Problem 38 - Prealgebra

Question

The SubShop had \(36,45,41,\) and 38 customers during the lunch hour the last four days. Find the mean of the number of customers per day.

Step-by-Step Solution

Answer

The mean number of customers per day is 40.

Step 1: Sum the Numbers

To find the mean, we first need to sum the number of customers over the four days. So, add 36, 45, 41, and 38 together: \[ 36 + 45 + 41 + 38 = 160 \]

Step 2: Count the Days

Determine the number of days over which the data was collected. In this case, there are 4 days.

Step 3: Calculate the Mean

Divide the total sum of customers by the number of days to find the mean number of customers per day:\[ \text{Mean} = \frac{160}{4} = 40 \]

Key Concepts

Average

Finding the average, also known as the mean, is a fundamental skill in mathematics and data analysis. When we calculate the average, we are looking for the value that best represents a set of numbers. It's like finding a balance point for all the numbers present. For example, in the SubShop problem, calculating the average number of customers helps us understand how many customers, on average, visit the shop each day. This can be very useful for understanding trends over time. A higher average might indicate a busy period, while a lower one can signal quieter times.

Sum

The sum is the result of adding two or more numbers together. It's like gathering them into one single value. This is the first step in calculating the average. We add together all the individual data points. In our problem, we summed the number of customers from four different days:

• Day 1: 36 customers
• Day 2: 45 customers
• Day 3: 41 customers
• Day 4: 38 customers

These numbers total to 160 customers. Without summation, we cannot proceed to find the mean because we need a single value that represents the collective data.

Division

Division comes into play as the final step in calculating the average. After summing all the numbers, we must divide the total by the number of data points. In division, we distribute the total sum equally among the data points. In the given exercise, the sum of customers was 160, and we divided it by the number of days, which was 4: \[ \text{Mean} = \frac{160}{4} = 40 \]This division tells us roughly how many customers there were on each day, on average. Understanding division helps us break down large totals into manageable pieces, a vital skill not just in math, but in daily life as well.

Data Analysis

Data analysis is the crucial process of examining, cleaning, and interpreting data. In most cases, like our exercise, this starts with simple steps like summation and division to derive meaningful insights. Through data analysis, we can detect patterns, trends, and outliers. Analyzing data such as customer visits to a store can help store managers make informed business decisions. For instance, they might decide to increase staff during peaks or evaluate why certain days are less busy. A well-analyzed dataset is an excellent decision-making tool, helping translate numbers into actionable insights.