CNSL 503 Statistics Portage Exam 2 2025

Frequency distribution - -presents the frequency of every value in a dataset Frequency tables - -displays the number of times (ex: frequency) a certain value appears within the dataset in a table format What does each column represent in frequency tables? - -one column represents the category, the other column represents the frequency Absolute frequency - -raw count What type of frequency do you use when answering " how many student out of the total number of students scored a letter grade?"? - -relative frequency Relative frequency - -the ratio between the absolute frequency of a category and the total frequency Formula for relative frequency - -frequency in category/total frequency What type of frequency do you use when answering the question "how many students scored a b or better?"? - -cumulative frequency Cumulative frequency - -the sum of frequencies of all preceding categories Frequency tables can be used for what type of variables? - -qualitative or quantitative variables When using frequency tables for quantitative variables, group the quantitative scores into groups called what? - -bins Frequency graphs - -pie charts, bar charts, histograms, frequency polygons, stem and leaf plots What type of frequency graphs are used for qualitative variables? - -pie charts and bar charts What type of frequency graphs are used for quantitative variables? - -histograms, frequency polygons and stem and leaf plots CNSL 503 Pie charts - -displays relative frequencies (and not necessarily absolute frequencies) of each category for qualitative variables in a pie Each portion of a pie represents... - -a different category The size of each portion is proportional to... - -the relative frequency of that category The entire pie represents... - -100% of the scores Pie charts are good to visualize... - -frequencies Pie charts are only useful for... - -small number of categories Bar charts/bar graphs - -display absolute and relative frequencies of qualitative data using bars Each bar represents a - -category The height of a bar represents... - -the frequency Do the bars touch in a bar graph? - -no Histograms - -displays absolute and relative frequencies of quantitative data using bars Each bar represents... - -a category The height of the bar represents... - -the freuqeuncy Do the bars in a histogram touch? - -yes The width of the bars represent... - -the size of the range of values Frequency polygons - -display absolute and relative frequencies of quantitative data using dots and lines Each dot is placed... - -above the score an the height of the frequency The dots are connected with a line that begins and ends at... - -zero frequency Stem and leaf plot - -display frequencies of quantitative data, particularly when the dataset is small The stem represents... - -the first digits of the score The leaf consists of... - -he last digit of the score CNSL 503 CNSL 503 The length of the leaf represents... - -the frequency of the category 3d graphs don't add any information when... - -the data is 2d 3-dimensional graphs - -use when data is measured on 3 different axis' What type of graph should you use when studying co2 emissions on function of year and country? - -3-dimensional graph Mode - -the value with the highest frequency The mode is shown by... - -the number of peaks in a graph Unimodal distributions have ____ peaks and ____ modes. - -1;1 Bimodal distributions have ____ peaks and ____ modes. - -2;2 Multimodal distributions - -distributions that have more than one mode Trimodal distributions have ____ peaks and ____ modes. - -3;3 Uniform distribution - -all scores have the same frequency Symmetrical distribution shape - -bell curve Symmetrical distribution mean, median and mode - -same mean, median and mode Negatively (left) skewed distribution - -majority is on the higher end Negatively (left) skewed distribution mean, median and mode - -increasing order: mean--median--mode Positively (right) skewed distribution - -majority at lower values, outlier at high values Positively (right) skewed distribution mean, median and mode - -increasing order: mode--median--mean Central tendency - -a single value that describes the middle of the distribution Measures of central tendency - -mean, median, mode Mean - -the arithmetic average of a set of scores Population mean symbol - -μ CNSL 503 CNSL 503 Sample mean symbol - -x or m The mean is calculated by... - -adding up all the values in a distribution and dividing by the number of scores Formula for the population mean - -μ=σx/n Μ= population mean Σ= "sum of" X= score N= population size Σx= the sum of all scores Formula for the sample mean - -x=σx/n X ̅ = sample mean Σx= sum of all scores N= sample size The mean is the preferred measure of central tendency if the distribution is... - symmetrical The mean can be influences by... - -outliers Outliers - -extreme values in a dataset The mean may not be appropriate when there are... - -outliers Median - -the midpoint of a distribution of scores; may be more appropriate to use when there are outliers ____% of scores fall above the median and ____% of scores fall below the median. - 50;50 How to calculate median when there is an odd number of scores? - -arrange scores in ascending order and identify the middle value How to calculate median when there is an even number of scores? - -arrange scores in ascending order and take the average of the 2 middle values Is the median affected by outliers? - -no The median is preferred when... - -the distribution contains extreme scores or is skewed or variables measured on an ordinal scale Mode - -the most common score in a dataset CNSL 503 CNSL 503 The mode is most useful for.... - -variables measured on a nominal scale or to describe the shape of a distribution (unimodal, bimodal, trimodal) Use mean for... - -symmetric data Use median for... - -skewed data Use mode for... - -describing the peak Variability - -describes the spread of the distribution Measures of variability - -range, interquartile range, sum of squares, variance, standard deviation The range and interquartile range are based on... - -only 2 scores The sum of squares, variance and standard deviation are based on... - -all the scores related to one another Range - -the difference between the highest value and the lowest value in a dataset The range is calculated by... - -subtracting the lowest value and the highest value in a dataset Formula for range - -range= xmax- xmin X=score Is the range sensitive to outliers? - -yes Interquartile range (iqr) - -calculated by subtracting the lower quartile from the upper quartile Quartiles - -values that divide a data set into four equal parts Formula for interquartile range - -iqr= q3-q1 Lower quartile/first quartile (q1) - -separates the lowest 1/4 of the data from the upper 3/4 of data; the median of the lower half of data Middle quartile/second quartile (q2) - -the overall median of the dataset Upper quartile/ third quartile (q3) - -separates the highest 1/4 of the dataset from the lowest 3/4 of the dataset; the median of the upper half of the score CNSL 503 CNSL 503 Because the iqr only accounts for the middle 50% of the distribution, it is less susceptible to influence by... - -outliers Box plot (box and wisker plot) - -graph the quartiles in a box and the minimum and maximum values as "wiskers" extending outside the box Variability - -the average distance from the mean Standard deviation - -the average distance between each score and the mean Sum of squares (ss) - -sum of the squared deviations between each score and the mean Formula for population ss - -ss=σ(x-μ)^2 Ss= sum of squares Σ= sum up X= score X-μ= deviation between the score and the mean Formula for sample ss - -ss= σ(x-x)^2 Ss=sum of squares Σ= sum up X ̅ = sample mean X=score Variance - -the average squared deviations between each score and the mean Population variance symbol - -σ² Sample variance symbol - -s² Population variance - -the average squared deviations between each score and the mean Formula for population variance - -σ²= ss/n or σ²= σ(x-μ)^2/n