M7D1.a: Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes. Population: Census: Biased: Sample: The entire group of objects or individuals considered for a survey. The procedure of systematically acquiring and recording information about ALL members or objects in a population. Favoring one person or side over another. prejudiced. A survey that includes only a portion of the population. M7D1.a: Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes. Random Sample: Biased Sample: A sample where members of a population are chosen at random. A sample that does not fairly represent the population. *Convenience Sample: A sample based on members of the population that are readily available.
M7D1.b: Construct frequency distributions. Frequency Distribution: A systematic way to order a set of data from lowest to highest value showing the number of occurrences at each value or range of values. Usually done using a frequency table. Cumulative Frequency: A column in a frequency table used to keep a running total of the number of data items. M7D1.b: Construct frequency distributions. Sample: Size Frequency Cumulative Frequency 7.5-8 8.5-9 9.5-10 10.5-11 The last number in this column should be the total number of data pieces in the set.
M7D1.c: Analyze data using measures of central tendency (mean, median and mode), including recognition of outliers. Mean: The sum of the data values divided by the number of data items. Median: The middle value of an odd number of data items arranged in order from least to greatest. For an even number of data items, the median is the mean of the two middle values. M7D1.c: Analyze data using measures of central tendency (mean, median and mode), including recognition of outliers. Mode: The value or values that occur most often. When all the data values occur only once, there is no mode. It is also possible to have more than one mode in a data set. Outlier: An extreme value in a data set. - Lies way outside the rest of the data. Outliers can greatly affect the mean of a data set.
M7D1.c: Analyze data using measures of central tendency (mean, median and mode), including recognition of outliers. Central Tendency: The center or middle of a distribution (data set). Measure Mean Median Mode Most useful when: the data are spread fairly evenly the data set has an outlier the data involve a subject in which many data points of one value are important such as election results M7D1.d: Analyze data with respect to measures of variation (range, quartiles, interquartile range) Measures of variation: lengths between various points within the distribution. It is used to describe how spread out or close data in a set are. Range: Measure of variation used to describe the spread of ALL data pieces. To find the range, subtract the minimum value from the maximum value.
M7D1.d: Analyze data with respect to measures of variation (range, quartiles, interquartile range) Quartiles: sample data set 1st: Remember median (middle value) divides the data into a lower and upper half. The lower quartile is the middle value of the lower half of the data. The upper quartile is the middle value of the upper half of the data. 12, 15, 15, 18, 21, 22, 25, 29, 40 M7D1.d: Analyze data with respect to measures of variation (range, quartiles, interquartile range) Interquartile Range: Why know measures of variation? the range between the lower quartile and the upper quartile (the middle of the data). To find the IQR subtract the LQ from the UQ. Measures of variation can describe how predictable a data set is. Large range or IQR ~ data is spread out which means it is less predictable. Small range or IQR ~ data is close together which means it is more predictable.
Pictographs uses pictures to display data. Includes a key to tell what each picture represents. Histogram A bar graph that shows the frequency of data within equal intervals. There are no spaces between the bars.
Bar graphs: Used to compare the amounts or frequency of occurrence of different characteristics of data. Line graphs: A graph that uses line segments to show how data changes (usually over time).
Line Plot: A number line with marks or dots that shows the frequency distribution of a data set. Circle graph: A graph that uses sectors of a circle to compare parts to the whole and parts to other parts.
Box -nwhisker plot: a graph used to display a set of data so you can easily see where most of the numbers are. ~ Data is broken into four quartiles with each quartile representing 25% of the data. Constructing a box-n-whisker plot: Step 1: Find the 5 points! 1. minimum or least value 2. maximum or greatest value 3. median 4. lower quartile (LQ) 5. upper quartile (UQ)
Constructing a box-n-whisker plot cont.: Remember: ~ LQ is the median of the lower half of the data. ~ UQ is the median of the upper half of the data. ~ Median is the middle number of the data when the data is arranged from least to greatest. Constructing a box-n-whisker plot cont.: Start by lining up your data from least to greatest. 17, 17, 19, 20, 21, 23, 26, 28, 29 min. LQ = 18 median UQ = 27 max.
Constructing a box-n-whisker plot cont.: Step 2: Draw a number line that starts just below the min. value and ends just above the max. value. * Make sure you make equal intervals on the number line. 10 15 20 25 30 Constructing a box-n-whisker plot cont.: ~ Above the number line, plot a point for each of your 5 numbers. min.. LQ.. UQ median.. 10 15 20 25 30 max.
Constructing a box-n-whisker plot cont.: Draw a box from the LQ to the UQ. Inside the box draw a line for the median. Then draw the whiskers from the LQ to the min. and the UQ to the max. min.. LQ. median. UQ.. max. September 01, 2009 10 15 20 25 30 Constructing a box-n-whisker plot cont.: The box represents the middle 50% of the data. It shows where the middle tends to lie. 1st quartile (min to LQ) bottom 25% 2nd quartile (LQ to median) middle 50% 3rd quartile (median to UQ) 4th quartile (UQ to max) upper 25%
Outliers on a box-n whisker * An outlier is a piece of data that is way outside the rest of the data. On a boxn-whisker it shows up when one of the whiskers is much longer than the box itself. Outlier *Outliers on a box-n whisker 5th period only Outliers must lie at least 1 1/2 times below or above the distance of the IQR (the box). To find out if a data piece is an outlier: If it's low ~ LQ - (1.5 x IQR) If it's high ~ UQ + (1.5 x IQR)
*Outliers on a boxn whisker Sometimes outliers (extremes) are taken out of a data set in an attempt to give a more accurate picture of the dispersion of the data.. Scatter Plots: A graphical display used to show a trend between two sets of data. One set is dependent (y) One set is independent (x) Each value in data set (x) corresponds to a value in data set (y).
Scatter Plots: To construct a scatter plot: ~ Pair each set of corresponding values in an ordered pair (x,y) and graph them. y Make sure you use the x-axis for the independent variable and the y-axis for the dependent variable. (dependent) (independent) x Scatter Plots: * Use equal intervals on both axis. (by 2's or 5's or 10's, etc.) y 80 60 40 20 The scales don't have to be the same on both axis. 5 10 15 20 25 30 x
types of data sets: There are two types of data sets: Numerical and categorical. ~Numerical data are ordered numerically. The shape of the graph is used to analyze the data. ~Categorical data can be arranged in any order without affecting the analysis. Because there is no established order for the arrangement of categorical data, the shape of the data set will vary. Therefore, the shape of the graph is not used in the analysis of categorical data. M7D1.g: Analyze and draw conclusions about data, including describing the relationship between two variables. Box -nwhiskers You can see and describe data sets using box-n-whiskers. ex) A B Quiz Scores 10 20 30 40 50 60 70 80 90 100 ~ The middle 50% of class A scored between 55 & 70. ~ The middle 50% of class B scored between 40 & 80. ~ That makes class A more predictable. It has a smaller box or IQR.
M7D1.g: Analyze and draw conclusions about data, including describing the relationship between two variables. Scatter Plots: Remember, Scatter plots are used to see if there is a relationship between 2 sets of data. If the scatter plot looks like: y........ x or y...... x there is a positive correlation. That means that as "x" increases, it generally causes y to also increase. M7D1.g: Analyze and draw conclusions about data, including describing the relationship between two variables. Scatter Plots: If the scatter plot looks like: y.............. or y x x there is a negative correlation. That means that as "x" increases, it generally causes y to decrease.
M7D1.g: Analyze and draw conclusions about data, including describing the relationship between two variables. Scatter Plots: If the scatter plot looks like: y.......... x there is a no correlation. You see no pattern at all which indicates that "x" has no effect on "y" at all. M7D1.g: Analyze and draw conclusions about data, including describing the relationship between two variables. Scatter Plots: Examples of data sets: x y correlation time spent studying test scores positive miles driven in car gas in tank negative shoe size no. of pets no