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Chapter 12: Problem 7

Find the mean for each group of data items. \(1.6,3.8,5.0,2.7,4.2,4.2,3.2,4.7,3.6,2.5,2.5\)

Short Answer

Expert verified
The mean (average) of the group of data items is approximately 3.44 (to 2 decimal places).

Step by step solution

01

Write Down the Data

First, list all the numbers given in the problem: \(1.6,3.8,5.0,2.7,4.2,4.2,3.2,4.7,3.6,2.5,2.5\)
02

Add all the Numbers

The next step is to add all the numbers together: \(1.6 + 3.8 + 5.0 + 2.7 + 4.2 + 4.2 + 3.2 + 4.7 + 3.6 + 2.5 + 2.5 = 37.8\)
03

Calculate the Number of Items

Count the number of items in the group: \(11\)
04

Compute the Mean

Finally, divide the sum of all numbers by the number of items to get the mean (average): \( \frac{37.8}{11} = 3.43636\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Data Analysis
Data analysis involves evaluating data to draw meaningful insights. Here, we've been given a set of data items: \(1.6, 3.8, 5.0, 2.7, 4.2, 4.2, 3.2, 4.7, 3.6, 2.5, 2.5\).
To analyze this data, we will calculate the mean, which gives us an idea about the average value of these numbers. Calculating a mean is a fundamental aspect of data analysis. It helps to summarize information and is the foundation upon which most quantitative analysis is built.
Understanding such an average is crucial for spotting patterns or anomalies in data, thereby making informed decisions.
Mathematical Operations
To find the mean, we perform basic mathematical operations: addition and division.
The first operation involves adding all numbers in the data set: \(1.6 + 3.8 + 5.0 + 2.7 + 4.2 + 4.2 + 3.2 + 4.7 + 3.6 + 2.5 + 2.5\).
  • The sum calculated is: \(37.8\).

Key points to remember when adding numbers:
  • Ensure all data items are included.
  • Be cautious of decimals, as they can affect the sum.
The next operation is division: take total sum and divide it by the number of data items \(11\).
This calculation yields the mean, which is \(3.43636\).
These operations form the building blocks of more complex mathematical computations.
Step-by-Step Solutions
Following a clear and structured step-by-step process is fundamental for solving mathematical problems. It ensures accuracy and aids in understanding.
In the given exercise, each step logically leads to the next, starting from listing the data, through computing the sum, to dividing for the mean.
Step-by-step solutions help focus on each small task, making sure complex problems become manageable:
  • Write down all data values.
  • Sum all the values carefully.
  • Count the total number of data items.
  • Divide the sum by this count to get the mean.
This structured approach not only reduces the chance of errors but also builds a solid understanding of the concepts at play.
By practicing step-by-step methods, students can enhance their problem-solving skills and gain confidence in handling similar exercises in the future.

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Most popular questions from this chapter

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20.Find the score that is \(2 \frac{1}{2}\) standard deviations above the mean.

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 44

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 40

Find the standard deviation for each group of data items. Round answers to two decimal places. \(7,9,9,15\)

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