Data Projects

Data Projects

You now have the tools to ask a question, organise observations, describe their centre and spread, and present a graph. A project uses those tools together. Choose one short investigation first; the longer and group activities are choices, not a requirement to complete everything at once.

Before collecting data, decide what one observation will mean. Record the unit, group, time period, and any missing entries. Use the same procedure for comparable observations. After collecting, keep the original record so another reader can check how your graph and calculations were made.

How Long is a Sentence?

Choose one text-rich page from each of two books on different subjects. Count words in each sentence and compare the two distributions. Define your counting rule before starting, because hyphenated words, abbreviations, and headings can otherwise produce inconsistent observations.

Keep headings separate from sentences unless your stated rule includes them. Write one sentence’s word count per observation. Make one dot plot for each page on the same horizontal scale. Then calculate the mean and median counts. A larger mean describes longer sentences in these selected pages, not necessarily in every page or every book from those subjects.

What is in a Name?

Record a consistently chosen form of each classmate’s name, such as the first name. Decide whether spaces and punctuation count as letters; a simple rule is to count alphabetic letters only. Explain your rule so the observations can be reproduced.

Calculate numerical name lengths, then make a dot plot and find their mean, median, and range. Starting letters form a different kind of data: use alphabetical order to organise them, or count their frequencies to identify more and less common starting letters. Do not perform ordinary arithmetic on letters as though they were centimetre measurements.

For a median starting letter, sort the starting letters alphabetically. If there is one middle letter, it gives the central alphabetical position. For an even count, identify the two middle letters rather than averaging their alphabet positions without defining a new convention. A middle letter near M does not prove there are equal numbers strictly in A–M and N–Z, because repeated letters and the boundary choice matter.

Use the convention A, E, I, O, U for this written-letter task and state how you treat any unusual characters. Count each chosen name once in the four categories. A double-bar graph can compare the two groups. It describes this class’s chosen names and counting rules, not a general rule about names everywhere.

In and Out

Track how many times you leave your house each day for a month, or for a clearly stated period of at least two weeks. Define a departure consistently. A day with no departures is a genuine zero; a day when you forget to record is missing.

Retain a dated table so weekday or weekend patterns can be investigated. A dot plot then shows how frequently each count occurs, but removes the dates unless you label them. Calculate centre and spread for the recorded days and report the observation count. If a family member participates, use the same period and definition before comparing.

Our heights vs. our family’s heights

In a small group of eight to ten students, each can record their own height and family members’ heights in centimetres using a consistent measuring method. Each family’s dot plot can be described separately. Then place each student’s height beside their family’s mean height in a double-bar graph.

Family sizes and ages differ. Including young children can strongly affect the mean, as the earlier lesson showed. Do not treat a difference between families as evidence of its cause or as a judgement about a person. The useful learning task is to describe a distribution and choose a suitable comparison.

Estimating time

Close your eyes and open them when you think one minute has passed, without counting. Have a helper measure the elapsed seconds. Collect family estimates, then repeat the procedure for a three-minute target. These are two different targets: 60 seconds and 180 seconds.

Make a dot plot for each target and mark the actual target as well as the mean and median. Compare the pattern with the target and examine the spread. If you graph the two mean estimates as paired bars for each family, keep seconds as a shared unit. A larger three-minute mean is expected because the target itself is three times as long.

For a fair accuracy comparison, examine each estimate’s distance from its own target. Otherwise a family that averages 175 seconds for a three-minute target might look less accurate merely because its numerical value is larger than a one-minute mean of 59 seconds. Preserve both the target and the observed values.