Consider a group of 17 students with the following heights (in cm): 106, 110, 123, 125, 117, 120, 112, 115, 110, 120, 115, 102, 115, 115, 109, 115, 101. The sports teacher wants to divide the class into two groups so that each group has an equal number of students: one group has students with height less than a particular height and the other group has students with heights greater than the particular height. Suggest a way to do this. Can you guess the age of these students based on the tabular data in the 'Telling Tall Tales' section?
Step 1: Sort the heights and find the median. Sorted heights: 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125
Step 2: Find the median (9th value). With 17 students, the median = 115 cm
Step 3: Use 115 cm as the dividing point.
- 7 students below 115 cm
- 5 students above 115 cm
- 5 students at exactly 115 cm
Answer: Use 115 cm as the dividing point. Based on the height data, these students appear to be around 5-7 years old.
Explanation
To divide 17 students into two equal groups, we need to find the median height. With 17 values, the median is the 9th value when sorted. The median is 115 cm. Students below 115 cm (7 students) go in one group, students above 115 cm (5 students) go in another, and 5 students are exactly 115 cm. Comparing with the 'Telling Tall Tales' data showing average heights for different ages, heights of 101-125 cm correspond to approximately 5-7 year olds.
Solution Steps
Step 1: Sort the heights: 101, 102, 106, 109, 110, 110, 112, 115, 115, 115, 115, 115, 117, 120, 120, 123, 125
Step 2: Find median (9th value): 115 cm
Step 3: Count students below 115 cm: 101, 102, 106, 109, 110, 110, 112 = 7 students (less than 115)
Step 4: Count students above 115 cm: 117, 120, 120, 123, 125 = 5 students
Step 5: Students at 115 cm: 5 students
Step 6: Use 115 cm as dividing point