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Statistics & Probability

Learn about data displays, mean, median, mode, range, and data interpretation. Practice with random samples and analyze how sample sizes affect accuracy and representation. Improve statistical skills through hands-on exercises.

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Statistics & Probability

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  1. Statistics & Probability Level I Parts 1,2,3

  2. Statistics:Level I A census is a survey of the entire population Census @ School Numerical Categorical Male/female State/country Year level ATSI Eye colour Language spoken at home Favourite food Breakfast Mode of travel to school Internet access Internet use Favourite sport Favourite music Source of money Conservation actions taken • Money earned • Pulse rate • Height • Height (belly button) • Arm span • Length of foot • Age • Concentration • Hours of leisure time • Hours of sleep • Travel time to school • Importance of issues • Reaction time – dominant hand • Reaction time – non-dominant • Number of languages spoken

  3. Statistics:Level I Building on skills (level H); I can: • Constructdata displays (including stem-and-leaf plots &dot plots) • Calculate mean, median, mode and range for sets of data. • Mean Sum of all values /number of values • Median Middle value in set, organised in ascending order. • Mode Most represented (frequent) value in a set • Range Maximum value – Minimum value of set • Describe and interpret data and data displays using median, mean and range.

  4. Statistics:Level I Focus of in Level I • Techniques of data collection (including: census, sample and observation) • Random sampling • Randomsamples as a measure of a population • Effects of individual data values , (including outliers, on themean and median)

  5. Statistics:Level I Part 1 Download census @ school sample data ‘6 random samples’ female or male Focus on one question (E.g. bellybutton height); calculate mean, median, mode and range  for each random sample. Display the means, medians, modes and ranges in a table. Respondto questions: 1.Do the means differ (vary) by much? What does this tell us?   2.Describe the variation, and identify the highest and lowestmeans. 3.Look at the data for the highest & lowestmeans. Look for reasons that the mean in each case is either high or low, then explain these reasons.(Clue: It could be related to the median, or maybe an extreme data value called an outlier.) 4.Do you think that a sample of 10 accurately reflects the population? 5.Do you think any of your calculated means and medians might closely match those of the census? Why or why not? Create a blog post which includes: The question your data and calculations refer to. The table of calculated Means, Medians, Mode and Ranges for each sample The responses to the questions in order.

  6. Statistics:Level I Part 2 Continue focusing on the same question. Based on your understanding; increase the sample size at the census at school website: http://www.abs.gov.au/censusatschool Calculate mean, median, mode and range Respond to questions. 1. Create a stem-and leaf plot for your data, use it to help identify outliers, explain how they affect the accuracy of your mean. 2. Do you think the new sample size was big enough to accurately reflect the population? 3. What are the benefits of conducting a larger sample size. 4. What are the considerations (or problems) that need to be addressed as the sample size increases? Open the Census data (2013), Calculate the percentage that your mean, median and mode agree. How would you adjust your sample size to be accurate and efficient? Create a blog post which includes: The question your data and calculations refer to. mean, median, mode and range The Stem-and –leaf plot The responses to the questions in order. Percentage comparison between your sample and the census

  7. Statistics:Level I Part 3 Investigate your question by sampling students in the learning space What sample size will you attempt, justify your answer. What sample size did you end up with? Was your sample strictly random (why)? Do you think it accurately reflects the population of the year-level? Identify sampling biases that might reduce how well your sample represents the student population? Calculate mean, median, mode and range. Create a stem and leaf plot for your data Open the Census data (2013), Calculate the percentage that your mean, median and mode agree  Create a blog post which includes: The question your data and calculations refer to. mean, median, mode and range The Stem-and –leaf plot The responses to the questions in order. Percentage comparison between your sample and the census

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