Which box-and-whisker plot shows the data?38, 28, 41, 48, 45, 28, 30, 35, 34, 36, 34, 34, 30, 37, 33
Unfortunately, as an AI text-based model, I am not able to create or display images or plots. However, I can help you understand how to create a box-and-whisker plot for this data set.
1. Organize the data in ascending order:
28, 28, 30, 30, 33, 34, 34, 34, 35, 36, 37, 38, 41, 45, 48
2. Calculate the quartiles:
Q1 (1st quartile) = median of the first half = 32.5 (30+33)/2
Q2 (2nd quartile, or median) = median of the whole data set = 34
Q3 (3rd quartile) = median of the second half = 38.5 (38+39)/2
3. Calculate the IQR (Interquartile Range) = Q3 - Q1 = 38.5 - 32.5 = 6
4. Identify the smallest and largest data points (lower and upper bounds), which are the whiskers in the plot:
Minimum = 28
Maximum = 48
Now, to create the box-and-whisker plot, you would visually represent the data using a number line and the calculated values above. The box is formed between Q1 and Q3, with a line inside the box indicating the median (Q2). Then the whiskers extend from the box to the minimum and maximum values.