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Summer Assignment 2. What is Statistics? Statistics is the science of data. It is used to gain insight and to draw conclusions. 3. What is the difference between categorical and quantitative variables? Give examples of each. Categorical variables places individuals into groups such as gender, religion and color. Finding the average of these things have no meaning. Quantitative variables have numerical values such as price, GPA and height. Finding the average has meaning. Age is quantitative. Ex. Average age of a sophomore is 14.5 years. Year is categorical. Ex. Average year is 1982.4???? That makes no sense!!! 4. Quantitative variables are broken down into discrete and continuous variables. Give three examples of each. Discrete variables are countable values, such as the number of children in a family, the number of students in a classroom or the number of calls in one day. Continuous variables have an infinite amount of values for example temperature, height and weight. 5. What is the difference between a bar graph and histogram? Bar graphs are used to represent categorical data. They bars never touch. Histograms are used to represent quantitative data. The bars must be touching and the equally sized classes must be created. The similarity is that they are both frequency graphs. 6. What is a circle graph used for and can it always be used in place of a bar graph? Circle graphs are used to display the percent values of categorical variables ONLY is the sum of all the percents is 100% at a set point in time. A circle graph can always be used in place of a bar graph as long as all percents add up to 100%. If this does no occur, create an other category. 7. When is a time plot appropriate and what is meant by a trend and a seasonal variation of a time plot? Time Plots are used when variables are measured in intervals over time. Always mark the time scale on the x-axis. Trends are upward and downward patterns. Seasonal Variation are patterns that repeat themselves. 8. What does it mean for the shape of a distribution to be a. Normal means the distribution is symmetric on both sides. It is also called bell-shaped. b. skewed right means the curve has a long tail to the right. c. skewed left means the curve has a long tail to the left. 9.You received a standardized test score report stating that you were in the 80th percentile of all test takers. Explain what this means. This means that 80% of everyone who took the test scored less than or equal to your score. The other 20% scored higher than you did. 10. In considering a frequency distribution, is it a good idea to have overlapping classes such as 10-20, 20-30, 30-40? Explain. No, some data points will be counted twice and this makes the graph meaningless. 11. Can histograms be drawn using vertical and horizontal bars or only one way? Explain. Histograms can only be drawn vertically. The explanatory/independent variable must be on the x-axis. 12. What is an Ojive and what is it used for? An ojive is a relative cumulative frequency graph which gives information on the relative standing of an individual. The ojive gives us the percentile of individuals with respect to all the others. 13. Define a. Mean is the average of a set of numbers. Add all the numbers and divide by how many numbers we have. b. Median is the middle number when all the numbers are put in order. If there are two middle numbers, find the average of the two. c. Mode is the number that appears the most frequently. d. Range is the largest number minus the smallest number. 14. b. Describe the center, spread, shape, outliers, gaps and clusters from the graph. Center: between $1 and $2 Spread: $0 - $10 Shape: Right Skewed Gaps: From $7 - $9 Clusters: From $0 to $6 and $10 Outliers: $10 # 19 Ojive Extra Practice Relative Cumulative Frequency Distribution Finding Relative Frequency Class Frequency 40-44 2 45-49 6 50-54 13 55-59 12 60-64 7 65-69 3 Total 43 AP Statistics, Section 1.1, Part 4 28 Finding Relative Frequency Class Frequency Relative Frequency 40-44 2 2/43=4.7% 45-49 6 6/43=14.0% 50-54 13 13/43=30.2% 55-59 12 12/43=27.9% 60-64 7 7/43=16.3% 65-69 3 3/43=7.0% Total 43 AP Statistics, Section 1.1, Part 4 29 Finding Cumulative Frequency Class Frequency Relative Frequency Cumulative Frequency 40-44 2 2/43=4.7% 2 45-49 6 6/43=14.0% 8 50-54 13 13/43=30.2% 21 55-59 12 12/43=27.9% 33 60-64 7 7/43=16.3% 40 65-69 3 3/43=7.0% 43 Total 43 AP Statistics, Section 1.1, Part 4 30 Finding Relative Cumulative Frequency Class Frequency Relative Frequency Cumulative Frequency Relative Cumulative Frequency 40-44 2 2/43=4.7% 2 2/43=4.7% 45-49 6 6/43=14.0% 8 8/43=18.6% 50-54 13 13/43=30.2% 21 21/43=48.8% 55-59 12 12/43=27.9% 33 33/43=76.7% 60-64 7 7/43=16.3% 40 40/43=93.0% 65-69 3 3/43=7.0% 43 43/43=100% Total 43 AP Statistics, Section 1.1, Part 4 31 Percentiles Class Relative Cumulative Frequency 40-44 2/43=4.7% 45-49 8/43=18.6% 50-54 21/43=48.8% 55-59 33/43=76.7% 60-64 40/43=93.0% 65-69 43/43=100% It is easy to see the percentiles at the breaks. “A 64 year old would be at the 93rd percentile.” What do you do for a 57 year old? Total AP Statistics, Section 1.1, Part 4 32 Ogives (o-JIVE) or “Relative Cumulative Frequency Graph” Class Relative Cumulative Frequency 40-44 2/43=4.7% 45-49 8/43=18.6% 50-54 21/43=48.8% 55-59 33/43=76.7% 60-64 40/43=93.0% 65-69 43/43=100% Total 33 AP Statistics, Section 1.1, Part 4 Bill Clinton was 46 years old when inaugurated. He falls in the 10th percentile. Means: 10% of all US presidents were the same age or younger than Bill Clinton when inaugurated. What age corresponds to the 60th percentile? 57 years Means: 60% of all presidents were 57 years or younger when inaugurated. What is the center of the distribution? 50%-56 years Review Data Categorical Places individuals into groups Quantitative Created numerical values Ex. Male or female Ex. Price Color Religion **Year Height GPA **Age Discrete •Can be counted •# of children in a family •# of students in a class Continuous •Can assume all values b/w any 2 specific values. Obtained my measuring. •Temperature •Height •Weight Graphs Categorical: Bar Graph Circle Graph Quantitative Dot Plot-Small # of data Spread Outliers Stem Plot-Small # of data Center Histogram-Larger # of data Shape Ojive tells us what percentile an individual falls into. Time Plot plots variables against time. Time is always on the horizontal axis. 2 Quantitative variables-scatterplot 2 categorical variables-side by side bar graph