4/19/13 Have out: Bellwork: total: pencil, red pen, highlighter, GP notebook, textbook, graphing calculator 4/19/13 Have out: Bellwork: Determine the following: end 1) 2) 3) start = 4(1) + 4(2) + 4(3) + 4(4) + 4(5) +1 = 4 + 8 + 12 + 16 + 20 = 60 +2 total:

Bellwork: total: Determine the following: 2) 3) +1 +1 = (1)3 + (2)3 + (3)3 + (4)3 = (3 + 2) + (4 + 2) + (5 + 2) + (6 + 2) = 1 + 8 + 27 + 64 = 5 + 6 + 7 + 8 = 100 = 26 +2 +2 total:

Introduction to Standard Deviation Range measures the spread of a set of data from low to high. For example, yesterday we discussed the range of heights of an 8th grade class from 60 to 71 inches. The spread is from 60 to 71. There are two other measures of spread. Today, we will focus on the first measure: ____________ ____________. standard deviation Standard Deviation measures the spread of the data from the mean. The larger the standard deviation, the more spread out the data is from the mean. Example #1: Suppose you are given the following data set: 4, 6, 9, 6, 5. Sketch a histogram of the data.

Introduction to Histograms Example #1: The heights (in inches) of 20 8th graders are as follows: 63, 65, 69, 61, 62, 63, 65, 67, 69, 64, 65, 66, 66, 67, 64, 69, 68, 62, 60, 71 Rewrite the list in ascending order (or use sort on calculator). 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 66, 66, 67, 67, 68, 69, 69, 69, 71 STAT 1: Edit 2nd LIST  OPS 2: SortA( L1 ) Enter data in L1. ENTER STAT 1: Edit

Range = _____ – _____ = _____ 71 60 11 Max Min 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 66, 66, 67, 67, 68, 69, 69, 69, 71 The ______ of the data is the difference between the highest and lowest data. range Range = _____ – _____ = _____ 71 60 11 Max Min Since all measurements are to the nearest inch, there are _____ + _____ = _____ possible data points. 11 1 12 histogram We are going to make a _________ (bar graph) where we are going to group the data into intervals. To keep each interval the same length, use 4 intervals because 4 is a factor of ____. 12 class size 12 3 Each __________ will be ____ = ___ 4 frequency table Make a ______________ to organize the data.

Class Interval Frequency 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 66, 66, 67, 67, 68, 69, 69, 69, 71 Class Interval Frequency 60 – ____ ____ – ____ ____ – 71 Make each interval 3#s wide  62 Make a tally of the heights within each interval 63 65 66 68 69 Mean = ______ 65.3 Use your calculator to compute the following: Median = ______ 65 Use the frequency table to make a histogram on graph paper. Height (inches) Frequency Make sure that the bars touch!

Class Interval Frequency Height (inches) Frequency 60 – 62 63 – 65 66 – 68 69 – 71 2 4 6 8 Class Interval Frequency 60 – ____ ____ – ____ ____ – 71 62 63 65 66 68 69 Make sure to include a “break.”

Let’s make the same histogram on a graphing calculator Let’s make the same histogram on a graphing calculator. First, however, clear all functions of the menu. Y = 2nd STAT PLOT 1: Plot 1 ENTER ON TYPE Make sure all other plots are turned off. Choose histogram Arrow over, highlight, and hit ENTER

Once you select histogram, make sure the screen shows: X list: L1 Freq: 1 Select ZOOM 9: ZoomStat ENTER Arrow down 6 This makes ____ intervals, but we just want 4 intervals. Therefore, we need to change the window.

Select WINDOW 60 72 3 –1 8 1 Select Select GRAPH TRACE Xmin = ___ Xmax = ___ Xscl = ___ Ymin = ___ Ymax = ___ Yscl = ___ MIN MAX + 1 Class size Most at any interval + 1 Select Select GRAPH TRACE Notice the intervals and frequency

Example #2: A police officer clocked the following speeds (in mph) in a Wal-Mart parking lot. 45 52 46 42 40 51 47 36 34 59 32 56 38 29 15 49 35 41 39 64 24 55 10 25 48 21 Record the data into L1 and sort ascending (see your notes from day 1). Be sure to clear the previous data from L1. To avoid data entry mistakes, make sure that the mean of the above data is about 39.8125. 2nd QUIT 2nd LIST  MATH 3: mean( L1 )

To make one, complete the following steps: 1. Draw a vertical line A ______ - ____ - _____ Plot is a way to organize and analyze statistical data. stem and leaf To make one, complete the following steps: 1. Draw a vertical line 2. On the left side of the line, list all the numbers that are in the 10s place from the set of data. 3. List each number in the ones place on the right side of the line in ascending order. Stem Leaves 1 5 2 1 4 5 9 3 2 2 4 5 5 6 6 8 9 4 1 1 2 5 5 6 7 8 9 5 1 2 2 5 6 9 6 4 By the way, if you turn the stem–and–leaf plot 90 degrees, it looks like a histogram.

Since there are 32 data points, the median is equal to the average between the ____ and ____ points when data is in ascending order. 16th 17th Stem Leaves 1 5 2 4 9 3 6 8 7 Median = 40 + 41 2 = 40.5 On graph paper, make a histogram for the car speed data with 5 intervals of equal length. speed (mph) Frequency

But first, let’s answer the following: Range = ____ – ____ = ____ 64 10 54 Max Min 54 Class size = = ____ 55 = ____ 11 5 Make a frequency table to organize the data. Stem Leaves 1 5 2 4 9 3 6 8 7 Class Interval Frequency 10 – ____ ____ – ____ ____ – 64 20 21 31 32 42 43 53 54

Class Interval Frequency 10 – ____ ____ – ____ ____ – 64 20 21 31 32 42 43 53 54 speed (mph) Frequency 10 – 20 21 – 31 32 – 42 43 – 53 4 8 12 16 2 6 10 14 54 – 64

Assignment #2 DS 29, 30, 50, 53 – 57 c) CST Packet #49 – 56