Quick Talk Think of a situation where you need to organize data? (any kind of data) What can you do after you collected the data and organized it?

Answer You can graph it, calculate the range, midpoint, find a frequency then analyze the data.

Please Draw this frequency table in your notebook, we will be filling it out Lower interval limit Upper interval limit Lower interval boundar y Upper interval boundar y TallyInterval midpoi nt

Frequency Table A frequency table partitions data into intervals and shows how many data values are in each interval. The intervals are constructed so that each data value falls into exactly one interval. Note: intervals are known as classes. The book uses the word “classes”, but I use “intervals” because it makes more sense.

How do you create a frequency table? Consider this situation: You are collecting how many minutes each student study for a particular class. You interviewed 50 students and here is the chart

How do you create a frequency table? 1) Determine how many intervals you want. between 5-15 is usually preferred Anything less than 5, you risk losing information Anything more than 15, data might not be sufficiently analyzed Let’s use 6 intervals for this case. (remember you can any number between 5 and 15) With this, you can find the width of each interval.

Finding the width of the interval

The lower interval limit is the lowest data value that can fit in an interval. The upper interval limit is the highest data value that can fit in an interval. The interval width is the difference between the lower class limit of one interval and the lower class limit of the next interval. In our case, our lowest number is 1, so 1+8=9, therefore, 9 would be the start of the next interval (remember we will have 6 intervals total)

Activity Find the starting number of each interval

Answer Start of 1 st interval=1 Start of 2 nd interval=9 Start of 3 rd interval=17 Start of 4 th interval=25 Start of 5 th interval=33 Start of 6 th interval=41 Start of 7 th interval=49

Therefore, the interval limit Lower interval limit Upper interval limit

Now tally all the numbers that fall in each interval

Activity Now tally up all the numbers that fall in each interval. Find the frequency also

Answer Lower interval limit Upper interval limit Tally

Midpoint (within the interval)

Activity Find the midpoint of each interval

Answer Lower interval limitUpper interval limitInterval midpoint

Finding interval boundary Upper interval boundaries, add 0.5 to the upper interval limit. Lower interval boundaries, subtract 0.5 from the lower interval limits.

Activity Find the interval boundaries for all interval.

Answer Lower interval limit Upper interval limit Lower interval boundary Upper interval boundary

Relative Frequency

Activity Find the relative frequency of each interval

1313/50= /50= /50= /50=0.1 33/50= /50=0.08

Review How to create frequency table. 1) Determine how many intervals you want 2) Find interval width 3) Determine the lower/upper interval limit for each interval 4) Determine the lower/upper interval boundaries for each interval 5) Do the tally and find the frequency (they are the same number) 6) Find the midpoint 7) Find the relative frequency

Group activity: Now try to do this by yourself or with a partner. This is a data represent glucose blood level after 12 hour fast for a random sample of 70 women. Use 6 intervals (classes)

Answer Lower interval limit Upper interval limit Lower interval boundar y Upper interval boundar y TallyInterval midpoi nt

Homework practice Pg #1-4 all, 5-10 (only do frequency table) (Will start in class if time permits)

Before we talk about how to graph a histogram, let’s talk about different shapes of a distribution

Different distribution shapes

Distribution definitions Mound-shaped symmetrical: the term refers to a histogram in which both sides are the same when the graph is folded vertically down the middle. (Normal curve) Uniform or rectangular: These terms refer to a histogram in which every interval has equal frequency. From one point of view, a uniform distribution is symmetrical with added property that the bars are of the same height Skewed left or skewed right: These terms refer to a histogram in which one tail is stretch out longer than the other. Bimodal: This term refers to a histogram in which the two classes with the largest frequencies are separated by at least one interval. The top two frequencies may have slightly different values.

Graphing a histogram You use the frequency table to graph a histogram (use the example we did together in class about study minutes with 50 students) You use lower/upper interval boundaries for the x axis because you don’t want any gaps. Let’s graph both frequency histogram and relative- frequency histogram

This is how a frequency histogram looks like

This is how relative frequency histogram looks like

Activity Compare the two graphs. What do you guys notice? What can you say about the distribution of data?

Quick talk If we were to construct a normal distribution curve or mound-shaped symmetrical histogram for IQ, Newton and Einstein would be considered an “outlier”. What do you guys think outlier mean?

What is outlier? Outliers are data values that are very different from other measurements in the data set. Two types: or

Cumulative Frequency Cumulative Frequency for an interval is the sum of the frequencies for that interval and all the previous intervals. Example: Let’s take a look at the class example again.

Lower interv al limit Upper interv al limit Lower interval boundar y Upper interval boundar y Tall y Interval midpoi nt Cumulati ve frequency

Ogive Graph Ogive is a graph that displays cumulative frequencies

Ogive graph of the example

So then what does this graph tell us? Example: I can say that 31 students had studied no more than 16 minutes, because it is cumulative.

Activity Find the cumulative frequency and do an ogive graph Lower interval limit Upper interval limit Lower interval boundar y Upper interval boundar y TallyInterval midpoi nt

Answer Lower interval limit Upper interval limit Lower interval boundary Upper interval boundary TallyCumulativ e frequency

Ogive graph

Quick Talk What can you conclude about 88 minute?

Homework Practice Pg #6-10 (do cumulative frequency and draw ogive graph) (Will start in class if time permits)

Are there other types of graphs? Yes! There are bar graphs, circle graphs, and Time- Series Graphs

Bar Graph Bars can be vertical or horizontal. Bars are of uniform width and uniformly spaced. The lengths of the bars represent values of the variable being displayed, the frequency of occurrence, or the percentage of occurrence. The same measurement scale is used for the length of each bar. The graph is well annotated with title, lables of each bar, and vertical scale or actual value for the length of each bar.

Examples of bar graphs

Note: Look at the number where y-axis started. You might see the graph with squiggle on the changed axis. Sometimes, if a single bar is unusually long, the bar length is compressed with a squiggle in the bar itself. (look at pg 51 example 2-11b with the graph)

Another example of bar graph

Activity Use the info below to create a bar graph. Average annual income (in thousands) of a household headed by a person with the stated education level is as follows: 16.1 for highschool, 34.1 for highschool graduates, 48.6 for associated degrees, 62.1 for bachelor’s degrees, 71.0 for master’s degrees and 84.1 for doctoral degrees What can you conclude?

Pareto Chart Pareto chart is a bar graph in which the bar height represents frequency of an event. In addition, the bars are arranged from left to right according to decreasing height.

Example of Pareto chart Consider this situation: Causes for lack of sleep(two month study 61 days) CauseFrequency Playing x-box or ps314 Texting9 Watching movie/TV5 Talking on the phone10 Doing homework/project20 Other3

Pareto Chart

Activity Use the info below to create a pareto chart. Here are a list of the most common stolen items per cases: 10.1 electronics; 15.6 jewelries; 7.3 cars; 20.4 cash; 26.7 identity What can you conclude?

Circle graph or Pie chart Circle graph or pie chart, wedges of a circle visually display proportional parts of the total population that share a common characteristic.

Example of Circle graph or pie chart Consider the situation: Monthly Financial Budget (based on $4000 monthly) CategoriesAmount spentFractionPercentag e Degree of the pie Food800800/ *360°=72° Investment500500/ *360°=45° Bills/debt / *360°=157.5° Rent950950/ *360°=85.5°

Circle Graph or Pie Chart

Quick Talk Is the chart consistent with our data?

Activity Create a circle graph with the following info: Gamestop took a survey on the first 500 customers to see what genre of games they bought. 70 Fighting, 123 shooter, 150 action-adventure,53 role-playing, 12 strategy, 92 others. What can you conclude?

Time-Series Graph Time-series graph, data are plotted in order of occurrence at regular intervals over a period of time

Example of Time-series graph Consider this situation: Points Scored in a game (49er 2012) Week Points Week Points

Time Series Graph

What can you conclude about the graph? Is there a pattern? Is there anything you can conclude?

Activity Create a time-series graph from the following data What can you conclude? Week Distance Week Distance

Determine Which Type of Graph to Use Bar graphs are useful for quantitative or qualitative data. Pareto Charts identify the frequency of events or categories in decreasing order of frequency of occurrence. Circle graph display how a total is dispersed into several categories. Time-series graph display how data change over time. Note: Make sure you provide title, label axes and identify units of measure in all type of graphs!!

Technology You can create bar graphs, pareto charts, circle graphs, time-series graph in powerpoint or words. You first open up the powerpoint or words. On the top, you press insert, and click on charts. Choose the chart you want and input data. TI-83/TI-84. You can create time-series. Place consecutive values 1 through the number of time segments in list L1 and corresponding data in L2. Press Stat Plot and highlight an xy line plot (will try in class)

Homework Practice Pg #1-12 (Will start in class if time permits)

Stem-and-leaf display Stem-and-leaf is a method of exploratory data analysis that is used to rank-order and arrange data into groups.

Why do we use stem-and-leaf instead of histogram? Similarity: Both display frequency distributions Difference: In histogram, we lose most of the specific data values (because of intervals). Stem-and-leaf display is a device that organizes and groups data but allow us to recover the original data if desired.

Stem-and-leaf example Write out all the numbers

Activity Put this chart into a stem-and-leaf display

Homework Practice Pg #1-9 even

Group Project (2 in a group) Situation: You are to conduct a short survey or poll (school appropriate and you have to interview at least 50 students), and represent your survey in a graph that we have learned. You are then to type a short 1 page report on the following: What is the variable? What method did you conduct your survey? What are the advantages and disadvantages of your method collection? Are there potential bias? How did you try to create randomness? What is your sample size (how many people total)? What kind of sampling did you use? Explain and label your graph What conclusion can you make about your result? Can you use your result and apply to the entire population? Why or why not? Sample survey/polling topics: movies, music, war, politics, clothing, pets, celebrities