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Statistical Analysis Worksheet

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Statistical Analysis Worksheet

Use the carnival data and visuals to investigate variation, compare groups, and explain what the statistics show. Show working where asked. Give answers in context.

The carnival data

At a swimming carnival, students recorded their 25 m freestyle times and favourite events. The results below are fictional.

Student

Time (s)

Tevita

Sione

Zoe

Aria

Tui

Leilani

Ravi

Ruben

Event

Year 7

Year 8

Freestyle

Backstroke

Relay

Investigate the times

1.Classify each carnival variable as categorical, discrete numerical, or continuous numerical: favourite event; number of races entered; freestyle time measured to the nearest hundredth of a second.

2.Put the eight freestyle times in order from least to greatest. Then state the median time.

3.Calculate the mean freestyle time. Show the total and division you used.

4.Find the mode and range of the freestyle times. What does the range tell you about the spread?

5.Ravi’s time is 50 seconds, much slower than the others. Identify this possible outlier. If Ravi’s result is removed, what is the new median? Explain briefly how an outlier affects the mean and median here.

Read the visuals

Use the printed displays below. Each ● represents one student.

Time (s)

Students

●

●●●

●

6.Describe the dot plot’s main cluster and the isolated value. What does the isolated value suggest about the distribution?

7.From the favourite event table, which event was most popular in Year 7? How many students were surveyed in Year 8 altogether?

8.A student says, “More Year 7 students chose relay than Year 8 students, so relay was more popular in Year 7.” Is this comparison fair? Explain using the totals surveyed.

9.The carnival raffle has 12 equal tickets: 5 are blue, 4 are yellow, and 3 are red. What is the probability of drawing a blue ticket? What is the probability of not drawing a blue ticket?

10.A fair three-colour carnival spinner has equal red, blue, and green sections. In 12 spins, red appears 7 times. What is the theoretical probability of red, and why might the experimental result differ? If the spinner is used for many more spins, what should happen to the experimental proportion in the long run?