How do you compare to the Vitruvian man?

Year 8 Statistics Assignment

Leonardo da Vinci (1452-1519) was a man of many talents: a painter, sculptor, architect, musician, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer. He is often categorised as having “unquenchable curiosity” and a “feverish imagination”. On the right is a picture of his Vitruvian man, a combination of his love of science and art. The proportions of the human body fascinated Leonardo; one of his findings was that “the length of the outspread arms is equal to the height of man”. In this assignment you will be investigating his finding to see how it holds true for your classmates.

This assignment can be completed on paper or computer. Your teacher will advise you how you can best present it and look after it.

Task 1: You will need to collect the measurements for height and arm span of yourself and your classmates (to the nearest centimeter). Add the measurements to a table in the following format:

  1. (Complete table)

Height (cm) / Arm Span (cm)
Person 1

Person 40
  1. Were most people’s height and arm span the same or different? How did your own measurements compare?

Task 2: Analyse the class data by calculating the mean, median, mode and range for the height and arm span. Use the following table format:

  1. (Complete table)

Mean / Median / Mode / Range
Height (cm)
Arm Span (cm)
  1. You will need to explain howyou found each of the above. Please explain using words by using the sentence starters below. You can submit any rough working out on a separate page also.

I calculated the mean by…

I calculated the median by…

I calculated the mode by…

I calculated the range by…

  1. Looking at the spread of heights in your class, which one of mean, median or mode best represents your class? Hint: are there many outliers (people who are particularly short or tall)? Explain your choice.
  1. After summarising the data, how does your height compare to the class? Use data to back up your answer (refer back to the mean, median, mode etc.)

Task 3:Create a frequency table and then use it to draw a histogram. Graphs provide a visual representation of data that can give a quick impression of the distribution. Collect your data by counting the number of people that belong in the height brackets. Use the table format below: The first row is an example.

  1. (Complete table).

Interval (Heights cm) / Tally / Frequency
150-154 / ||| / 3
155-159
165-169
170-174
175-179
180-184
185-189
190-195
  1. (Create histogram). Your histogram should look similar to the example below: Speak to your teacher about using Excel to create this type of graph (if you wish).
  1. Is the histogram skewed, bimodal or symmetrical?
  1. What new information can you draw from the histogram about how you compare to the class? (Look at the interval your height belongs to and compare to the most frequent).

(Extension) Task 4: Display height and arm span data in a back-to-back stem and leaf plot.

It should look similar to the example below:

  1. (Complete back-to-back stem and leaf plot).
  2. What does the stem and leaf plot tell you about the correlation between height and arm span? Is there enough evidence to back up Leonardo’s claims?

Task 5: How do you compare to Australian students? The final part of your investigation involves comparing yourself to a sample of Australian students in your year. Go to and get a sample of 40 students in year 8. (Choose numerical data so that you can look at height).

  1. How does the sample size affect the reliability of the data presented? Is it favorable to have a bigger or smaller sample size? Discuss.
  1. Once you have downloaded the data in Excel, you can calculate the following in the table below:

Sample of Australian Year 8 Students’ Heights
Mean / Median / Mode / Range
Height (cm)
  1. Finally, complete the table below to summarise:

Typical Student Compared to Me
Me / Mean (My class) / Mean (Aus student)
Height (cm)
  1. Conclusion: Write a summary that describes the following, (focusing on height):

Your class, including each of the four measures (mean, median, mode range).

Any findings from the stem and leaf plot

What is a typical student in your class?

Are you a typical student in your class, or in Australia?

How do you compare to the Vitruvian man, whose height should equal arm span?

Marking Rubric
Below Level / At Level / Above Level
7.1 I can compare primary and secondary sources of data.
7.2I can compare data using stem and leaf plots and dot plots
7.3I can calculate, display and describe the mean, median, mode and range of data.
7.4I can describe and interpret data displays using median, mean and range. / 8.1 I can use different techniques to collect data, including census and sampling
8.2 I can explain the benefits and problems of different data collection techniques, including sampling
8.2 I can investigate the effect of outliers and other data values on the mean and median.
8.3 I can explore how the mean and proportions of data changes when different samples are taken from the same population / 9.1I can form questions and investigate problems using categorical and numerical data.
9.2I can collect and use data from secondary sources.
9.3I can Draw back-to-back stem-and-leaf plots and histograms
9.4I can describe data using terms including ‘skewed’, ‘symmetric’ and ‘bi-modal’.
9.5I can describe the location (centre) and spread of numerical data, using mean, median and mode.
9.6I can use different techniques to collect data, including census, sampling and observation

Task 1

  1. 8.1
  2. 7.1

Task 2

  1. 7.3
  2. 7.4
  3. 8.2
  4. 7.4

Task 3

  1. 8.1
  2. 9.3
  3. 9.4
  4. 9.5

Task 4

  1. 9.3
  2. 9.1

Task 5

  1. 8.3
  2. 7.3, 9.2
  3. 7.3, 9.2
  4. 7.4, 8.3, 9.5 (depending on the extent of response).