Stat Unit 1

Unit 1 Review: Exploring Data

Amit Morar

Kiran Rao

Vincent Lu

Vocabulary

Key Topics covered in this Chapter

Important Formulas

Calculator Key Strokes

Section 1.1

Example Problems

• Dot Plots/ Histograms: Stat, Enter, Input Data L1, Input Data L2, 2nd, Y=, Enter, On, Switch Type to Histogram, Graph
• Time Plot: Stat, Enter, Input data L1, Input Data L2, 2nd, Y=, Enter, On, Switch Type to Time Plot, Graph
• Five Number Summary: Stat, Enter, Input Data L1, Input Data L2, Stat, Calc, 1-Variable Stats
• Box Plots: Stat, Enter, Input Data L1, Input Data L2, 2nd, Y=, Enter, On, Switch Type to Box Plot, Graph.

• Construct a stem-plot given the following glucose levels in patients ages 20-50:

141 158 153 134 95 96 78 148 172 200 271 103 172 359 145 147 255

• Describe the distribution of the data (SOCS)
• Construct an Ogive graph
• With the graph, what percent of glucose levels were between 90 and 130
• What relative cumulative frequency is associated with a blood glucose level of 140?

Relative cumulative frequency graph

i)Relative frequency: Divide count by total frequency. Multiply by 100 to convert to a percent.

ii)Cumulative frequency: Add the counts in the frequency column that fall in or below the current intervals.

iii)Relative cumulative frequency: Divide entries in cumulative frequency column by total frequency.

•Mean- add values of observations and divide by the number of observations.

•Median- Arrange observations from smallest to largest. If n is odd, median=center observation in list. If n is even, median=average of two center observations in list.

•Range-Difference between largest and smallest observations.

•Five-number summary- Min Q1 M Q3 Max

•Finding outliers: Is an outlier if it is smaller than Q1-(1.5 x IQR) or larger than Q3+(1.5 x IQR).

•IQR= Q3 – Q1

•Variance-

s^2= (x1-mean)^2 + (x2-mean)^2 + ... + (xn-mean)^2/(n-1)

•Standard Deviation- Square root of the variance

• Analyzing Statistical Variables
• Displaying Distributions
• Analyzing Distributions
• Constructing Various Graphs:
• Time Plots, Dot Plots, Histograms, Stem Plots, Box Plots, Pie Charts, and Bar Graphs
• Measuring the Center and Spread of a distribution
• Linear Transformations
• Comparing Distributions
• Five Number Summary

The Big Idea

•Distribution- tells us what values a variable takes and how often it takes these values.

•Bar graphs and pie charts display the distributions of categorical variables. Use counts or percents.

•Stem plots and histograms display the distributions of quantitative variables. Stem lots separate each observation into a stem and a one-digit leaf. Histograms plot the frequencies (counts) or percents of equal-width classes of values.

•Shape- symmetric, skewed. Number of modes (major peaks) is another aspect of overall shape

•Center-mean and median. Mean=average. Median=midpoint of the values.

•Using median to indicate center of a distribution: describe spread using quartiles.

•First Quartile Q1 has about ¼ of observations below it, third quartile Q3 has about ¾ of observation below it.

•Spread-variance (s2) and standard deviation (s) are common measures of spread about the mean as center.

•Deviations

•Outliers-observations that lie outside the overall pattern of a distribution.

•Relative cumulative frequency graph (ogive) is a god way to see the relative standing of an observation.

•Time plot-graphs time horizontally and values of variable vertically. Reveals trends or other changes over time.

•Five-number summary consists of the median, the quartile, and the max and min. Provides quick overall description of distribution. Median describes center, quartiles and extremes show spread.

•Boxplots (based on five-number summary)- useful for comparing two or more distributions.

•Median is a resistant measure of center because it is relatively unaffected by extreme observations. The mean is nonresistant.

•Linear transformations-used for changing units of measurements. Have the form xnew = a + bx.

•Back-to-back stemplots and side-by-side boxplots are useful for comparing quantitative distributions.

Helpful Hints

Section 1.2

A school system employs teachers with a salary between $30,000 and $60,000. The teachers want a raise of $1,000 given to every teacher.

• How much will the mean and median salary increase?
• How will this change affect the spread of the data?
• What will this change do to the standard deviation of the data?

• When constructing a stem plot, remember, stem plots do not work well for large data sets because each stem will have a lot of leaves.
• Use a pie chart to emphasize a categories relationship to the entire data set
• When constructing a histogram, make sure that each bar width is the same, and choose a scale that helps to display each bar equally
• When analyzing distribution do not forget to use SOCS- Shape, Outlier, Center, Spread
• Remember, outliers are based on judgment, so when looking for outliers, look for points that are in the extremes in either direction
• The mean is a non-resistant measure, meaning it will fluctuate depending on a few extreme observations
• When graphing quantitative variables, use either a bar graph or a pie chart, when graphing categorical variables use either a time plot, histogram, stem and leaf plot or box plot.

• Unit 1 covers analyzing and interpreting the distributions and graphs of data.
• It shows all the different types of graphs and charts as well as when to use them with quantitative or categorical data
• This unit also shows how to interprets the graphs using numbers and words (SOCS) and finding the mean, median, and quartiles of certain graphs.

Graphs

Pie Chart

Bar Graph

Time Plot

Histogram

Box Plot

Stem and Leaf Plot