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The median is a fundamental concept in descriptive statistics that helps us find the middle value of a dataset. When you have an ordered set of numbers, the median is the point that divides your data into two equal halves.
If you were to line up all the responses to the question on dining frequency, from the least to the greatest, the middle point is known as the median. In this exercise, the total number of responses given was 570. To locate the median, you use the formula \( \frac{n + 1}{2} \) to determine the position in the data. Here, that is \( \frac{570 + 1}{2} = 285.5 \).
Since we cannot have a fraction of a response, this suggests we need to find the average of the 285th and 286th responses. Both of these fall in the '1 time' category. Thus, the median is 1. Interestingly, even changing the initial '0 times' responses to '7 times' would not shift the 285th and 286th positions out of the '1 time' category, securely maintaining our median at 1 time per week.

The mean is another essential aspect of descriptive statistics, often called the average. To calculate the mean, every response is accounted for, and then we determine the average frequency.
The calculation for the mean is done by multiplying each category of response by its frequency, adding all these results together, and then dividing by the total number of responses. So, in this case:

• 0 times: 84 students, contributing 0 to the sum
• 1 time: 290 students, contributing 290
• 2 times: 100 students, contributing 200
• 3 times: 46 students, contributing 138
• 4 times: 30 students, contributing 120
• 5 times: 13 students, contributing 65
• 6 times: 5 students, contributing 30
• 7 times: 2 students, contributing 14

The sum of these products is 857. Dividing this by the total of 570 responses gives us approximately 1.5. Thus, the mean frequency of dining out is 1.5 times per week. If we hypothetically change the 84 '0 times' responses to '7 times', the mean would rise significantly to 2.54.

A frequency table is a useful tool in descriptive statistics for organizing and presenting data in a clear format. It displays each unique value in your data along with the count, or frequency, of how often it occurs.
In this exercise, a frequency table was used to organize how students responded to the survey question about dining frequency per week. Each row of the table represented one of the possible answers – from '0' times to '7' times – and the corresponding frequency, which is the number of students selecting that response.
For example, the table showed that 290 students reported dining out once per week, while 84 students stated they do not dine out at all. This makes it easy to visualize the distribution and helps in calculating descriptive statistics like the median and mean. Using a frequency table simplifies spotting trends, making calculations more intuitive, and enhances understanding of the dataset.