A researcher wanted to examine the age of men when they get married.

Question

The following data was collected:
38 32 27 37 33 28 27 38 35 28 34 21
34 29 37 36 25 20 28 41 28 35 36 40
31 25 31 33 34 39 20 29 24 30 31 26
62 23 33 35 27 22 36 39 42 38 29 36

Is your data approximately symmetric or is it skewed?

Answer 1

To assess whether the given data is approximately symmetric or skewed, we can use several methods, including calculating descriptive statistics (mean, median, mode) and creating visualizations (histograms or boxplots).

Here's how you can analyze the skewness of the data:

1. Sorting the Data: First, let's arrange the data in ascending order:

20, 20, 21, 22, 23, 24, 25, 25, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 33, 33, 33, 34, 34, 34, 34, 35, 35, 35, 35, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 39, 39, 40, 41, 42, 62

2. Calculating Descriptive Statistics:

   • Mean: The average age of marriage.
   • Median: The middle value when the data is sorted.
   • Mode: The most frequently occurring value(s).

3. Find the mean and median:

   • Mean: (Sum of all ages) / (Number of ages)
   • Median: The middle value in the ordered list (or the average of the two middle values if there is an even number of observations).

4. Analyzing Results: Typically, you can determine skewness by comparing the mean and median:

   • If the mean is less than the median, the data is negatively skewed (left-skewed).
   • If the mean is greater than the median, the data is positively skewed (right-skewed).
   • If the mean and median are approximately equal, the data is likely symmetric.

5. Visualizing the Data: Creating a histogram or a box plot to visualize the distribution of the data can be very helpful. A histogram that is symmetric around the mean would indicate symmetry, while a histogram that has a longer tail on one side would indicate skewness.

Summary Analysis:

• Calculate mean, median, and mode:

  • Mean = (20 + 20 + 21 + ... + 62) / 48 = 34.75 (approx)
  • Median = (31 + 31) / 2 = 31 (since there are 48 observations)
  • Mode = 28 (most frequent value)

• Comparison: Since the mean (approximately 34.75) is greater than the median (31), this suggests that the data is positively skewed (right-skewed).

• Histograms and Boxplot: Visualizing these results could provide further insight. The presence of outliers (like 62) could also impact the skewness.

Conclusion:

In summary, the data is positively skewed since the mean is greater than the median, indicating that there are some higher ages pulling the average up.