Student Fitness Survey: A Data Project from Start to Finish

Plan the survey and collect fitness data

A survey asks the same question to many people. A good fitness survey follows these rules:

• One clear question. Example: "How many push-ups can a student do in 1 minute?"
• Same test for all. Same surface, same start signal, same way of counting.
• Fair group. Pick students by lottery or by roll number, not only your friends. A group chosen like this is called a sample.
• Write units. Counts, seconds, centimetres. Use a table with one row per student.
• Safety and kindness. Warm up first. Nobody is forced. Keep names private; use roll numbers.

Other tests you can use: 50 m run time (seconds), sit-and-reach (cm), standing long jump (cm).

Organise and sort the data

Raw data is a messy list. Put it in a table, then sort it from smallest to biggest. Sorting is the first step for the median and quartiles. For our 15 students the sorted counts are: 10, 12, 14, 15, 16, 18, 18, 20, 22, 22, 22, 25, 28, 30, 45.

Also check the data. A count of 450 instead of 45 is probably a typing slip. Fix real mistakes. Never delete a result just because you do not like it.

Find the centre: mean, median, mode

Mean = sum ÷ number of values. Here 317 ÷ 15 ≈ 21.1.

Median = middle value of sorted data. With 15 values it is the 8th one: 20.

Mode = the value that comes most often: 22.

The mean is pulled by very big or very small values. The median is not. That is why we use the median when there is an unusual score such as 45.

Quartiles and the box plot

Quartiles cut sorted data into four equal parts. Q2 is the median. Q1 is the median of the lower half. Q3 is the median of the upper half. (If n is odd, leave the middle value out of both halves.)

For our data: Q1 = 15, median = 20, Q3 = 25. The interquartile range IQR = Q3 − Q1 = 10. It tells how wide the middle half of the class is.

A box plot draws five numbers: smallest, Q1, median, Q3, largest. The box runs from Q1 to Q3 with a line at the median. The lines (whiskers) go to the smallest and largest normal values. A value more than 1.5 × IQR above Q3 (here above 40) is an outlier, drawn as a dot. So 45 is an outlier.

Write the report

A short report has five parts:

1. Question and who was tested (15 students, Class 8).
2. Method: the test, the rules, the date.
3. Results: the sorted table, the five numbers, the box plot.
4. Finding, in plain words: "Half of the students did between 15 and 25 push-ups; the median was 20. One student did 45."
5. Limits and next step: only 15 students, one day, tiredness. Repeat after a term of training and compare the two box plots.

Never claim more than the data shows. 15 students cannot speak for the whole country.

Try it: your own class survey

Pick a test (for example, standing long jump). Test 10 classmates the same way. Write the results in a table, sort them, find the median, Q1 and Q3, and sketch the box plot on squared paper. Then open the 3D above and change one score. Which numbers move, and which stay?

Key formulas and definitions

• Mean = sum of values ÷ number of values
• Median = middle value of sorted data (average of the two middle values if n is even)
• Q1 = median of lower half; Q3 = median of upper half
• IQR = Q3 − Q1
• Outlier rule: above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR
• Five-number summary: min, Q1, median, Q3, max

Worked examples

Common mistakes

• Finding the median without sorting first.
• Testing different students in different ways, then comparing the results.
• Including the middle value in both halves when n is odd.
• Deleting an outlier only because it looks strange. Check it, then keep it if it is real.