Unit 5 Stats

Section 1 – Key Statistical Concepts (representing data)

A collection of individuals (data) about which we want to draw conclusions The students at West Ottawa The collection of information from the WHOLE POPULATION Polling ALL students at West Ottawa Random Biased Selecting in the IB program A subset of the population. Selecting students as they walk in the door Polling the students we have selected from walking in the door A subset of the population.

Information about the population that can be represented by numbers More on these to come! Information about the population that can be represented by categories The quantities we are polling about More on these to come! How the population is “spread” Data values that are much larger (or smaller) than the general body of data

Example 1:   The Student Senate is counting the number of students wearing black and white for Spirit Week. There are 2200 total students enrolled at West Ottawa High School. The Student Senate President counts the number of students wearing black and white in a randomly selected classroom containing 30 students. Population?________________ Sample? _____________ Variable? ___________________ Wearing black and white Selected class Students of WO

Example 2 Determine whether each situation would produce a random sample. Write yes or no and explain your answer. surveying of students at the Galaxy Dance of whether or not they like to dance b. polling every 5th person who walks into the mall about what is their favorite color no yes

Frequency Histograms Column Graph vs Histogram

Studying the number of students who attended Homeless for a night Example 3: Determine whether each situation would produce a discrete or continuous set:   Studying the number of students who attended Homeless for a night b. Studying the length of a strand of mutated bacterial discrete continuous

Center: discussions of the middle of data Spread: How spread out (distributed) is data most frequently occurring value Advantage: can be used for non-numeric data Disadvantage: can take more than one value Average! Advantage: Takes into account all of the data Disadvantage: Can be skewed by outliers Middle number Advantage: Is not skewed by outliers Disadvantage: Does not take into account all the data

Example 4

Example 5

Example 6 Mean: 3.25 Median: 3 (28th data value : half of the 55) Mode: 3

Example 7

4.2: Representing Data

5 number summary 5-number summary   Min: _____ Q1: ______ Median: _______ Q3: _______ Max: ________ IQR (interquartile range): _______________ Middle Median of first grouping Median of second grouping Q3 – Q1

Min: _____ Q1: ______ Median: _______ Q3: _______ Max: ________    Min: _____ Q1: ______ Median: _______ Q3: _______ Max: ________   IQR (interquartile range): _______________

answer Box and Whiskers

14.D/E Cumulative Frequency Tables

add to notes Mean:

Mean from a Freq Table Median: 32+16+2 = 50 freq therefore the median is the av of 25th and 26th items Med: 0 Med: 0 Mean: .4 (0 passengers)

add to notes Cumulative Frequency graphs measure data up to a certain value.

Percentiles What percent of the data is BELOW you! 90% means 90% of population is below you. Is it possible to be in the 100th percentile?

Merits: The Median is the only measure that will locate the true center The Mean is only an accurate measure if the data is distributed evenly