Topic 4:Statistics Learning Intention: to solve a statistics problem using the PPDAC enquiry cycle. To classify data as discrete or Continuous. Success Criteria: Y9 maths P 422 Ex13A References: 28, 29 and 30 Work book p 14 Check list.

Topic 4. Statistics Statistics is the art of solving problems and answering questions by collecting and analysing data. We solve a stats problem using the PPDAC enquiry cycle. Problem Plan Data Analysis Conclusion

Writing Strategy – PEEL (adapted from MRGS Maths) Writing Strategy – PEEL 3

Posing a Statistical Question Variable: 1.Catogorical 2. quantitative Two Groups: Comparing Word: faster, taller, longer, fewer, lighter Population: Data source 4

Inference Analysis 5

(adapted from Nayland Maths) DISCUSS (adapted from Nayland Maths) 6

1 The Problem: Investigate this possible question: 32.01 1 The Problem: Investigate this possible question: Do Year 10 students have larger neck sizes than Year 9 students in the Beta data set? (Population)

Use the data for Year level and neck size circumference. 32.01 2 The Plan Use the data for Year level and neck size circumference. The data has been provided here, but in an actual investigation you would need to look at how the neck circumference was measured. A shirt size measurement would give a good indication of what data to expect. The circumference could be measured using a tape measure, placed snugly but not too tightly around the neck at its narrowest point. The tape measure should have a scale in mm or cm, and care would need to be taken in reading the scale from the 0 point, and ignoring any other scales such as inches.

32.01 2 The Plan To avoid measurement errors, one possibility could be to take two or three separate measurements and only record them if they agree. In an actual investigation you should probably survey a lot more than 40 students. The students should be chosen at random from a large group, so that every student had an equal chance of being chosen. It is probably only realistic for a student to carry out a survey like this at their own school, unless the student had access to a larger database of measurements, such as Census at School.

32.01 4 Analysis Plot the data for the neck circumferences of year 9 and year 10 students. Year 9 33 34 36 35 37 38 40 39 42 41 Neck Circumference (cm) 33 34 36 35 37 38 40 39 41 Year 10 Neck Circumference (cm) The graphs show a fairly similar spread for each group, with a shift of about 1 cm to the right for the Year 10 neck sizes compared to the Year 9 neck sizes. The plots overlap to a considerable extent. The neck sizes are fairly similar, and it would not be possible to separate the two groups if neck size was the only available information.

32.01 4 Analysis Use the five number summary for each group, and the mean to draw a pair of box and whisker diagrams 37.95 36.95 Mean 41 Top 39 38 37 Median 36 35 34 Bottom Year 10 Year 9 Lower quartile Upper Year 10 Year 9 33 34 36 35 37 38 40 39 42 41 Neck Circumference (cm) These confirm that there is a 1 cm shift upwards for the Year 10 data compared with the Year 9 data.

Since the medians of neck sizes of both year levels overlap into each 32.01 5 Conclusion Based on these fairly small samples, it does appear that generally Year 10 students do have larger neck sizes than Year 9 students. This is what you would expect, because at that age people are still growing. Since the medians of neck sizes of both year levels overlap into each others Boxes , we cannot make the claim that year 10’s have bigger neck circumference than year 9 students in the Beta data set. Another sample may give me different results due to sample variation In which I may be able to make the call because in this sample there Is just a little overlap.