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STATS quiz c10-12
zfriday 10/24
| Question | Answer |
|---|---|
| qualitative variables | also called CATEGORICAL variables -puts an individual into one of several groups |
| quantitative variables | also called NUMERICAL variables -applies numerical values for which arithmetic operations make sense |
| examples of quaNtitative variables | -price of menu items -IQ score -number of years |
| examples of quaLitative variables | -eye color -grade (A,B,C,D,F) -items on a menu |
| bar graph | stand alone, vertical (sometimes horizontal) bars -displays DISTRIBUTION -bars represent qualitative data (usually as count or #) -length of bars represent the quantitative data -bars have equal width and are equally spaced |
| pie charts | displays proportional parts of the total population that share a common characteristic. -DISTRIBUTION graph -circle with wedges that represent the parts -parts are shown as percentages -angle out of 360 is in proportion to the size/% of the wedge |
| how to find degree of percentage in a pie chart (equation) | .213 x 360 degrees = 76.86 degrees example: 21.3% of the population prefers color blue -divide percent by 100 -- 21.3/100 = .213 -take divided percent and multiply by 360 degrees |
| line graph | also called time series -displays how quaNtitative variables changes over time -plots each observation (data) in order of occurrence at regular intervals, over a period of time -each category is a different line |
| x and y axis of line graph | x= time y=variable being measured |
| what does 'truncated' mean | the squiggle on the bottom of the Y axis -indicates that Y axis does not start at zero |
| example of how a graph could be set up in a misleading way | -differences can be exaggerated truncated graphs can be used to guide readers to incorrect conclusions |
| why should graphs be labeled on the axes correctly? | so that the magnitude of the differences is apparent to the reader |
| what do line graphs help you see? | to see an overall PATTERN or TREND |
| seasonal variation | when a graph has a regular pattern that repeats each year at known REGULAR INTERVALS |
| seasonally adjusted | seasonal variation in a graph is removed before data are published |
| graphs END OF CHAPTER 10 | -helps see what data says visually -choice of which graph depends on the type of data |
| Histogram | -similar to bar graph, BUT the bars are touching -bars represent quaNtities of classes, and are equal in width |
| why do the bars touch in a histogram | because the data is of a continuous type |
| number of classes (bars) in a histogram | the bars represent classes of the data, in equal intervals -depends on how many data there are and how spread out the data value is (maximum to minimum) |
| how to compute number of bars to use in histogram | 1. take the square root of the total number of data points 2. round up |
| Class Width (CW) | -how wide each class (bar) is -determines the limits of the classes always a whole number |
| how to calculate Class Width (CW) | (data max - data min) / number of classes |
| class limits | the range of each class, where each group starts and ends -determined by class width *take lowest data value and make groups in amounts of the Class Width |
| class boundary | halfway (0.5) between the upper limit of one class, and the lower limit of the next -if the lower class limit is 4, the boundary would be 3.5 |
| what values are shown on the x axis in a histogram | the UPPER class boundaries are the numbers shown on the x axis |
| midpoint | middle value of each class -found by taking ( (class max + class minimum) / 2) |
| first 4 steps to graphing a histogram | 1. find min and max data points 2. find total number of data points 3.decide how many bars/classes there are. take total number of data and take the square root 4. find class width by taking min - max data points, divided by number of classes |
| last steps to graphing a histogram | 5. start at lowest data and make groups in sizes of the CW 6. find class boundaries (.5 away from limit) 7.plot the all upper boundaries 8. find how many (frequency of) data fall into each group and use that as the y axis value |
| what makes a stem&leaf display different than a histogram? | it displays all of the individual data variables |
| stem&leaf display | used to rank-order and arrange data in a similar way to a bar graph, but retains all of the original data values -digits of each stem/leaf must be an equal width/distance apart (cant skip around in stem digit values) -requires a key saying (x/x =x.x) |
| stem | the left side of the line -consists of all the numbers except the last digit |
| leaf | the right side of the line -consists of one digit, the final digit -with a data with too many digits, the final digit can be found after rounding the data |
| distribution of a variable shows what | tells us what values the variable takes and how often it takes each value. |
| characteristic of patterns in histograms and stem&leaf displays | shape: symmetric, skewed to the left/right |
| outliers in a graph END OF CHAPTER 11 | deviations from the overall pattern/shape of the graph |
| parameters | measures found by using all data values in a population |
| statistics | measures found by using data values from a sample |
| measures of central tendency (MCT) are also called what | averages are what else they are called |
| mean | the arithmetic average -represented as x̄ for SAMPLE mean -represented as μ (mu) for POPULATION mean |
| calculating the mean | adding the values of the data and dividing by the total number of values |
| median | the middle of an ordered list -represented as MD or Med |
| calculating the median | arrange the data from smallest to largest -the middle of the values -if an odd number, find middle of the two middle values |
| mode | the value in the data set that occurs the most often -data sets can have more than one, or none |
| what measure of central tendency can be used in categorical/qualitative data | mode can be used |
| a MCT is resistent when? | when an extremely high or low data value (outlier) does NOT change the value of that measure -MEDIAN AND MODE are RESISTANT |
| which is a better average? median or mean | median because it is a more resistant MCT |
| spread is also called what | other name is standard deviation |
| what is standard deviation | the average distance of every data value from the mean. |
| first 3 steps to finding standard deviation | 1.find the mean 2. take each data value and subtract the mean from it 3. square the differences 4.find the average of the total number of differences 5. divide averages by the number of data values MINUS 1 (n-1) |
| how to find variance | taking the average of the squared differences, and dividing by the number of data values MINUS 1 / (n-1) |
| last step to finding standard deviation | after finding variance, take its square root |
| quartiles are shown as what | Q1, Q2, and Q3 |
| what quartile is the median | Q2 |
| how to find which quartile a value lies in/belongs to | arrange data in order, find median. -take the values below Q2 and find their median to find Q1, and same to find Q3 with above |
| IQR (the interquartile range) | the difference between the third and first quartiles * Q3- Q1 |
| finding an outlier | put data in order, find the IQR. -multiply the IQR by 1.5 -take that product and add it to Q3, subtract from Q1 -if there are values that are below or above that number, they are outliers. |
| two common descriptions of center and variability | -five number summary -mean and standard deviation (for roughly symmetric distributions) |
| a boxplot displays what | the five number summary of a data set |
Created by:
liz gelles