Final answer:
The five number summary includes the minimum value (1), first quartile (1), median (2), third quartile (2), and maximum value (3). The interquartile range (IQR) is 1. These values help in constructing a box plot to visualize the data distribution.
Step-by-step explanation:
Calculating the Five Number Summary
To determine the minimum, maximum, and quartiles, it is crucial to first arrange the data in ascending order. In the provided example, the sorted data set is: 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3. From this set, we can directly identify the minimum and maximum values.
- a. Minimum value: The smallest number in the dataset, which is 1.
- b. First quartile (Q1): The median of the lower half of the data. Since there are six numbers in the lower half, the first quartile will be the average of the third and fourth values: (1+1)/2 = 1.
- c. Median: Also known as the second quartile (Q2), it's the middle value of the ordered dataset. With 12 numbers, the median is the average of the sixth and seventh values: (2+2)/2 = 2.
- d. Third quartile (Q3): The median of the upper half of the data. Similar to Q1, Q3 will be the average of the ninth and tenth values: (2+2)/2 = 2.
- e. Maximum value: The largest number in the dataset, which is 3.
- f. Width of IQR: The interquartile range (IQR) is the difference between Q3 and Q1, so IQR = 2 - 1 = 1.
To visualize this data distribution, one could construct a box plot, which requires plotting these five summary numbers on a number line and drawing a box from Q1 to Q3 with 'whiskers' extending to the minimum and maximum values.