Homework: Frequency & Histogram worksheet

1. It is the middle number of the interval with the highest frequency 26 Between 66 & 118 1. It is the middle number of the interval with the highest frequency

Two Main Uses of Statistics TO DESCRIBE (Data Analysis) TO PREDICT (Statistical Inference)

Definitions Data: A collection of information in context. Population: A set of individuals that we wish to describe and/or make predictions about. Individual: Member of a population. Variable: Characteristic recorded about each individual in a data set.

Types of Variables Categorical Variable: A variable that records qualities or characteristics of an individual, such as gender or eye color. Quantitative Variable: A variable that measures a characteristic of an individual, such as height, weight, or age. In this unit, we will focus on quantitative data.

What type is it? Categorical Quantitative Go over the Collect student data worksheet and discuss which type of variable each one is.

Categorical or Quantitative Data? Birth month Number of siblings Height in inches Average amount of time (in minutes) of your ride to school. Number of pets Model of the car you drive Age of your youngest parent Predicted letter grade of your next Math 1 test.

Describing Data Two ways to describe data: Graphically Numerically

Describing Data Graphically Dotplot Histogram Boxplot

Describing Data Numerically Measures of Center – mean, median Measures of Spread – range, interquartile range, standard deviation

Describing Data Graphically A line plot uses a number line and x’s or other symbols to show frequencies of values. *Also known as a dot plot

Additional Example 2: Making a Line Plot Students collected tennis balls for a project. The number of balls collected by the students is recorded in the table. Make a line plot of the data. Tennis Balls Collected 10 14 11 16 15 Step 1: Draw a number line. x x x x x x x x x x x Step 2: For each tennis ball, use an x on the number line to represent how many were collected. x 5 6 7 8 9 10 11 12 13 14 15 16

Check It Out: Example 2 Students collected aluminum cans for a project. The number of cans collected by the students is recorded in the table. Make a line plot of the data. Cans Collected 5 7 11 14 15 Step 1: Draw a number line. X X x x x x x x x x x Step 2: For each aluminum can, use an x on the number line to represent how many were collected. x 5 6 7 8 9 10 11 12 13 14 15 16

Make a dot plot of the number of siblings that members of your class have

Describing Data Graphically A frequency table tells the number of times an event, category, or group occurs.

Pages Read per Student Last Weekend Additional Example 3: Making a Frequency Table with Intervals Use the data in the table to make a frequency table with intervals. Pages Read per Student Last Weekend 12 15 40 19 7 5 22 34 37 18

Pages Read per Student Last Weekend Additional Example 3 Continued Use the data in the table to make a frequency table with intervals Pages Read per Student Last Weekend Number 1–10 11–20 21–30 31–40 Frequency 2 4 1 3 Step 1: Choose equal intervals. Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row. This table shows that 2 students read between 1 and 10 pages, 4 students read between 11 and 20 pages, 1 person read between 21 and 30 pages, and 3 people read between 31 and 40 pages last weekend.

Number of Miles Driven per Person on Saturday Check It Out: Example 3 Use the data in the table to make a frequency table with intervals. Number of Miles Driven per Person on Saturday 17 29 9 19 7 5 27 34 21 38

Number of Miles Driven per Person on Saturday Check It Out: Example 3 Continued Use the data in the table to make a frequency table with intervals. Number of Miles Driven per Person on Saturday Number 1–10 11–20 21–30 31–40 Frequency 3 2 3 2 Step 1: Choose equal intervals. Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” row. This table shows that 3 people drove between 1 and 10 miles, 2 people drove between 11 and 20 miles, 3 people drove between 21 and 30 miles, and 2 people drove between 31 and 40 miles on Saturday.

Describing Data Graphically A histogram is a bar graph that shows the number of data items that occur within each interval.

What’s the difference? Bar Graph Histogram

Additional Example 4: Making a Histogram Use the frequency table in Additional Example 3 to make a histogram. Step 1: Choose an appropriate scale and interval. Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap. Step 3: Title the graph and label the axes.

Number of Pages Read per Student Last Weekend Check It Out: Example 4 Use the frequency table in Check It Out: Example 3 to make a histogram. Step 1: Choose an appropriate scale and interval. Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap. Number of Pages Read per Student Last Weekend Number of Pages Students Step 3: Title the graph and label the axes.

Describing Distributions Shape Center Spread Outliers In order to describe a distribution, we address the following things: the shape of the distribution, the center or most typical value, how spread out the data is, and if there are outliers, we note them.

Shape Mound shaped & symmetrical Skewed left (extreme low values) Skewed right (extreme high values) Uniform Go over 4 types of shapes. What shape does our links distribution have?

Center When describing a distribution at first, the center can be “eyeballed.” Remember, you are trying to answer the question: “What is the most typical value?” When first discussing how to interpret graphs, have students give an eyeball estimate of the center of the distribution. Then formalize with the numerical calculations later on in the unit. What is the approximate center, or typical value, for the number of links put together in one minute?

Spread BE SURE TO STATE EVERYTHING IN CONTEXT!! Range Remember, you are trying to answer the question: “How much do values typically vary from the center?” BE SURE TO STATE EVERYTHING IN CONTEXT!! Again, when first describing distributions, we do not need to go into the numerical calculations of the interquartile range or the standard deviation – just focus on the max and min values and use the range to describe the distribution of the data. What was our max number of links? Our min number? So what is the range? Do we have any apparent outliers? (What is an outlier? An informal definition is fine – a data value that does not fit the overall pattern.) Have students write a one to two sentence summary describing the shape, center, spread, and outliers – in context! For example: The distribution of the number of links a student can put together in one minute is skewed to the right. Students can typically hook up about 35 links in one minute, with a few really dexterous students able to link together 60 or more. The number of links put together varied from 16 to 68.

NFL Rushing Statistics Group activity: Make a frequency distribution table for your assigned column of data. Draw the corresponding histogram on graph paper. Write a paragraph about your data that addresses shape, center, spread, and outliers. Guided practice: Divide students into groups and assign each group a column from the 2011 NFL Rushing Statistics for Top 50 Rushers: Rushing Attempts, Total Yards for the Season, Average Yards per Attempt, Average Yards per Game, Number of Rushing Touchdowns, Longest Run of the Season (if you have more than 6 groups, have 2 groups use the same category). Have each group present their graph and description to the class. If time is limited, ask students to work on the same column of data.

Age (in months) of First Steps Create a frequency distribution table & histogram for the following set of data: Age (in months) of First Steps 13 9 12 11 10 8.5 14 12.5 13.5 9.5 6 7.5 15 8 11.5 10.5