Year 7AC9M7ST03

Planning a Statistical Investigation

Plan and conduct statistical investigations involving data for discrete and continuous numerical variables; analyse and interpret distributions of data and report findings in terms of shape and summary statistics.

An investigation is a loop: ask, collect, display, interpret, report. Skipping straight to the graph is the usual mistake.

Method

Write the question first

A vague question produces data you cannot use.

Discrete counts, continuous measures

Shoe size is discrete. Height is continuous. It changes how you display it.

Report shape, centre and spread

All three. A centre on its own describes very little.

Worked example

e.g.

\text{Investigate: how long do students in this class take to get to school?}

Write the question precisely, naming who and what. $\text{travel time in minutes, students in 7B}$
Decide how to measure and how to record. $\text{nearest minute, tally on a sheet}$
Collect the data. Note anything unusual as you go.
Choose a display that suits the data type. $\text{continuous} \ \Rightarrow\ \text{dot plot or stem-and-leaf}$
Calculate the summary statistics. $\text{median, range}$
Report shape, centre and spread, then state the limitations. $\text{one class only — cannot speak for the school}$

Practice

Judge the plan, not the arithmetic.

\text{Is 'do people like sport?' a good question?}

Answer

\text{No — 'like' is not defined and cannot be measured.}

\text{Is number of siblings discrete or continuous?}

Answer

\text{Discrete — it is a count.}

\text{Why report the range as well as the median?}

Answer

\text{Two groups can share a median and differ hugely in spread.}

\text{You survey only your friends. What is the limitation?}

Answer

\text{The sample is not representative of the class.}

\text{One student took 90 minutes. Delete it?}

Answer

\text{No — investigate it, then report with and without.}