Common Core Math I Unit 2 Day 2 Frequency Tables and Histograms

Warm up Solve the following equation: 5(3h + 2) = -9h – 34 Vocabulary A group of teens were asked how many APPs they downloaded to their cell phones last month. The results are shown in the table below. Warm up a. How many teens were surveyed? b. How many total APPs were downloaded by this group of teens? c. Give one number that you think best represents the typical number of APPs that a teen downloads in one month. Justify your answer. Number of APPs Downloaded Frequency 0-2 13 3-5 7 6-8 4 9-11 1 12-14 Solve the following equation: 5(3h + 2) = -9h – 34 Vocabulary Draw a radical, label the radicand and the index.

HW answers: 1. Determine whether the following data is categorical (C) or quantitative (Q) a. The candidate a survey respondent will support in an upcoming election. C b. The length of time of people’s drive to work. Q c. The number of televisions in a household. Q d. The distance kickers for a football team can kick a football. Q e. The number of pages copied in the copy room each day. Q f. The kind of tree in each person’s front yard in a neighborhood. C g. The type of blood a person has. C h. The jersey numbers of the football team. C i. The heights of the tallest buildings in the world. Q  j. The language spoken by 2000 people coming in to JFK Airport. C  

HW cont’d 2. A math student is interested in figuring out the average price of vehicles at Glentown High School. She takes a sample of 50 cars in the school’s parking lot and finds the average value to be $13, 400.  a. What is the population? all cars in Glentown High School’s parking lot b. What are the individuals? one car c. What data is being collected? (Include units if applicable) the value of each car in dollars d. What type of data is it (categorical or quantitative)? How do you know? quantitative – the data is numerical and its mean has meaning in relation to the data

Bar Graph vs. Histogram Histogram: Bar graph: Bars touching Use for quantitative data (divided into intervals) Bars not touching Used for categorical data (most of the time)

Link Up With your partner: -1 person is time keeper -1 person links paperclips Goal: -How many can you link in 1 minute? When finished: -Count paper clips, record on your paper -Switch How many links can you put together in one minute? Show how to make a histogram from this by hand. Make sure that you are not just making a bar graph. The bars should be touching (like the next slide) to show the continuity of the data. Usually the lower value for each interval is marked on the x-axis on the left side of the corresponding “bar”, although you can also use the midpoint of the interval as well. Discuss with students – what is the difference between a bar graph and a histogram? (bars touching; bar graphs used with categorical data & histograms used with quantitative data divided into intervals)

Frequency Distribution Table: # of paper clips linked Tally marks frequency 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 Useful to make Histogram (by hand) Fill out according to our data Create histogram Intervals must be the same Collect data in a dot plot on the board and have students record on the board in a frequency distribution table. Show how to make a histogram from this by hand. Make sure that you are not just making a bar graph. The bars should be touching (like the next slide) to show the continuity of the data. Discuss with students – what is the difference between a bar graph and a histogram? (bars touching; bar graphs used with categorical data & histograms used with quantitative data divided into intervals)

Histogram

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 Skewed right 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 (use paper clip data) Range: The difference between the lowest and highest values (describes the distribution) Max number: Min number: Range: Outliers: a data value that does not fit the overall pattern Do we have any outliers in our paper clip data set? If so, what are they? 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.

Write summary describing with the following in your sentences: Steps: Start with distribution: The distribution of the number of paper clips put together was skewed right. Mention the center: Most students can put together ___ paper clips. The Spread: The number of links a student can put together varied from ___ to ___ so the spread is ___. The outliers: The outliers were ___. OR There were no outliers.

NFL Rushing Statistics Group activity: Make a frequency distribution table for your assigned column of data. (must have at least 4 intervals) 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.