Problem 22 - Basic College Mathematics

Question

The most popular fruit in the world is the mango, which is grown in over 2000 varieties. The following prices per pound of mangoes were found at five supermarkets: $$ \begin{array}{lllll} 2.49, & \$ 1.59, & \$ 2.29, & \$ 2.49, & \$ 2.29 . \end{array} $$ What was the mean price per pound? the median price? the mode?

Step-by-Step Solution

Answer

The mean price is 2.23, the median price is 2.29, and the modes are 2.29 and 2.49.

Step 1: List the Prices

Write down all the provided prices per pound of mangoes: 2.49, 1.59, 2.29, 2.49, 2.29.

Step 2: Find the Mean Price

To find the mean price, add up all the prices and then divide by the number of prices. Sum: 2.49 + 1.59 + 2.29 + 2.49 + 2.29 = 11.15 Number of Prices: 5 Mean Price: \[ \frac{11.15}{5} = 2.23 \]

Step 3: Find the Median Price

To find the median price, first arrange the prices in ascending order: 1.59, 2.29, 2.29, 2.49, 2.49. The median price is the middle value in the ordered list. In this case, the median price is 2.29.

Step 4: Find the Mode Price

The mode is the price that appears most frequently in the list. Looking at our list 1.59, 2.29, 2.29, 2.49, 2.49, the prices 2.29 and 2.49 both appear twice. Hence, both are the modes.

Key Concepts

mean calculation

The mean, often referred to as the average, provides a measure of the central value of a data set. To calculate the mean, you sum up all the values and then divide by the number of values.
For example, given these prices per pound of mangoes: 2.49, 1.59, 2.29, 2.49, and 2.29, start by summing these values:
2.49 + 1.59 + 2.29 + 2.49 + 2.29 = 11.15.
Next, count the number of prices provided, which is 5.
Then, divide the total sum by the number of values: \[ \text{Mean Price} = \frac{11.15}{5} = 2.23 \]
This gives you a mean price per pound of mangoes of 2.23.

median calculation

The median is the middle value in a dataset after it has been arranged in ascending order. This can help you understand the central tendency of the data without being affected by extremely high or low values.
Given the same prices per pound of mangoes: 2.49, 1.59, 2.29, 2.49, and 2.29, first rearrange them in ascending order: 1.59, 2.29, 2.29, 2.49, 2.49.
The middle value in this ordered list is 2.29, which is the median. If there were an even number of values, the median would be the average of the two middle numbers.

mode calculation

The mode is the value that appears most frequently in a dataset. Understanding the mode helps identify which value appears most often, indicating its popularity or frequency.
For the mango prices: 2.49, 1.59, 2.29, 2.49, and 2.29, rearrange the values in ascending order for easy comparison: 1.59, 2.29, 2.29, 2.49, 2.49.
In this case, both 2.29 and 2.49 appear twice. This means the dataset has two modes, making it bimodal.

data analysis

Data analysis involves evaluating data using various statistical measures to extract useful information and insights.
By calculating the mean, median, and mode for the prices of mangoes, you can gain different perspectives on the pricing pattern:

• The mean price (2.23) tells you the average price per pound.
• The median price (2.29) indicates the central value, giving a sense of what a typical price might be without being skewed by extremes.
• The mode (2.29 and 2.49) shows the most frequently occurring prices, suggesting common competitive pricing points.

This type of analysis can help retailers, consumers, and analysts make informed decisions regarding pricing strategies and market trends.