Chapter 1: Exploring Data Get out p. 6 & 20 HW Get out notes & 1.2 Slides Get both a TI & HP calculator Chapter 1: Exploring Data Sec. 1.2: Displaying Quantitative Data with Graphs, cont.

Histograms Histogram - a graph of the distribution of one quantitative variable where nearby values are grouped together. How to make a histogram: Divide the range of data into classes of equal width. Find the count (frequency) or percent (relative frequency) of individuals in each class. Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals.

Example, p. 33 - 34 This table presents data on the percent of residents from each state who were born outside of the U.S. Start by deciding on a width for each class: Identify the smallest and largest values. Think of a range that contains both. 0 - 30 Pick a number that divides the range evenly. 5 They chose 0 to 30 and 5 in the book.

Example, p. 33 - 34 This table presents data on the percent of residents from each state who were born outside of the U.S. Next, make a frequency table: Frequency Table Class Count Total 0 to < 5 20 5 to < 10 13 10 to < 15 9 0 to < 5 contains numbers up to 5, but not 5. 5 is in the next class. Notice all of the classes are of equal width. 15 to < 20 5 20 to < 25 2 25 to < 30 1 50

Example, p. 33 - 34 Next, make a histogram: Frequency Table Class Count Total 20 18 16 14 12 10 8 6 4 2 0 to < 5 5 to < 10 10 to < 15 15 to < 20 20 to < 25 25 to < 30 20 13 9 5 2 1 50 Number of States 0 5 10 15 20 25 30 Percent of foreign-born residents

Count vs. Percent

Describing Histograms Shape – skewed right and unimodal. Outliers – No obvious observations outside the overall pattern. Center – Would fall somewhere between 5 to 9.9%. Spread – Varies from less than 5% to over 25%. (Could also go back to original data: 1.2% to 27.2%) Example on p. 35 ***Same example as before, but they’ve changed the class width to be 2.5.***

Using Histograms Wisely Cautions! Don’t confuse histograms and bar graphs. Don’t use counts (in a frequency table) or percents (in a relative frequency table) as data. Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations. Just because a graph looks nice, it’s not necessarily a meaningful display of data.

Histograms on the TI-calculator Push STAT. Push ENTER.

Histograms on the TI-calculator 9 6 7 8 4 3 5 6.5 11 10 4.5 Enter data. (All in the L1 column.) After you have entered one observation, press ENTER to go to the next line. Push 2nd and QUIT (MODE). Press 2nd STAT PLOT (Y=).

Histograms on the TI-calculator Push ENTER. Make sure Plot 1 is On – Highlight On and press ENTER. Select the Histogram under Type. Make sure your Xlist matches the list you entered your data. Push GRAPH. For a better picture, press ZOOM 9:ZoomStat.

Histograms on the TI-calculator If you want to change the class width: Press WINDOW and change settings. Push TRACE. This allows you to see what the range is for each class and the number that fall in that class.

Histograms on the HP Prime 9 6 7 8 4 3 5 6.5 11 10 4.5 Push Apps. Highlight or press Statistics 1 Var Enter data.

Histograms on the HP Prime Push Plot. To Zoom in, Press Menu Press Zoom Select 3 In

Histograms on the HP Prime To change window, push 2nd, Plot. Push Plot.

Histograms on the HP Prime If you want to Trace, press Menu and check to see that there is a dot beside Trace. Press Menu again.

Data Analysis: Making Sense of Data MAKE and INTERPRET dotplots and stemplots of quantitative data DESCRIBE the overall pattern of a distribution IDENTIFY the shape of a distribution MAKE and INTERPRET histograms of quantitative data COMPARE distributions of quantitative data

Homework – Due Monday P. 44 – 45 #52 & 57