Sections 2.3 and 2.4
Quiz 2.3 – 2.4 tomorrow (or next school day) -May use 1 side of a 4 x 6 note card for the quiz
Percentiles and Cumulative Relative Frequency Plots Percentiles measure position within a data set.
Percentiles and Cumulative Relative Frequency Plots Percentiles measure position within a data set. Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest Median is ______ percentile
Percentiles and Cumulative Relative Frequency Plots Percentiles measure position within a data set. Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest Median is 50th percentile Q3 is the _____ percentile
Percentiles and Cumulative Relative Frequency Plots Percentiles measure position within a data set. Q1 is 25th percentile - - the value that separates the lowest 25% of the ordered values from the rest Median is 50th percentile Q3 is the 75th percentile
Percentiles and Cumulative Relative Frequency Plots In general, a value is at the kth percentile if k% of all values are less than or equal to it.
Suppose you have a set of univariate data (data that involves a single variable per case). The data consists of the weights of the students in a class. What are the cases? What is the variable?
Suppose you have a set of univariate data (data that involves a single variable per case). The data consists of the weights of the students in a class. What are the cases? Individual students What is the variable?
Suppose you have a set of univariate data (data that involves a single variable per case). The data consists of the weights of the students in a class. What are the cases? Individual students What is the variable? The weight for each student
The data consists of the weights of the students in a class. List all the measures you know to describe the data set. Hint: Should list 11 measures
List all the measures you know to describe the data set. x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers
List all the measures you know to describe the data set. x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers Now categorize these measures in terms of describing shape, center, or spread.
List all the measures you know to describe the data set. x, sx, median, Q1, Q3, min, max, range, IQR, mode, and outliers Now categorize these measures in terms of describing shape, center, or spread. None of these alone describe the shape.
How do you describe the shape?
How do you describe the shape? uniform normal distribution skewed left or right bimodal
Page 80, P28
P28 (Rescaling) (a) converting height from inches to feet is rescaling Which measures are affected by rescaling?
P28 (Rescaling) (a) converting height from inches to feet is rescaling Which measures are affected by rescaling? mean median standard deviation and IQR
P28 (Rescaling) (a) Divide each of the summary statistics by 12 so: the mean is
P28 (Rescaling) (a) Divide each of the summary statistics by 12 so: the mean is 4 feet the standard deviation is
P28 (Rescaling) (a) Divide each of the summary statistics by 12 so: the mean is 4 feet the standard deviation is 0.2 foot the median is
P28 (Rescaling) (a) Divide each of the summary statistics by 12 so: the mean is 4 feet the standard deviation is 0.2 foot the median is 3.75 feet and the IQR is
P28 (Rescaling) (a) Divide each of the summary statistics by 12 so: the mean is 4 feet the standard deviation is 0.2 foot the median is 3.75 feet and the IQR is 0.25 foot
P28 (b) each child growing 2 inches is ____________
P28 (Recentering) (b) each child growing 2 inches is recentering
P28 (Recentering) (b) each child growing 2 inches is recentering Which measures are affected by recentering?
P28 (Recentering) (b) each child growing 2 inches is recentering Which measures are affected by recentering? Only the centers: mean median
P28 (Recentering) (b) Add 2 to the measures of the center so mean is 50 inches median is 47 inches Recentering does not change the spread so standard deviation stays 2.4 inches IQR stays 3 inches
P28 (Recentering and Rescaling) (c) each child growing 4 inches is recentering and converting heights to feet is rescaling.
P28 (Recentering and Rescaling)
P28 (Recentering and Rescaling)
Plot this data into a stem-and-leaf plot: 23, 125, 8, 23, 50
Plot this data into a stem-and-leaf plot: 23, 125, 8, 23, 50 0 8 2 3 3 5 0 12 5
Plot this data into a stem-and-leaf plot: 23, 125, 8, 23, 50 0 8 2 3 3 5 0 12 5 5 0 represents 50
Page 69, P15
P15 The new mean height will be about 4 feet 4 inches. x = [5(4) + 6]÷ 6
P15 The new mean height will be about 4 feet 4 inches. The median will not change because it will still be one of the heights of the 3rd graders, who all are about 4 feet tall. 4 4 4 4 4 6
Page 70, P21 Use calculator to find (a) 5-number summary and (e) to draw a modified boxplot. Also answer (b), (c), and (d),
P21
P21
P21
Page 72, E33 Enter Predator data in List 1 Enter NonPredator data in List 2
Page 72, E33 Enter Predator data in List 1 Enter NonPredator data in List 2 Use L1 for Plot 1 and L2 for Plot 2 to display both modified boxplots on same screen
E33
Page 73, E43
Page 73, E43 Enter Weights in List 1 Enter Frequency in List 2
E43
Page 81, E53
Page 81, E53 Median: 23 or 24 cents. To estimate this, find the amount of change that corresponds to the 50th percentile
Page 81, E53 Median: 23 or 24 cents. To estimate this, find the amount of change that corresponds to the 50th percentile b. Q1 ≈ 10 cents and Q3 ≈ 70 cents. Q1 corresponds to 25th percentile and Q3 corresponds to 25th percentile IQR = 60 cents
E53
Page 82, E54
E54
Page 82, E57
E57
Questions?