Data Analysis

I. Mean, Median, Mode A. central tendency is a value that describes a A. central tendency is a value that describes a data set. data set. B. Mean, median, and mode are three B. Mean, median, and mode are three measures of central tendency. measures of central tendency. C. Mean C. Mean 1. sum of the data values divided by the 1. sum of the data values divided by the number of data values number of data values 2. also called the average of a set of data 2. also called the average of a set of data values values 3. What is the mean of the following set of 3. What is the mean of the following set of data? data? 76, 94, 88, 256, 90, 95, 92 76, 94, 88, 256, 90, 95, 92 Sum = ÷ 7 = 113 is the mean Sum = ÷ 7 = 113 is the mean

D. Median D. Median 1. the middle value of a data set when 1. the middle value of a data set when the numbers are arranged in order the numbers are arranged in order 2. For a set with an even number of data 2. For a set with an even number of data values, the median is the average of values, the median is the average of the two middle values. the two middle values. 3. Find the median of the above set of 3. Find the median of the above set of data: data: a. arrange in order a. arrange in order 76, 88, 90, 92, 94, 95, , 88, 90, 92, 94, 95, 256 b. the median is the middle number: b. the median is the middle number: 92 92

E. Mode 1. the data value that occurs most often 2. a data set may have no mode, one mode, or more than one mode 3. Find the mode of the above set of data: No data values are repeated, so there is no mode

II. GRAPHS - visual display of info / data II. GRAPHS - visual display of info / data A. line graphs A. line graphs 1. info/data is plotted on a grid 1. info/data is plotted on a grid 2. shows trends/how data chngs. over time 2. shows trends/how data chngs. over time 3. can have an increasing trend, a decreasing trend, or no trend at all 3. can have an increasing trend, a decreasing trend, or no trend at all 4. X-axis (horizontal) 4. X-axis (horizontal) * independent variable * independent variable * adjusted or determined by experimenter * adjusted or determined by experimenter * ex: time * ex: time 5. Y-axis (vertical) 5. Y-axis (vertical) * dependent variable * dependent variable *occurs b/c of independent variable *occurs b/c of independent variable * ex: temperature * ex: temperature 6. You can use a line graph when the independent variable is 6. You can use a line graph when the independent variable is continuous. continuous. 7. Steps for creating a line graph: 7. Steps for creating a line graph: a. Draw the X and Y axes a. Draw the X and Y axes b. Label the X-axis with the independent variable. b. Label the X-axis with the independent variable. c. Label the Y-axis with the dependent variable. c. Label the Y-axis with the dependent variable. d. Create a scale on each axis with equally spaced d. Create a scale on each axis with equally spaced numbers. numbers. e. Plot a point for each piece of data. e. Plot a point for each piece of data. f. Connect the plotted points. f. Connect the plotted points. g. Add a title. g. Add a title.

B. bar graphs B. bar graphs 1. displays data in a number of separate categories categories 2. shows info collected by counting 2. shows info collected by counting 3. useful for comparing amounts at a glance 3. useful for comparing amounts at a glance 4. does NOT show trends/predictions 4. does NOT show trends/predictions (that’s why info. is not connected) (that’s why info. is not connected) 5. Steps for creating a bar graph: 5. Steps for creating a bar graph: a. Draw the X and Y axes a. Draw the X and Y axes b. Write the category names along the b. Write the category names along the X-axis and label. X-axis and label. c. Label the Y-axis with the name of the c. Label the Y-axis with the name of the dependent variable. Include units of dependent variable. Include units of measurement. Create an equal scale of numbers. measurement. Create an equal scale of numbers. d. Draw a bar for each category to the appropriate height. d. Draw a bar for each category to the appropriate height. e. Add a title to your graph. e. Add a title to your graph.

C. circle (pie) graphs C. circle (pie) graphs 1. shows how different parts of a whole compare 1. shows how different parts of a whole compare to one another to one another 2. parts are usually expressed as % - sum of all parts 2. parts are usually expressed as % - sum of all parts equaling 100% equaling 100% 3. shows data at one particular time, not over a 3. shows data at one particular time, not over a period of time – does not show trends period of time – does not show trends 4. Steps for creating a circle graph: 4. Steps for creating a circle graph: a. Draw a circle a. Draw a circle b. Calculate the percentage of each part by b. Calculate the percentage of each part by taking (part ÷ whole) * 100 = % of each taking (part ÷ whole) * 100 = % of each part part c. Calculate the angle for each part by c. Calculate the angle for each part by multiplying the % (in decimal form) by 360. multiplying the % (in decimal form) by 360. d. Using angles calculated, divide circle into d. Using angles calculated, divide circle into parts. parts. e. Label each part with name and % e. Label each part with name and % f. Add a title to your graph. f. Add a title to your graph.

III. Scatterplots III. Scatterplots A. graph with data points that show a A. graph with data points that show a relationship between two sets of data relationship between two sets of data C. Correlations C. Correlations 1. can be positive (upward slope) or negative (downward slope) 1. can be positive (upward slope) or negative (downward slope) 2. can be strong (points cluster around line of best fit) or weak (they do not) 2. can be strong (points cluster around line of best fit) or weak (they do not) 3. if data points are random there is no correlaton 3. if data points are random there is no correlaton

C. Correlations C. Correlations 1. can be positive (upward slope) or negative (downward slope) 1. can be positive (upward slope) or negative (downward slope) 2. can be strong (points cluster around line of best fit) or weak (they do not) 2. can be strong (points cluster around line of best fit) or weak (they do not) 3. if data points are random there is no correlaton 3. if data points are random there is no correlaton

IV. Stem and Leaf Plots IV. Stem and Leaf Plots A. chart that shows groups of data arrangedA. chart that shows groups of data arranged by place value by place value B. a display that organizes data so that youB. a display that organizes data so that you can see how they are spread out can see how they are spread out C. stem – digit to the left side of the verticalC. stem – digit to the left side of the vertical line line D. leaves – the ones digits to the right side ofD. leaves – the ones digits to the right side of the vertical line the vertical line E. range – difference b/t the greatest and theE. range – difference b/t the greatest and the least numbers in a data set least numbers in a data set

V. Probability V. Probability A. a way to measure the likelihood that an event will occur B. formula: P = number of favorable outcomes number of possible outcomes

C. independent events C. independent events 1. outcome of one event has NO effect on the outcome of the other event(s) 2. when finding the probability of independent events occurring: *find the probability of each event occurring occurring *multiply the probability of all the events together events together

3. example: What is the probability of tossing a coin and getting tails, and rolling a # cube and getting a number less than 5? STEP 1 Coin: P tails = #favorable outcomes = 1 # possible outcomes 2 Cube: P <5 = # favorable outcomes = 4 = 2 # possible outcomes 6 3 STEP 2 Multiply the probabilities of each event: P tails * P <5 = 1 * 2 = 2 = The probability is 1 3

D. Dependent events 1. outcome of one event DOES have an effect on the outcome of the other effect on the outcome of the other event(s) event(s) 2. to find the probability of all events occurring you do the same as with occurring you do the same as with independent events independent events 3. number of possible outcomes changes as events occur. as events occur.

4. example: A bag contains 5 blue, 3 red, and 2 yellow marbles. What is the yellow marbles. What is the probability of drawing a blue marble probability of drawing a blue marble and then a red marble? and then a red marble? STEP 1 Find the probability of each event: * 5 of the 10 marbles are blue → P blue = 5 = * 3 of the 9 remaining marbles are red → P red = 3 = STEP 2 *multiply the probabilities 1 * 1 =