 essential activity presenting data overview this activity will produce the information students need to determine whether their hypothesis was supported or not students will calculate basic descriptive statistics and then will analyze the data using two basic principles whether two things are related correlation or whether groups of things are different which technique is used depends in part on the data the primary goal is for students to produce meaningful graphs depicting results and to interpret the results to judge whether the hypothesis was supported or not  materials data spreadsheet or table produced in activity a either of the following graph paper calculators or computers with spreadsheet software eg ms excel  activity procedure   getting ready this activity will use the data spreadsheet or table produced in activity a if using a spreadsheet program students will need access to computers and that program if using hard copy data sheets students will need calculators graphs can be created manually by plotting on paper graph paper is especially handy or on the board some students might have access to and facility with graphing programs on computers which can also be used this activity describes manual graphing of the data computer graphing will need to be explored and tested by the teacher as each school s computer and software combination is unique completing the manual graphing process will encourage a better understanding of why the results and datapoints show up where they do on a graph instead of magically appearing via the software depending on the research question and class dynamics this can be a small group activity or the class can work as a whole this activity requires teacher explanation of basic statistical operations like calculating a mean and an explanation of relationships and differences among groups doing the activity first students will calculate and record basic descriptive statistics about their data begin with a brief description of what the following variables are and then ask students to calculate these statistics for mercury in their data set example dataset 1 3 4 8 12  mean  the average of all the data values for a given variable add all the data values together sum then divide by n the number of data values there are if the data were 134812 then n is 5 there are 5 numbers the sum is 28 and the mean would be 56 median  the median is the value halfway through the ordered data set below and above which there lies an equal number of data values in our example the median would be 4 the middle value minimum  the smallest value the minimum would be 1 maximum  the largest value the maximum would be 12 range  a measure of the spread or the dispersion of the observations it is the difference between the largest and the smallest observed value of some quantitative characteristic and is very easy to calculate if the data were 134812 then the range would be 121 11 standard deviation  for more advanced analysis classes this is another measure of the spread of the data set it tells you how tightly all the various data points are clustered around the mean in a set of data the formula is more complex and can be found in any statistics text the standard deviation of the number set above 439  next students will work on techniques that allow them to find patterns and relationships in the data two key techniques will be used are two things related  you must have two columns of data that are numbers or continuous variables also called a ratio scale  say students think that bigger fish will have more mercury one way to evaluate whether that is the case or not is to graph fish size and mercury on paper or on the computer  a set up a graph with an x horizontal and y vertical axis typically we put the response or dependent variable on the y axis and the predictor or independent variable on the x axis ask students to identify which is the independent and which is the dependent variable in our example fish size is independent and mercury content is dependent we re asking if mercury content depends on fish size don t forget to label the axes with what they represent and the units of measure the graph should look something like this  b now plot the data points the graph that results will be called a scatterplot or an xy plot for each fish size value trace up to the corresponding mercury value the graph might look something like this although where the points are will be different based on your data  c to assess whether the two things are related students need to understand a bit more about what the relationship might look like there are three main types of relationship    i    positive as size increases so does mercury    ii  negative as size decreases mercury increases      iii  no relationship there s no clear pattern between size and mercury  d if time and the class dynamic permits you might ask students to find the best fit line for the data if using software such as microsoft excel the software can display an equation and an r 2 value on the chart if plotting by hand students can use a piece of string and manipulate the two ends so the string appears to cross the center of the data points it is recommended that you practice this manual technique before completing the exercise on data analysis software  e here is an example of a scatterplot with a best fit line  are groups of things different  you will need numeric data for one variable and a categorical variable named groups for the other for example students might be looking to find whether different fish species had different mercury concentrations their hypothesis might be that perch have more mercury than bass  a set up a graph with an x horizontal and y vertical axis or use the boxplot or dot density graph introduced in the warmup activities above typically we put the response or dependent variable on the y axis and the predictor or independent variable on the x axis ask students to identify which is the independent and which is the dependent variable in our example fish species is independent and mercury content is dependent we re asking if mercury content depends on fish species don t forget to label the axes with what they represent and the units of measure the graph should look something like this  b calculate the mean for each group in our example the mean mercury in perch was 307 ng g the mean mercury in bass was 719 ng g c start by plotting the mean for each group as a dot on the graph  d we need to get an idea of how variable the data are for each species plot the minimum and maximum above and below the mean and fill in with the other values like this  e if time and lesson plans permit students can plot standard deviation rather than the range as a more appropriate measure of variability  now that you have some statistics about the data and a graph showing the patterns or differences it s time to interpret what the results mean think of the graph and data as evidence and the scientists students now need to judge whether the hypothesis was supported or not in the graph above showing perch versus bass mercury the means are different and there s not much overlap in the data so the scientists would conclude that bass had more mercury than perch in their study and that fish species does matter if the hypothesis was that perch would have more mercury it would not be supported by the data note that scientists avoid the terms right and wrong and do not say that we prove a hypothesis try to encourage students to adopt the language of supporting a hypothesis or not  enrichment question set why would a scientist avoid the terms right and wrong and rather use support a hypothesis what kinds of things are useful to label on graphs what kind of traits does a line of best fit have  documents these documents can be viewed by clicking the links below individual pdfs of each document can be downloaded from the attachments at the bottom of this web page handouts student worksheet  mercury in watersheds  