Chapter 14 Statistics and Data Analysis

Data Analysis Chart Types Frequency Distribution

Data Analysis Chart Types Line Plot Uses a symbol to show frequency

Data Analysis Chart Types Bar Graph Uses bars to indicate frequency

Data Analysis Chart Types Back-to-Back bar graph A special bar graph that shows the comparisons of two sets of related data

Data Analysis Chart Types Three Dimensional Bar Graph Used when showing three aspects of a set of data at the same time

Data Analysis Chart Types Stem and Leaf Plot Used to organize a large number of data Stem Column on the left usually digits in the greatest common place value of data Leaf Column on the right one digit numbers, which are in the next greatest place value after the stem

Data Analysis Chart Types Create a stem and leaf plot for the data below. The following are the grades scored on a quiz with 50 possible points 42, 49, 36, 32, 10,19,38,40,41, 50,40,49,30,20,48,47,40,41,32, 37,25,41,43,37,39 What is the first thing you need to do? Write in numerical order

Data Analysis Chart Types Histogram Most common way of displaying frequency distributions Type of bar graph in which the width of each bar represents a class interval and the height of the bar represents the frequency in that interval.

Data Analysis Chart Types

Data Analysis Chart Activity Get in groups of 3 or 4 You will be making a data analysis chart to display and explain to the class You can look at things like: Brothers and Sisters How many days you workout, go to the beach, read a book, play a sport, etc each week States visited Be creative!

Frequency Distribution Used when individual data is too big to be considered alone

Frequency Distribution Range The difference between the greatest and the least values in the set Class Interval Range of each class, will also be equal in a frequency distribution Class Limit The upper and lower values in each interval Class Marks Midpoints of the classes

Frequency Distribution ScoresFrequency

Frequency Distribution Frequency polygon Is drawn by connecting the class marks on the graph The class marks are graphed as the midpoints of the top edge of each bar

Frequency Distribution Cumulative Frequency Distribution The cumulative frequency of each class is the sum of the frequency of the class and the frequencies of the previous classes.

Example Cumulative Frequency

Frequency Distribution Create a frequency and cumulative frequency distribution for the data below from prior example. The following are the grades scored on a quiz with 50 possible points 42, 49, 36, 32, 10,19,38,40,41, 50,40,49,30,20,48,47,40,41,32, 37,25,41,43,37,39

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Find the Range, Class Intervals, Marks, and Limits Create a frequency distribution, histogram, and cumulative frequency distribution. What can you determine from the graph and distributions?

Measures of Central Tendency Measures of averages Mean Median Mode Arithmetic Mean X, adding the values of the set of data and dividing by the number of values of the data

Measures of Central Tendency General Formula Find the mean of (36.8, 29.5, 29.1, 33.3, 30.0, 20.7, 39.5) About 31.3

Measures of Central Tendency Median The middle value If there are two middle values, then it is the mean of the two middle values What is the median of (5,6,8,11,14)? 8 What is the median of (3,4,6,7,8,10)? (6+7)/2=6.5 Doesn’t have to be part of original data set

Measures of Central Tendency Mode Most frequent value Some sets may have multiple modes and others can have none Data with two modes are called “bimodal” Mode, unlike mean and median, has to be part of the data set

Example What is the mean, median and mode of the data? Mean  45.2 Median  46.5 Mode  46 Year# of HR

Measures of Central Tendency Recall this example from Lesson 1: The following are the grades scored on a quiz with 50 possible points 42, 49, 36, 32, 10,19,38,40,41,50,40,49, 30,20,48,47,40,41,32, 37,25,41,43,37,39 Now, use your steam and leaf plot to help find the mean, median, and mode for the data Mean  Median  40 Mode  40,41

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Find the mean, median, and Mode

Measures of Central Tendency in a Frequency Distribution Mean of the data in a Frequency Distribution Where X is the class marks Where F is corresponding frequencies Where N is the total number of samples/frequencies

Measures of Central Tendency in a Frequency Distribution Find the mean of the following frequency distribution Mean = 508/30  about 17 Class Limits Class Marks FrequencyF(X)

Measures of Central Tendency in a Frequency Distribution Median Class The median of the data in a frequency distribution Cum Freq  68-40=28 Class Limites  50-40=10 M Cum Freq  50-40=10 M Class Limits  M-40=X 28 = X X = M-40=X M =  Median of Data

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Find the Mean and Median for your frequency distribution How do these values compare to the previous ones you calculated from the data?

Warm Up Pick up Calculator and Warm Up Book Have homework out on desk 1. Reflect on how the mean and mode calculations are different for a data set and frequency distribution. Why? 2. What is the difference between a histogram and bar graph? 3. What is a frequency polygon?

Box and Whisker Plot Measures of Variability Range of a data set Quartiles  Q 1, Q 2, Q 3 Which Quartile is the median of the data? Q 2 Interquartile Range (Q 3 -Q 1 ) Semi-Interquartile Range (Q 3 -Q 1 )/2

Box and Whisker Plot Find the interquartile range of the following test scores 82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99 Write in order first. What is the mean, median, and mode?

Box and Whisker Plot 82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99 Mean 77 Median 78 Mode 82 What are Q 1, Q 2, Q 3 ? Q 1 =69 Q 2 =78 Q 3 =86 Interquartile Range 17 Semi-interquartile Range 8.5

Box and Whisker Plot Box-and-whisker plots Used to summarize data and illustrates the variability of the data Displays median, quartiles, interquartile range, and extreme values Box consists of Quartiles 1 and 3 Whiskers stop at the extreme values of the set Outliers Values that are more than 1.5 times the interquartile range beyond the upper or lower quartiles

Box and Whisker Plot Draw a box-and-whisker plot for the test scores in first example. 82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99

9.1 Warm Up Grab Calculator NO NEED FOR WARM UP BOOK Compare box and whisker plots from homework with neighbor Are you ready for the quiz? Do you have specific questions to review? Gather your thoughts and be ready to review for/take quiz.

Measures of Variability in Data Set Mean Deviation The average absolute value distance each piece of data is from the mean Formula MD= What is the mean deviation of our example?

Mean Deviation Example Recall previous box and whisker example: 82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99 Find Mean Deviation

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Make a Box and Whisker Plot with all necessary information for your specific data set. Find the mean deviation for your data set.

9.2 Warm Up Get Calculators AND LAPTOP Sign out your laptop Make sure it turns on Check Homework answers 13   0.672

Measures of Variability in Data Set Standard Deviation Measures of the average amount each piece of data deviates from the mean Formula

Measures of Variability in Data Set Variance Describes the spread of the data Mean of the squares of the deviations from the average =δ 2 Therefore standard deviation is the positive square root of the variance

Measures of Variability in Data Set What is the variance and standard deviation for our test score example? Variance Standard Deviation

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Variance and Standard deviation for your data set. Reflect on what these measures tell you about the data.

Measures of Variability in Frequency Distribution Standard Deviation of the Data in a Frequency Distribution

Measures of Variability in Frequency Distribution Variance of the Data in a Frequency Distribution =δ 2

Measures of Variability in Frequency Distribution Make a frequency distribution for the test score example from the box and whisker plot lesson below. 82, 78, 94, 68, 74, 88, 64, 42, 72, 82, 79, 99 What is the variance, standard deviation, and mean deviation from this frequency distribution?

Frequency Distribution Activity Get into partners and complete the following with your specific data set: Variance and Standard deviation for your frequency distribution.

Warm Up Find the mean and median of the frequency distribution below

The Normal Distribution A frequency distribution that occurs when there is a large number of values in a set of data Looks like a symmetric bell-shaped curve called a normal curve Shape of the curve comes from a large number of frequencies falling in the middle of the distribution; small percent fall at the extreme values

The Normal Distribution About 68% of the data are within 1 standard deviation from the mean. About 95.2% of the data are within 2 standard deviations from the mean About 99.6% of the data are within 3 standard deviations from the mean

The Normal Distribution Represents those values that fall between one and two standard deviations above the mean Represents those values that fall between two and three standard deviations below the mean Mean Value

The Normal Distribution The average healing time of a certain type of incision is 240 hours with a standard deviation of 20 hours. What does the normal curve look like? First put in the mean; Then figure out each interval How many patients healed in the hour interval if there were a total of 2000 patients? 68.3%*(2000)=1366 How many patients healed in the hour interval if there were a total of 2000 patients? 1994

Review 14.3 Find the variance and standard deviation for the data set below: 12, 22, 25, 27, 15, 18 Put the following data into a frequency distribution and then find the variance and standard deviation: 11, 16, 18, 25, 29, 22, 24, 5, 9, 2