Question

Data from the StudentSurvey dataset are given. Construct a relative frequency table of the data using the categories given. Give the relative frequencies rounded to three decimal places. Of the 361 students who answered the question about the number of piercings they had in their body, 188 had no piercings, 82 had one or two piercings, and the rest had more than two.

Short answer

The relative frequency table is as follows: No Piercings: 52.075%; 1 or 2 Piercings: 22.715%; More than 2 Piercings: 25.210%.

Step-by-step solution

Compute the Missing Value

Before starting with the relative frequency table, let's first compute the missing value. The total number of students is given as 361. We know that 188 students have no piercings and 82 students have one or two piercings. Hence, number of students with more than two piercings would be: 361 - (188 + 82).

Calculate Relative Frequencies

Now, we calculate the relative frequency for each category. It is the ratio of the count of values in the category to the total count, expressed as a percentage up to three decimal places. For instance, for 'no piercings' category, the relative frequency would be: (188/361)*100.

Construct the Table

Finally, create a table with two columns. First column represents the category ('No piercings', '1 or 2 piercings' and 'More than 2 piercings') and the second column gives the corresponding relative frequency calculated in the previous step.

Key concepts

Data Analysis

Data analysis is the process of systematically applying statistical and logical techniques to describe, illustrate, and evaluate data. In the case of our exercise, the data analysis involves summarizing the information collected from a survey about body piercings among students.

Firstly, the raw data is organized by counting the number of students in each category of body piercings. Then, the critical step is to convert these counts into relative frequencies, which tell us the proportion of the total for each group. This process enables us to see the distribution of body piercings among students in a way that's easier to understand and compare.

Good data analysis in education should not only provide a straightforward computation of figures like relative frequencies but also offer insights. For example, it could lead to discussions about cultural trends, peer influence, or health education. By rounding the relative frequencies to three decimal places, we maintain precision and also make the data more digestible.

Statistics Education

Statistics education is crucial because it equips students with the skills to collect, analyze, and interpret data, skills that are essential in many fields. Considering our sample problem, understanding how to create a relative frequency table is fundamental in statistics. It's a tool that helps compare different categories with respect to the whole.

In teaching statistics, it's important to emphasize the conceptual understanding behind statistical tools. Students should know why relative frequency is useful: because it offers context. For instance, stating that '188 students have no piercings' is less informative compared to saying 'around 52.1% of students surveyed have no piercings'.

To improve the educational experience, examples like the one provided should be used to illustrate the procedures in a context that is relevant to the students’ experiences. Including real-world applications of statistics, like opinion polls or medical studies, can make lessons more engaging and memorable.

Frequency Distribution

The concept of frequency distribution is a fundamental part of data analysis, involving a summary of how often each value in a set of data occurs. In statistical terms, frequency refers to the count of how many times an event or a value appears. The frequency distribution for our exercise categorizes the number of piercings students have.

When constructing a frequency distribution, the data is typically arranged in a table format. A crucial part of this table is the use of relative frequencies, which standardize the data by showing what fraction of the total each category represents. By doing so, it provides a clearer perspective on the data, particularly when comparing groups of different sizes.

To get a sense of the overall pattern of the distribution, one might look at the most common responses (mode), the spread of the frequencies (variance), and how they are centered around the mean. In educational settings, it's helpful to introduce visual aids such as histograms or pie charts alongside these tables to deepen students' understanding of the distribution's characteristics.