Problem 2 - Basic College Mathematics

Question

Summarize each set of data in Exercises \(1-4\) using a frequency table. Baby Names. The following list gives the most popular names for baby girls in the United States for \(2001-2016 .\) Emily, Emily, Emily, Emily, Emily, Emily, Emily, Emma, Isabella, Isabella, Sophia, Sophia, Sophia, Emma, Emma, Emma

Step-by-Step Solution

Answer

Emily: 7, Emma: 4, Isabella: 2, Sophia: 3

Step 1: List the Unique Names

Identify all the unique baby names in the given data set. The unique names are Emily, Emma, Isabella, and Sophia.

Step 2: Count the Frequencies

Count how many times each unique name appears in the list. Here are the counts for each name: Emily = 7, Emma = 4, Isabella = 2, Sophia = 3.

Step 3: Organize into Frequency Table

Organize the information into a frequency table with two columns: Name and Frequency. Fill in the table with the counts from Step 2.

Step 4: Create the Frequency Table

Here is the completed frequency table:| Name | Frequency ||----------|-----------|| Emily | 7 || Emma | 4 || Isabella | 2 || Sophia | 3 |

Key Concepts

data summarization

Data summarization is the process of simplifying large sets of data into understandable chunks. It involves collecting and presenting data in a concise form, allowing for easy interpretation. In the context of baby names, summarizing data helps identify trends and patterns. For example, if you have a list of baby names from 2001 to 2016, summarizing this data gives you a clear picture of the most popular names over the years. You start by picking out the unique names, then count how many times each name appears. Finally, you organize these counts into a straightforward format, like a frequency table. This makes the data less overwhelming and more insightful.

baby names statistics

Statistics for baby names can give us fascinating insights into cultural trends and preferences. By analyzing popular baby names over time, we can see which names were trending and when. For instance, in the exercise, the names Emily, Emma, Isabella, and Sophia were some of the top names in the United States from 2001 to 2016. By keeping track of these names and their frequencies, we can understand how naming trends evolve. This can be useful for parents looking to name their newborns, as well as for researchers studying cultural shifts.

counting frequencies

Counting frequencies is a fundamental step in summarizing any kind of data. It involves tallying the number of times each unique item appears in the dataset. For the baby names exercise, you would count how many times each name on the list is mentioned. In our example, 'Emily' appears 7 times, 'Emma' appears 4 times, 'Isabella' appears 2 times, and 'Sophia' appears 3 times. Frequency counting helps in understanding the popularity of each name and is crucial for further data analysis.

organizing data

Organizing data means arranging it in a clear and logical format, making it easier to read and analyze. A common method used is a frequency table. In this table, you list the unique items in one column and their frequencies in another. In our exercise, the baby names and their counts were organized into a table. This way, you can quickly see that 'Emily' was the most popular name, followed by 'Emma', 'Sophia', and 'Isabella'. Organizing data into tables or charts is essential for presenting information in a way that is easy to understand and interpret.