PROBABILITY & STATISTICS Day 4

CHECK FOR UNDERSTANDING STOP AND JOT Population Sample Individual Variable – Quantitative Variable – Categorical Variable

CHECK FOR UNDERSTANDING WHAT TYPE OF GRAPH WOULD YOU USE? – 1.) To display the number of Herron students who prefer Math, Science, and English. – 2.) To display the percentage of teachers who drive cars, vans, and trucks. – 3.) To display the weight (in pounds) of the dogs at the Indianapolis Humane Society. – 4.) To display the daily temperature from January to August in Indianapolis.

BRAIN WARM UP Answer the questions on your Guided Notes about Dot Plot #1 – What is the SPREAD? – What is the CENTER? – What is the SHAPE? – Are there any OUTLIERS? – What is the INDIVIDUAL? – What is the VARIABLE(S)? – Why was this study conducted?

REVIEW: STEM PLOTS REVIEW: How would we make a stem plot of the following data: DayNumber of Hours of Sleep Monday4.0 Tuesday6.8 Wednesday6.2 Thursday7.5 Friday12.0 Saturday10.2 Sunday10.0

DISPLAYING QUANTITATIVE DATA Histograms Histograms display data by grouping values together. WHAT ARE THE GROUPINGS? WHAT IS THE SHAPE? WHAT IS THE SPREAD?

SYMMETRY IN HISTOGRAMS SYMMETRIC: If right and left sides are approximately mirror images of each other. SKEWED TO THE RIGHT: If the right side of the histogram extends must further than the left. SKEWED TO THE LEFT: If the left side of the histograms extends much further than the right.

SYMMETRY IN HISTOGRAMS

HOW TO CREATE A HISTOGRAM ON YOUR GUIDED NOTES 1). Identify the spread of the data & decide on class intervals 2). Create a frequency table 3). Label and scale your axes and title your graph. 4). Draw in bars to represent the count for each group or category.

YOU TRY… CREATING A HISTOGRAM ON YOUR GUIDED NOTES

ANALYZE IT! USING THE HISTOGRAM YOU JUST CREATED: – SHAPE: – CENTER: – SPREAD: – OUTLIERS: – INDIVIDUAL: – VARIABLES: Extension: COULD WE HAVE USED ANOTHER TYPE OF GRAPH TO DISPLAY THIS DATA SET?

ANALYZE IT! USING THE HISTOGRAM YOU JUST CREATED: – SHAPE: The histogram does not have a particular shape. – CENTER: 302 – SPREAD: – OUTLIERS: none – INDIVIDUAL: Specific Car – VARIABLES: Mileage per tank of gas (in miles) Extension: COULD WE HAVE USED ANOTHER TYPE OF GRAPH TO DISPLAY THIS DATA SET?

LIMITATIONS OF HISTOGRAMS Histograms do not show us the relative position of an individual within a distribution. THINK ABOUT STANDARDIZED TEST SCORES… – If you are in the 80 th percentile, WHAT DOES THIS MEAN?

CUMULATIVE FREQUENCY GRAPHS A histogram shows us the distribution of variables. A relative frequency graph shows us relative frequencies, or percentages. BRAINSTORM: (STOP & JOT!) – Complete the analogy: BAR GRAPHS are to PIE CHARTS as… _________________ are to ________________.

HISTOGRAM (FREQUENCY) INTERVALFREQUENCY 0-20% % % % %11

CUMULATIVE FREQUENCY GRAPH INTERVAL FREQUENCY CUMULATIVE FREQUENCY 0-20% % % % %1126

RELATIVE FREQUENCY GRAPH INTERVALFREQUENCYRELATIVE FREQUENCY 0-20%4 15% 21-40%14% 41-60%28% 61-80%831% %1142%

RELATIVE CUMULATIVE FREQUENCY GRAPHS STEPS: – 1.) Identify the spread of the data & decide on class intervals. – 2.) Make a frequency table with columns for: frequency, relative frequency, cumulative frequency, and relative cumulative frequency. – 3.) Label & scale axis and title graph. – 4.) Plot a point corresponding to the relative cumulative frequency in each class interval at the left endpoint of the next class interval.

YOU TRY…ON YOUR GUIDED NOTES