ࡱ>  'bjbjVV ;Z<<:, , oo8/,[P\P^P^P^P^P^P^PRKUh^P^PoosPloR\P\PLX"$P/r~d$N(HPP0PLNU4UP$PU$P$^P^PPU, 5: Title: Tell it like it is! Achievement Objectives: S5-1F Presenting a report of findings Key Competencies: Thinking: Seek patterns and generalisations Deduce Using Language, Symbols and Texts: Demonstrate statistical literacy This activity explores the following key ideas: Using statistical language Writing conclusions Resources Student worksheet 91 set A 91 set BPrior Knowledge: Understanding measures of centre and spread Interpreting statistical graphs Language of sample and population Adapting for ICTIntroduction/Background As students progress through their statistical education, they usually develop very strong graphing skills. They also have a high understanding of measures of central tendency (mean, mode and median) and as well as measures of spread (range, inter-quartile range and for senior students, standard deviation). Students often feel it is enough to state a couple of obvious observations which is fine initially, but insufficient at Level 4+ of the curriculum. After this lesson students should be able to Use good statistical language in a conclusion Recognise the need to look at the data & graphs Think about the story the data tells Part A You may wish to start this activity by talking about why companies/statisticians etc. take a sample of the population rather than asking everyone in the population (a full census). Some of the main reasons are: Time Cost (reduces cost) Practicality (near impossible to ask population) Resources (People and materials) Tell the students where the data is from (bolded below). The 91: This activity is focussed on writing a conclusion and therefore data has already been collected and presented for writing a conclusion. The data has been collected from the 2005 91 database using the random sampler. The population is students who participated in the online survey. This activity could be done in groups. Problem What can we conclude from 91sets A and B?Plan Give out 91set A. Encourage students to make I notice statements about each graph and table. These could be collected on board for later reference as students complete the worksheet. Give out worksheet. Students fill in gaps. Discuss correct answers for Sample A. Give out 91set B. What questions could we answer using this dataset? [Ask students to pose questions for each graph and data set]. Explain that when students make a conclusion they should: Answer the questions A good beginning is Based on the evidence from the data/bar graph/table, it seems [This task has at least 4 implied questions!] Quantify their answer Quote numerical values (with units) of statistics/proportions and describe graph features. Generalise the answer (make an inference) to all students in the 91 database. One possible starter for the generalisation is I expect 91 91set A for Part A. 91set B for Part B. Analysis  I notice statements developed before each of Part A and Part B is attempted. Solutions to Part A From this particular 1sample_, the 2table of data suggests that there are 3slightly___ more girls than boys in the 91 4population. The 5_bar graph_ indicates that 6Auckland__ had the most respondents while 7Southland_ and 8West Coast had the least. From this data, it can be seen that the 9median__ age of a student in the sample was 12. If another sample of 200 students was taken, we could expect the age to be around 10___11-13 years old. Travelling to school by 11___motor car appears to be the most popular method. If another sample was taken, it is likely that the most popular method of travelling to school would most likely be 12__motor car _ . The data also showed that cell phone ownership is high for students with the data showing that 13 64% of the 14sample owning a cell phone. This 15suggests that more students own a cell phone than dont own a cell phone. 1 Population/sample 2 Table of data/ graph 3 Slightly / a lot 4 Population /sample 5 Histogram / bar graph 6 Auckland / North Island 7 Southland / Canterbury 8 West Cost / Gisbourne 9 Mean / median 10 9 -11 / 11 13 11 Motor car / Train 12 Motor car / walking 13 36% /64% 14 sample / population 15 proves / suggests Conclusion  Part B Class discussion to focus on positive features of student attempt. This section allows students to create their own conclusions. A list of suitable sentence starters has been included to assist students in creating their conclusions. When writing a conclusion, it is important that students avoid making causality statements in their findings. They should stress that the data is from a sample and that if another sample was taken the results may be different. Listed below are some useful conclusion statements that may be used in writing conclusion. For a more detailed analysis on writing conclusions, please refer to the BEAR HUGS 1, 2 & 3 support sheets. From these data From this sample It appears that The sample data collected from (Name source of data. E.g. 91 NZ 2005). There is evidence to suggest From the (type) graph From these data, it is likely that the population may (inference) Resampling the population may result in From this sample, the (average value) was This suggests that It appears that It does not appear that The data is Based on these data I noticed that Further investigation may assist I wonder if Below is a model answer, students are not expected to be as complete with their conclusions, especially if they have little prior skill at conclusion writing. It is also more difficult to write a conclusion with-out context. A MODEL ANSWER It appears that there are similar amounts of boys and girls from this sample. The sample also indicates that around 70% of both boys and girls play sport. Cell phone ownership appears more important to girls than boys, with about 20% more girls (70%) owning a cell phone than boys (50%). Boys, on the other hand are more likely to own their own TV than a girl with 51% of the boys owning their own TV compared to 40% for girls. The table of lunchtime activities indicates that as students get older they get less active during lunchtime. The main activity for Year 5 to year 8 students is running around and playing. For Year 9 and Year 10 students, the most common activity is sitting around and talking. The bar graph shows cell phone ownership by region as a percentage. All the students from Taranaki own a cell phone in this sample while no students from Southland or the Hawkes Bay regions owned cell phones. A larger sample may give a better view of the population as smaller regions a likely to be misrepresented due to having very few students representing their region. The scatterplot shows students heights against age. The height of students is generally increasing as age increases. This is what we would expect. There is an interesting outlier, a student who is 13 years old and has a height of 100 cm. This is much lower than expected for the average 13 year old. I wonder if this is a correct measurement or an error? A random sampling method was used to obtain this sample. There are 51 boys and 49 girls in the sample. The difference in the group sizes does not affect the conclusion. Samples such as these are subject to sampling variability. Larger samples would give a better understanding of the underlying population distributions. However, similar results should be expected if a new sample of size 100 was taken. The subjects for this research are school age Year 5 to 10 boys and girls from the 91 NZ 2005 population. Reflection To what extent have students learned to write appropriate conclusions? If I taught this lesson again, I would change _________________________ to ______________________ because ______________________________________ To extend this activity Ask students to collect all the conclusions for first graph and from there write a model answer. Repeat this for second graph and data tables.      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