Make a box-and whisker plot of the data. Average daily temperature in Tucson. Arizona, in December:
67,57,52,51,64,58,67,58,55,59,66,50,57,62,58,50,58, 50,60,63
To create a box-and-whisker plot of the data, we first need to order the temperatures in ascending order:
50, 50, 50, 51, 52, 55, 57, 57, 58, 58, 58, 58, 59, 60, 62, 63, 64, 66, 67, 67
Next, we need to find the median of the data set, which is the middle value. In this case, there are 20 temperatures, so the median is the average of the 10th and 11th temperatures:
Median = (58 + 58) / 2 = 58
Now, we need to find the lower quartile (Q1) and upper quartile (Q3), which are the medians of the lower and upper halves of the data set, respectively.
Q1 = median of the first half of the data set = median of (50, 50, 50, 51, 52, 55, 57, 57, 58, 58) = (55 + 57) / 2 = 56
Q3 = median of the second half of the data set = median of (59, 60, 62, 63, 64, 66, 67, 67) = (62 + 63) / 2 = 62.5
Next, we can find the lower and upper extremes, which are the smallest and largest temperatures in the data set:
Lower extreme = 50
Upper extreme = 67
Finally, we can plot the box-and-whisker plot with the following information:
- Lower extreme: 50
- Lower quartile (Q1): 56
- Median: 58
- Upper quartile (Q3): 62.5
- Upper extreme: 67
The box represents the interquartile range (Q3 - Q1), the whiskers extend to the lower and upper extreme, and any outliers would be shown as individual data points outside the whiskers.