when a dataset is relatively symmetric and free of extreme outliers, both the mean and the median serve as highly accurate indicators of central tendency.

Answer:

C. Both the mean and the median are accurate indicators of the central tendency of the exchange rate since there do not appear to be any outliers