All the students in fourth year in a school took part in a long-jump competition - Junior Cycle Mathematics - Question 6 - 2022

The modal group is the category with the highest frequency of students. Looking at the frequency table, the number of students in each category is:

• 200 – 250: 10 students
• 250 – 300: 15 students
• 300 – 350: 25 students
• 350 – 400: 32 students
• 400 – 450: 10 students
• 450 – 500: 3 students

The category with the highest number is 350 – 400 with 32 students. Therefore, the modal group is:

350 – 400

To determine the least number of students qualifying for the final (415 cm or more), we only consider the categories from 400 – 450 and 450 – 500:

• The 400 – 450 category (10 students) may include those who jumped exactly 415 cm or more.
• The 450 – 500 category (3 students) also qualifies as all of them jumped more than 415 cm.

Thus, the least number of students who could qualify is:

3

For the greatest number of students who could qualify (415 cm or more), we consider all students in the categories:

• 400 – 450 (10 students)
• 450 – 500 (3 students)

The total number of students in these categories who could have qualified is:

So, the greatest number of students that could qualify is:

13

To draw a histogram, plot each interval on the x-axis (Distance jumped) against the frequency (Number of students) on the y-axis. Each bar should represent the number of students corresponding to the distance ranges:

• 200 – 250: 10
• 250 – 300: 15
• 300 – 350: 25
• 350 – 400: 32
• 400 – 450: 10
• 450 – 500: 3

The histogram will have 6 bars corresponding to each category, with heights representing the respective frequencies.

The median distance jumped indicates that half of the students jumped less than 331 cm and half jumped more. This statistic shows that 331 cm is the middle value when all the distances are arranged in order. Therefore, a significant proportion of the students jumped distances below this median, highlighting the distribution of results.