Definitions Data: A collection of information in context. DAY 1 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.

Be sure to label the graph and use proper scales. Types of Data Categorical – places individuals into groups (sometimes referred to as qualitative) Example: gender, eye color, zip code, dominant hand Quantitative – consists of numerical values (it makes sense to find an average) Example: height, weight, income, vertical leap Graphs for Categorical data are Bar graphs and Pie charts Be sure to label the graph and use proper scales.

Example 1: Reading and Interpreting Bar Graphs Use the graph to answer each question. A. Which casserole was ordered the most? B. About how many total orders were placed? C. About how many more tuna noodle casseroles were ordered than king ranch casseroles? D. About what percent of the total orders were for baked ziti?

Use the graph to answer each question. Check It Out! Example 1 Use the graph to answer each question. a. Which ingredient contains the least amount of fat? b. Which ingredients contain at least 8 grams of fat?

Example 2: Reading and Interpreting Double Bar Graphs A double-bar graph __________________________________________ ____________________________________________________________________________________________ Example 2: Reading and Interpreting Double Bar Graphs Use the graph to answer each question. A. Which feature received the same satisfaction rating for each SUV? B. Which SUV received a better rating for mileage?

Check It Out! Example 2 Use the graph to determine which years had the same average basketball attendance. What was the average attendance for those years?

Tips for Making a Bar Graph

Making a Bar Graph Here are the distributions for car colors in North America in 2008. Color Percent of Vehicle White 20 Black 17 Silver 17 Blue 13 Gray 12 Red 11 Beige/Brown 5 Green 3 Yellow/Gold 2 a.) What percent of vehicles had colors others than those listed? b.) Display the data in a bar graph. c.) Would it be appropriate to make a pie chart? If not explain why. If it is appropriate for this data then create one.

Tips for Making the Pie (or Circle) Graph You must convert the __________________by multiply the percent value by_______. Draw a radius somewhere on the circle and start there and work your way around the circle counter-clockwise until you get back to the radius you started with.

Color Percent of Vehicle White 20 Black 17 Silver 17 Blue 13 Gray 12 Red 11 Beige/Brown 5 Green 3 Yellow/Gold 2

Measuring Centers Mean (“average”) – Median – Mode – X = X1 + X2 + X3 + … + Xn n Sum of observations Number of observations = Median – 1.) Place data in numerical order 2.) If there are an odd number of observations, the median is the center observation in the ordered list. 3.) If there are an even number of observations, the median is the average of the two center observations in the ordered list. Mode – It helps if you put the data into numerical order. (STAT, edit, enter numbers, STAT, sortA(, enter, 2nd (1 or 2), enter. Go back to list and the numbers will be in order.

If the Mean, Median and Mode for the following observations 78, 98, 48, 63, 84, 100, 95, 86, 91 ,87, 48, 94, 94, 89 ,95, 95, 97, 41 ,65, 85 Mean = 78+98+48+63+84+100+95+86+91+89+48+94+94+87+95+95+97+41+65+85 20 = 81.65 Median: 41, 48, 48, 63, 65, 78, 84, 85, 86, 87, 89, 91, 94, 94, 95, 95, 95, 97, 98, 100 median is 87+89 = 88 2 Mode is 95

Use the data set below to complete each table Measure of Center Brief Definition Value Mean Median Mode

1. The weights in pounds of six members of a basketball team are 161, 156, 150, 156, 150, and 163. Determine the mean, median, mode and range of the data set.

End of Day 1

Graphs for Quantitative Data Dotplots – Box and Whisker –

Dotplots A dotplot is a graph where dots are used to represent individual data points. The dots are plotted above a number line. Dotplots can be used to represent frequencies for categorical or quantitative data. Dotplots can be used to see how data items compare.

Draw a Dotplot Draw a dotplot for the data set below. 25, 25, 20, 25, 16, 20, 25, 30, 25, 31, 26, 28, 30

Box and Whiskers

Finding First and Third Quartile The first quartile lies one quarter of the way up the list. (25% of the data is below the first quartile.) The third quartile lies three quarters of the way up the list. (75% of the data is below the third quartile.) 1.) Find the median to divide the data is half. 2.) Find the “median” of the lower half, this point will be the first quartile. 3.) Find the “median” of the upper half, this point will be the third quartile. ***In the case of two data points being either the first or third quartiles, then use same method as the median (add together and divide by 2)

Measures of Spread How much do values typically vary from the center? Range – Interquartile Range (IQR)

Use the data to make a box-and-whisker plot. 13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23

Find the minimum, maximum, median (Q2), lower quartile (Q1), and upper quartile (Q3) for the following sets of data and draw the Box and Whisker plot (or Boxplot) 32, 40, 35, 29, 14, 32 6, 1, 7, 6, 5, 5, 0, 1, 0, 8, 4 121, 143, 98, 144, 165, 118

Now, check the previous data for outliners. Checking for Outliers An outlier is data point that is extremely far away from the rest of the data and may effect some of the measurements we take from that data. An outlier is any point that is farther than 1.5 x the IQR from the first or third quartile. Now, check the previous data for outliners.

Find any outliers, if any. 32, 40, 35, 29, 14, 32 6, 1, 7, 6, 5, 5, 0, 1, 0, 8, 4 121, 143, 98, 144, 165, 118

Examples Identify the outlier in the data set {16, 23, 21, 18, 75, 21} and determine how the outlier affects the mean, median, mode, and range of the data. outlier: _________________ with the outlier without the outlier

End of Day 2

Graphs for Quantitative Data DAY 2 Graphs for Quantitative Data Stem and Leaf Plots – The stem is the larger place value and the leaves are the smaller place values. This graph is used to give a description of the distribution while using the actual values. Important to have a key for the reader. Histograms –

Example 1A: Making a Stem-and-Leaf Plot The numbers of defective widgets in batches of 1000 are given below. Use the data to make a stem-and-leaf plot. 14, 12, 8, 9, 13, 20, 15, 9, 21, 8, 13, 19 Number of Defective Widgets per Batch The tens digits are the _________. The ones digits are the _________. List the leaves from ___________ to _____________ within each row. Stem Leaves 0 8 8 9 9 1 2 3 3 4 5 9 2 0 1 Key: 1|9 means 19 Title the graph and add a key.

Example 1B: Making a Stem-and-Leaf Plot The season’s scores for the football teams going to the state championship are given below. Use the data to make a back-to-back stem-and-leaf plot. Team A: 65, 42, 56, 49, 58, 42, 61, 55, 45, 72 Team B: 57, 60, 48, 49, 52, 61, 58, 37, 63, 48 Team A’s scores are on the left side and Team B’s scores are on the right. Team A Team B 3 4 5 6 7 The _________ digits are the stems. The _________ digits are the leaves. Title the graph and add a key. Key:

Check It Out! Example 1 Stem Leaves The temperature in degrees Celsius for two weeks are given below. Use the data to make a stem-and-leaf plot. 7, 32, 34, 31, 26, 27, 23, 19, 22, 29, 30, 36, 35, 31 Stem Leaves

The frequency of a data value is ___________________ ______________________________________________ A frequency table ______________________________

Example 2: Making a Frequency Table The numbers of students enrolled in Western Civilization classes at a university are given below. Use the data to make a frequency table with intervals. 12, 22, 18, 9, 25, 31, 28, 19, 22, 27, 32, 14 Step 1: ___________________________________ Step 2: ____________________________________________________

Example 2 Continued 1-10 1 11-20 4 21-30 5 31-40 2 Step 3: ________________________________________ _______________________________________________ Enrollment in Western Civilization Classes Number Enrolled Frequency 1-10 1 11-20 4 21-30 5 31-40 2

Check It Out! Example 2 The number of days of Maria’s last 15 vacations are listed below. Use the data to make a frequency table with intervals. 4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12 Step 1: Identify the least and greatest values. Step 2: Divide the data into equal intervals.

Check It Out! Example 2 Continued Step 3: List the intervals in the first column of the table. Count the number of data values in each interval and list the count in the last column. Give the table a title. Interval Frequency

What Is a Histogram? A histogram is a bar graph that shows the distribution of data. A histogram is a bar graph that represents a frequency table. The horizontal axis represents the intervals. The vertical axis represents the frequency. The bars in a histogram have the same width and are drawn next to each other with no gaps.

Constructing a Histogram Step 1 - Count number of data points Step 2 - Compute the range Step 3 - Determine number of intervals (5-12) Step 4 - Compute interval width Step 5 - Determine interval starting & ending points Step 6 - Summarize data on a frequency table Step 7 - Graph the data

Example 3: Making a Histogram A histogram is __________________________________________ _______________________________________________________ Use the frequency table in Example 2 to make a histogram. Enrollment in Western Civilization Classes Step 1: _____________________ ____________________________ Number Enrolled Frequency 1 – 10 1 11 – 20 4 21 – 30 5 31 – 40 2

Example 3 Continued Step 2: ______________________________________________ _____________________________________________________ All bars should be the same width. The bars should touch, but not overlap. Step 3: _______________________________________________

Number of Vacation Days Check It Out! Example 3 Make a histogram for the number of days of Maria’s last 15 vacations. 4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12 Step 1: Use the scale and interval from the frequency table. Number of Vacation Days Interval Frequency 4 – 6 5 7 – 9 4 10 – 12 13 – 15 2

The data below shows the number of hours per week spent playing sports by a group of students. What is the minimum, maximum, & range? Make a frequency tables using intervals you decide on. Draw a histogram. 2 7 17 9 6 13 8 4 5 12 3 11 1 15

Hours per week playing sports Frequency 0 3 6 9 12 15 18 1 2 3 4 5 Hours per week playing sports Frequency

End of Day 3 Quiz tomorrow

Describing Distributions Center Shape Spread Outliers

Center For describing the center of the data, we can use either the Median or the Mean. Both are useful, in cases where the data is skewed one way the Median is a better choice because it is more resistant to outliers.

Shape “Symmetrical/Normal” “Skewed Left” “Skewed Right”

Shape

Spread Even though we are not graphing a Box and whisker we still use these two measures of spread. Range - is the difference of the maximum and minimum value - spread of the entire data set Interquartile Range (IQR) - is the difference of the upper quartile (Q3) & the lower quartile (Q1) – spread of the middle 50% of the data We can also use the Standard deviation

Standard Deviation is another measure of spread DAY 6 Standard Deviation is another measure of spread is the typical amount that a data value will vary from the mean the larger the standard deviation, the ______ ________________the data set (the data points are far from the mean ) the smaller the standard deviation, the ______ _______________ the data set (the data points are clustered closely around the mean.)

Calculating Standard Deviation Step 1 – Step 2 – Step 3 – Step 4 – Step 5 – Step 6 –

Standard Deviation Find the standard deviation for this set of data. 3, 5, 5, 7, 8, 9, 9, 10 mean = variance = standard = deviation Value Deviation from mean Squared Deviation 3 5 7 8 9 10 3 – 7 =-4 5 – 7 = -2 7 5 – 7 = -2 7 – 7 = 0 8 – 7 = 1 9 – 7 = 2 10 – 7 = 3 16 4 0 16+4+4+0+1+4+4+9 = 42 = 6 1 (8 – 1) 7 9 √6 = 2.45

Find the Standard Deviation for the Following Data Example #1 1, 3, 4, 4, 4, 5, 7, 8, 9 Example #2 338, 318, 353, 313, 318, 326, 307, 317 Remember to find the mean first. Standard deviation = 2.55 Standard deviation = 14.99

The owner of the Ches Tahoe restaurant is interested in how much people spend at the restaurant.  He examines 10 randomly selected receipts for parties of four and writes down the following data. Find the standard deviation. 44,   50,   38,   96,   42,   47,   40,   39,   46,   50

Practice Problem #1: Calculate the standard deviation of the following test data by hand. Use the chart below to record the steps. Test Scores: 22, 99, 102, 33, 57, 75, 100, 81, 62, 29

Standard Deviation Find the standard deviation for this set of data. 2, 3, 5, 5, 7, 8, 9, 9, 10, 12 mean = variance = standard = deviation Value Deviation from mean Deviation Squared 2 3 5 7 8 9 10 12

Practice! Find the standard deviation for this set of data. 6, 12, 4, 13, 7, 12, 11, 5 mean = variance = standard = deviation Value Deviation from mean Deviation Squared 6 12 4 13 7 11 5

End of Day 5 Project tomorrow