Explanation:
To find the middle 50% of the lengths in the given stem-and-leaf plot, we need to identify the lower quartile (Q1) and the upper quartile (Q3). The middle 50% of the data lies between these two quartiles.
Recall that in a stem-and-leaf plot, the stem represents the tens digit, and the leaves represent the ones digit. The digits are arranged in ascending order within each stem.
Given Stem & Leaf plot:
2 | 3, 4, 6
3 | 0, 2, 4, 4, 7, 9, 9
4 | 0, 5, 5, 5, 6, 7, 7, 8
5 | 0, 2, 3, 4, 7
6 | 5, 5, 7
1. Find the Lower Quartile (Q1):
Q1 is the 25th percentile of the data, which means 25% of the data is below Q1. Since there are 28 data points in total, the 25th percentile is located at (25/100) * 28 = 7th data point.
Looking at the ordered data:
0, 0, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 9, 9
The 7th data point is 5. Therefore, Q1 = 5 cm.
2. Find the Upper Quartile (Q3):
Q3 is the 75th percentile of the data, which means 75% of the data is below Q3. Since there are 28 data points in total, the 75th percentile is located at (75/100) * 28 = 21st data point.
Looking at the ordered data:
0, 0, 2, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 9, 9
The 21st data point is 7. Therefore, Q3 = 7 cm.
3. Middle 50% of the lengths:
The middle 50% of the lengths is the range between Q1 and Q3, which is from 5 cm to 7 cm.
In conclusion, the middle 50% of the lengths of adult cats is from 5 cm to 7 cm.