Statistical Investigation & Data Display

Write a statistical question you could investigate in your class (e.g., 'How many hours of screen time per day do students have?').

How would you collect the data? What type of data is it?

Which graph would you use to display your results? Explain why.

What is one question you could answer from your results?

Class A: 2, 3, 3, 4, 5, 5, 6, 7, 7, 8. Class B: 1, 1, 2, 3, 4, 4, 5, 5, 10, 10. Find the range for each class.

Find the median for each class.

Which class has more consistent reading habits? Use the statistics to explain.

Data: 34, 41, 29, 35, 28, 47, 31, 45, 38, 27, 43, 33. Construct a back-to-back or single stem-and-leaf plot. Find the range and median.

What is the key difference between a bar chart and a histogram? When would you use each one?

A class measured their hand spans: 14, 15, 15, 16, 16, 16, 17, 17, 18, 19 cm. Would you display this in a bar chart or histogram? Explain and sketch the appropriate graph.

A dot plot shows the number of goals scored by a football team each game: 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 7. Describe the distribution: is it symmetric or skewed? What is the outlier? What does the mode tell us about this team's scoring?

A survey asks: 'Don't you agree that students should have more homework?' What is biased about this question? Rewrite it as an unbiased question.

To find students' favourite subject, a school surveys only students attending the maths extension class. What is the sampling bias? How would you fix it?

A survey of 40 students shows: 15 boys like sport (5 don't); 12 girls like sport (8 don't). Complete a two-way table. What fraction of all students like sport?

From the table: are boys or girls more likely to like sport? Express your answer as a percentage.

Choose a topic to investigate (e.g., sleep habits, sports participation, screen time). Write a clear statistical question. Describe how you would collect a random sample of at least 20 responses. What type of data will you collect (categorical, discrete, or continuous)?

Describe which graph you would use to display your results and explain why it is the most appropriate choice for your data type.

A histogram shows heights of students in intervals: 140–150 cm (5 students), 150–160 cm (12 students), 160–170 cm (15 students), 170–180 cm (8 students), 180–190 cm (2 students). Describe the shape of the distribution. What is the most common height interval? What is an estimate of the median?

A newspaper headline says: 'Screen time up 200% — teenagers in crisis!' The article shows a bar chart with y-axis starting at 3 hours. Average screen time went from 3 hours to 5 hours. (a) Is the 200% claim correct? (b) How is the bar chart misleading? (c) What would a fair representation look like?

A student measures plant growth over 8 days: 0, 1, 2, 3, 3, 4, 5, 6 cm. Display this data in a line graph. Calculate the range. What type of data is this? Describe the trend.

Another plant's growth was: 0, 0, 0, 0, 4, 8, 12, 16 cm. Compare the two plants' growth patterns. Which grew more consistently? What caused the step change in the second plant?

30 students chose their favourite season: Summer 12, Winter 6, Autumn 9, Spring 3. Calculate the angle for each sector. Draw the pie chart and label each sector with the percentage.

A scatter plot shows: as study hours increase from 1 to 6, test scores generally increase from 45 to 90. Describe the correlation (positive, negative, or none). Is it strong or weak?

A student studies 0 hours but scores 75. Is this consistent with the trend? What might explain it?

Heights (cm): 152, 163, 155, 171, 148, 165, 158, 174, 160, 145, 168, 177, 151, 162, 169. Organise into groups: 140–149, 150–159, 160–169, 170–179. Complete the frequency table and draw a histogram.

Describe the shape of this distribution of exam scores: most students scored around 70, fewer scored very high or very low. Is it symmetric, positively skewed, or negatively skewed?

A data set on reaction times shows most values clustered at 0.3 seconds with a long tail to the right up to 1.5 seconds. What distribution shape is this? What might cause the long tail?

A company collects data on its customers' shopping habits without telling them. List 3 ethical concerns with this approach. How should data be collected ethically?

A medical trial collects health data from 1000 people. Why is it important that participants give informed consent? What risks might they face if their data is misused?

Choose a topic: does amount of sleep affect academic performance? OR does exercise frequency affect mood? Write a statistical question, describe your collection method, list 3 potential sources of bias, choose an appropriate graph, and describe what results you would expect to find and why.

Australia's average annual rainfall has been recorded every year for 100 years. A line graph shows a slight downward trend. List 3 questions a scientist would ask to determine if this trend is statistically meaningful.

A school principal reports that the average class score improved from 68 to 72 between two years. One student's score improved from 40 to 80. Explain why this single student could have a large effect on the mean but not on the median.

You have data about 50 Year 7 students: favourite subjects (5 types), average study hours per week (range 0–15), and whether they play sport (Yes/No). Choose one graph type for each variable and explain your choice. Sketch one of the three graphs.

A spinner is spun 200 times: Red 85, Blue 60, Green 55. Calculate the relative frequency of each colour. How close is each to the theoretical probability if the spinner were fair (1/3 each)?

A box plot for test scores shows: minimum 35, Q1 55, median 65, Q3 75, maximum 90. What is the interquartile range (IQR = Q3 − Q1)? What does the IQR tell you about the middle 50% of students?

Another class has the same median but a much larger IQR. What does this tell you about the spread of scores in that class?

Class A results: Min 40, Q1 55, Median 70, Q3 80, Max 95. Class B results: Min 30, Q1 45, Median 65, Q3 85, Max 100. Compare the two classes on: (a) median score, (b) spread (IQR), (c) range, (d) which class performed better overall.

Choose a real question to investigate (e.g., 'Does exercise improve mood?'). Write: (a) your statistical question, (b) what data you need, (c) how you would collect it, (d) how you would display it, and (e) what conclusion you might expect.

A news article states: 'Our city has the highest average house price in the country at $1.2 million.' What questions should you ask before accepting this claim? Consider: which average was used, who collected the data, when was it collected, and what is the sample size?

List 5 key things you have learned about statistical investigation in this worksheet. Which one surprised you most?

Describe a real-world situation where you could apply the statistical investigation skills you have learned.

Headline: 'New study finds students who eat breakfast score 15% higher on tests.' List at least 4 questions you should ask before accepting this claim. What other factors might explain the difference?

Monthly average temperatures (°C) for a city: Jan 28, Feb 27, Mar 25, Apr 22, May 18, Jun 15, Jul 14, Aug 16, Sep 19, Oct 22, Nov 25, Dec 27. Find the range. Calculate the median. Display the data in a line graph. Describe the seasonal trend.