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.

\

$$\begin{array}{lllllll} 0.67 & 0.73 & 0.91 & 1.13 & 1.44 & 0.95 & 0.77 \\\\ 0.59 & 1.53 & 0.59 & 0.55 & 0.85 & 1.40 & 0.90 \\end{array}$$

a.) calculate the mean.
the mean is \\$ 0.929
(round to three decimal places as needed.)

b.) calculate the median.
the median is \\$
(round to the nearest cent as needed.)

Explanation:

🆕 New Concept Discovered: Median of a Dataset
Finding the middle value of an ordered list

Step 1: Order the data

To find the median, we first arrange the 14 data points in ascending order:

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

Step 2: Locate the middle values

Since there is an even number of observations (\(n = 14\)), the median is the average of the two middle values at positions \(\frac{n}{2} = 7\) and \(\frac{n}{2} + 1 = 8\).

• 7th value: \(0.85\)
• 8th value: \(0.90\)

Step 3: Calculate the average of the two middle values

$$ \text{Median} = \frac{0.85 + 0.90}{2} = \frac{1.75}{2} = 0.875 $$

Rounding to the nearest cent (two decimal places):

$$ 0.875 \approx 0.88 $$

Answer:

0.88