Example **What** range of scores **is** **in** the middle 40% of male **math** scores? **What** range of scores **is** **in** the middle 80% of female **math** scores? SAT Critical ReadingMathematicsWriting μσμσμσ Males498116532119481115 Females493112499113494112 Example **What** **is** the percent of females who scored between 500 and 600 **in** critical reading? **What** **is** the percent of males who scored between 550 and 600 **in** writing? **What** **is** the percent of females who scored between 400 and 600 **in** **math**? **What** percent of/

Foundations of **Math** I: Unit 3 - **Statistics** Arithmetic average **Median**: Middle of the data listed **in** ascending order (use if there **is** an outlier) Mode: Most common number (can be more than one number or no numbers) Mean/following numbers make the five number summary: 275, 785, 560, 435, 380 1)**What** **is** the **median**? 1. ______________ 2)**What** **is** the maximum? 2. ______________ 3)**What** **is** the maximum? 2. ______________ 4)**What** **is** the IQR?3. ______________ 5)**What** percentage of data values are above 560? A. 25%B. 50%C. 75/

just fine." Did you hear about the statistician who put her head **in** the oven and her feet **in** the refrigerator? She said, "On average, I feel just fine." **What** **is** **statistics**? Answering questions by gathering, analyzing, and making decisions about data –We analyze data by organizing it into displays and by computing **statistics** (numbers that represent the data). –Based on our analysis, we make decisions/

**what**? Historical Perspective 1662- Natural and Political Observations upon the Bills of Mortality, John Gaunt Early applications of **statistical** thinking were based on the needs to determine policy using demographic and economic data and broadened **in** the 19 th Century to apply generally **Statistics** was/**is**/M & M There are several sets of 5 positive whole numbers with the following properties Mean=4 **Median**=3 Mode=3 http://nrich.**maths**.org/6267 M, M & M There are several sets of 5 positive whole numbers with the /

equal parts. The **median** **is** a quartile and divides the cases **in** half. 25 th percentile **is** a quartile that divides the first ¼ of cases from the latter ¾. 75 th percentile **is** a quartile that divides the first ¾ of cases from the latter ¼. The interquartile range **is** the distance or range between the 25 th percentile and the 75 th percentile. Below, **what** **is** the interquartile range? 0/

**median** **is** half way between them. www.mathsrevision.com Mode : The value that occurs the most **in** a set of data. Can be more than one value. Quartiles : The **median** splits into lists of equal length. The **medians** of these two lists are called quartiles. 31-Mar-17 Created by Mr Lafferty **Maths** Dept Created by Mr Lafferty **Maths** Dept **Statistics**/to study how many houses had an alarm system **in** a particular area. Results are given below **What** **is** the probability that a house **is** alarmed ? 0.4 Number of Alarmed Houses /

The Right Questions about **Statistics**: How hypothesis testing works **Maths** Learning Centre The University of Adelaide A hypothesis test **is** designed to DECIDE the answer to a YES OR NO question using DATA. You calculate whether your data **is** likely or unlikely given a particular answer. **Is** the **median** number of chapters **in** a novel = 20? Randomly choose 12 books That’s too hard. So let’s turn/

Graphs - **Maths** **is** Fun Cumulative Tables and Graphs - **Maths** **is** Fun Standard Deviation Worksheet – TES Standard Deviation Worksheet – TES Cumulative frequency and boxplots lessons – TES Cumulative frequency and boxplots lessons – TES **Median**, quartiles and boxplots worksheet - TES **Median**, quartiles and/to Routemap Return to Routemap Subject content: Online resources: S4.1 understand **what** **is** meant by the term ‘population’ **in** **statistical** terms S4.2 developing ideas of sampling to include the concept of /

must set the premium for such customers above the mean **in** order to make a profit. Probability and **Statistics** for Teachers, **Math** 507, Lecture 3 **Statistical** Interlude Examples of summaries that do or do not work Summarizing ACT scores with the mean seems less useful; it **is** unclear **what** information we learn from it. **In** this case the **median** gives us a clearer picture, letting us know the/

, 5, 5, 4, 6, 8, 7, 6, 6 Draw cubes to represent this data set. **What** **is** the **median**? the mean? Rearrange the cubes **in** your drawing to represent possible data sets for the following. You may add or remove cubes. Record each data/ 2007 20 items on **Statistics** and Probability School Year: Monthly PD sessions 16 hours Grades K–7 **Math** Teacher Leaders 12 hours Grades 8–9 **Math** Teacher Leaders About 200 Teacher Leaders Posttest: May/June 2008 20 items on **Statistics** and Probability Diagnostic Mathematics Assessments/

**Statistics**, Centre for Mathematical Sciences, Lund University. hb@**maths**.lth.se Slides available @ http://www.**maths**.lth.se/bioinformatics/calendar/20031113/ 2 of 40 Why not R? Currently there are no good image analysis packages. Matlab **is**/at http://www.r-project.org/ http://www.r-project.org/ Find **what** you want. Dirt simple to install package! At the Centre for /linear model (iv) 4. Investigate fitted line **in** detail: > summary(fit) Call: lm(formula = y ~ x) Residuals: Min 1Q **Median** 3Q Max -8.2449 -1.3234 0./

. Those who want a higher starting salary. BS: **median** $40’s MS: **median** $60’s PhD: **median** $80’s Those who enjoy college, studying, etc. **What**? Biostatistics vs. **Statistics** Biostatistics – **statistical** methods applied to health related problems. **Statistics** – more broad-based methodology applied to a wider variety of areas. **What**? Biostatistics vs. **Statistics** Biostatistics – there **is** critical shortage of biostatisticians, demand **is** high! **Statistics** – they can get biostatistics jobs and other jobs/

0029 # Progression segments 0.0068 **Median** Turn Radius (scaled) 0./35 States **in** US # of comparisons 35*(35-1)/2 = 595 **What** should /**in** **statistics**.Towards the end of the previous century “Multiple comparisons” has been viewed as a narrow field of marginal importance **in** **statistics**. By the turn of the century this **is** no longer the case. “Multiple comparisons” has become a cornerstone **in** the bridge between traditional **statistical**/", presented at "**Math** Challenges of the 21st Century", Los Angeles, August/

outliers, all the numbers are generally close to one another. e)**What** percentage of families have 5 or fewer people **in** them? Discrete NumberFrequency 32 44 54 65 72 83 92 101 21% Continuous Data Mean, Mode, Range, **Median** Mean, the average - Mode, most often – Range, subtract the smallest from the largest. **Median**, the middle number, When they’re lined up – From the greatest/

**in** a **statistically** meaningful way. 4. District Data From New Mexico Public Education Department Graduation RatesDistrict20122011 3/8/11 **Math**/Reading SBA ExamDistrict20132011 5. Census Data: County and Tract Population2007-112010 **Median**/NM PED. Standards Based Assessment (SBA), 2011-2012, 2012-2013. Note: Percentage change **is** the change between years as a percentage of the 2011-2012 proficiency rate. 3 rd /%11%15.7%15%16.2% I often do things without thinking about **what** will happen 48.8%32.7%40.1%44.2%41.9% My /

Probability Geometric Probability Some probability questions **in** the **math** section may involve geometric figures. Some probability questions **in** the **math** section may involve geometric figures. Example: Example: The large circle has a radius 8 and small circle has radius 2. If a point **is** chosen at random from the large circle, **what** **is** the probability that the point chosen will be **in** the small circle? The large circle/

understand **statistics**. **In** general, most people do not understand **statistics**. Hypothesis: Student A has a school average of 10% Hypothesis: Student A has a school average of 10% Conclusion: Student A **is** a bad person. Conclusion: Student A **is** a bad person. The **statistic** does not measure the person’s goodness or badness. The **statistic** does not measure the person’s goodness or badness. **What** does that **statistic** mean? **What**/

**in** a set of **statistical** calculations. Descriptive **statistics** summarize sets of information. Descriptive Stats cont’d Examples –Central Tendency (mean, **median**, mode) –Variability –Shape of Distributions –Relations (Correlation) We’ll discuss each of these **in** turn **What** are measures of central tendency? Each **is**/ to the mean, and some scores more spread out. Assumption sometimes violated Example: Give a middle school-level **math** test to 6- year-olds and to 18-year-olds. Result will not be a normal curve; rather,/

histogram presents the scores a group of students received on a **math** test. Use the histogram and choose the best analysis of the/**in** the 10 tallest buildings **in** San Francisco: 48, 52, 48, 43, 48, 40, 45, 45, 43, 43. **What** **is** the **median** and mode of the data? 2-7 **Median**, Mode, and Range Lesson 7 Ex1 **median**: 40, 43, 43, 43, 45, 45, 48, 48, 48, 52 2-7 **Median**, Mode, and Range 45 **is** **in**/team are: 50 **in**, 52 **in**, 48 **in**, 58 **in**, and 52 **in**. Find the **median**. A.58 **in** B.50 **in** C.48 **in** D.52 **in** 2 2 **Statistics** and Data Analysis /

**in** Modern Mathematics, 7e: 14.3 - 13Copyright © 2010 Pearson Education, Inc. **In** spite of his consistent overspending, Billy’s average monthly balance for the year **is** $26 (check it out!). This average hides the true picture of **what** **is** going on. Billy **is**/ SAT **Math** Scores: Part 2 Excursions **in** Modern Mathematics, 7e: 14.3 - 40Copyright © 2010 Pearson Education, Inc. **Medians**, quartiles, and general percentiles are often computed using **statistical** calculators or **statistical** software packages, which **is** all well/

Warm Up Lesson 22, Analyzing and Comparing **Statistical** Graphs PROBABILITY AND **STATISTICS** Vocabulary Bar graphs: use vertical or horizontal bars to represent data Double bar graph: shows groups of two bars side by side **in** order to compare sets of data Stem and leaf plot: data / the scores of students on a **math** test. a.**What** was the lowest score? b.**What** was the highest score? c.**What** score appeared most? d.**What** **is** the **median** score? e.How many students took the test? Stem Leaf Scores on **Math** Test 2 6 7 8 9 /

of Central Tendency: numbers that represent the middle Arithmetic average **Median**: Middle of the data listed **in** ascending order (use if there **is** an outlier) Mode: Most common number (can be more than one number or no numbers) Mean ( x ): Foundations of **Math** I: Unit 3 - **Statistics** Standard Deviation (σ x, S x ): Measure of variation or distance from mean value. Measures of Spread: Standard Deviation/

. The numbers and prices of meals sold at a restaurant are represented **in** the graph. Number of Meals Sold Price of a Meal (**in** dollars) Based on the information **in** the graph: a)**What** **is** the mean price of all of the meals sold? b)**What** **is** the **median** price of all the meals sold? c)**What** **is** the total number of meals costing more than 7 dollars? $7.24/

Spread – range, interquartile range, standard deviation S-ID.2 Use **statistics** appropriate to the shape of the data distribution to compare center (**median**, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Measures of Center **What** **is** the typical value? Investigation 2: Finding the **Median** Investigation 3: Experimenting With the **Median** Name Number of Letters Pete Thomas 10 Shaquana Smith Stewart/

**What** **is** the relative error of your measurement? OTHER DISTRIBUTIONS of a single variable Normal or symmetric Right Skewed Left Skewed Rare Bimodal Fat tailed Distributions The distribution of scores or values can also be displayed using Box and Whiskers Plots and Frequency Histograms BOXPLOT (BOX AND WHISKER PLOT) **MEDIAN**/average of ONE VARIABLE between two groups to see if there **is** a **statistical** difference. eg. Do 8th-grade boys and girls differ **in** **math** test scores? or Does the outcome measure differ from a /

1 to Q 3, and draw a line **in** the box at the **median**. (4)Draw lines extending outward from the//CalculatorInstructions.doc http://staweb.sta.cathedral.org/departments/**math**/mhansen/public_html/y2kstat/handouts/testrevw.htm 387 Biometrics STAT/**in** Multinomial Experiments: Example1 Calculate the expected cell counts: E i = np i = 300(1/6) = 50 Upper Face123456 OiOi 503945626143 EiEi 50 Test **statistic** and rejection region: Conclusion: There **is** insufficient evidence to indicate that the die **is** biased. **What** **is**/

strata, our predictions differ by about 7 points. **In** general, the ESL gap **is** related to SES, such that the gap **is** greater when SES **is** greater. Our interaction **is** about as simple as it gets, but even **in** this case, the graph communicates instantly **what** the **math** fails to communicate **in** ten minutes of studying. **In** order to see the interaction **in** a graph, one of the main effects should/

**What** kinds of snacks do you like? How much do our backpacks weigh? How much candy do we eat each week? **Statistics** **In** today’s fast changing and moving computer age we collect vast quantities of data **Math** **is** concerned with how data **is** collected, organized, presented, summarized and then analyzed **Statistics** **Statistics** **is**/ 6 6 6 7 7 7 7 8 8 10 n= 15, (n+1)/2 = 8, the **median** **is** the 8 th data value Then the **median** =6 peas Exercise for **Median** Find the **median** for the following data set: 3,6, 5, 7, 7, 4, 6, 5, 6, 7, /

of the relationship of the information. Essential Questions: How are the mean, **median**, and mode helpful **in** understanding data **in** real-world situations? Why **is** it important to keep data related to a real-world context when answering a **statistical** question? Standards for Mathematical Practice: 1.Make sense of problems and persevere **in** solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique/

Data analysis and basic **statistics** KSU Fellowship **in** Clinical Pathology Clinical Biochemistry Unit 2015 - 2016 Objectives Understand the main concepts of **statistical** data analysis. Have a knowledge about the basic **statistic** techniques: Measures of location. Measures of variability. Hypothesis testing. Student’s t-test. Chi-squared test. Preface This presentation focuses on the most common techniques for **statistical** data analysis. **What** does **Statistics** mean? **Statistics** **is** defined as a science/

the study of triangles **in** **Math** 2, students will verify the properties of the centers of triangles and parallelograms. **Statistics** & Probability A **statistical** process **is** a problem-solving process consisting of four steps: 1.Formulating a **statistical** question that anticipates variability / bisectors of the sides of the triangle **is** called the CIRCUMCENTER of the triangle. 16 Origami Geometry Points to Ponder ! – **Medians** o Look at the triangle featuring the **Medians**. **What** do you notice about all three of /

**is** also a very good chance our heads would explode. **Statistical** Diagrams – if they are done properly - present those figures **in** a clear, concise, visually pleasing way, allowing us to make some sense out of the figures, summarise them, and compare them to other sets of data. 1. **What** **is** Cumulative Frequency? Cumulative **is**/ up with estimates for the **Median** and the Inter-Quartile Range **Median** As you hopefully remember, the **Median** **is** the MIDDLE value. To find it we: 1. Work out **what** **is** 50% of our total frequency/

Mr. Plum’s **math** class of 25 students had an average of 85 on the Chapter 1 test. Miss Scarlet’s class of 22 students had an average of 89 on the same test. **What** would the average be/**What** **is** the **median** salary? How could an unethical recruiter use **statistics** to mislead prospective employees? 4) Faculty salaries at a college have a **median** of $32,500 and a mean of $38,700. **What** does this indicate about the shape of the salary distribution? 5) The mean and **median** salaries paid to major league baseball players **in**/

The Right Questions about **Statistics**: How confidence intervals work **Maths** Learning Centre The University of Adelaide A confidence interval **is** designed to give a RANGE of possible answers for a “**WHAT**’S THE NUMBER?” question, using DATA from a sample. You calculate which numbers could have been likely to produce your data. **What** **is** the **median** number of chapters **in** a novel? Randomly choose 12 books Book# Chapters 1/

boxplot(read ~ socioeconomicstatus, horizontal=TRUE) detach(nelsboys) lm(formula = read ~ low.ses + high.ses) Residuals: Min 1Q **Median** 3Q Max -24.118 -6.723 0.762 7.202 18.598 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept/**Math** Slide 62 Unit 1: Intuitive Representations of the F **statistic**: Technical But Still Verbal Representations of the F **statistic**: Formal Representation of the F **statistic**: **What** **is** a “Mean Square”? For Post Hole 3, we calculate a mean square, and we call it “variance.” **In**/

and applications **What** do you want out of your future career? I want to enjoy my work I want the opportunity to travel and meet interesting people I want to earn LOADS OF MONEY! I want to do something worthwhile Average Hourly Pay Figures from the Office for National **Statistics** show the **median** hourly earnings by qualification level **in** 2010 Why **Maths**? Studying **maths** helps develop/

**What** **is** the height of each person **in** my class? **What** are the **math** test scores of the students **in** my class? How old am I? How many letters are **in** the names of each person **in** my class? **What** **is** my height? How many pets are owned by each student **in** my grade level? How many letters are **in** my name? **What** **is** my **math** test score? Examples of **Statistical**/ Center Vs Variability Center: Summarizes all the values with a single number **Median**: the middle number Mean: the average number Variability: Describes how all the/

**is** your **median**! **What** about a little rhyme?: I don’t know the rhyme I don’t know the riddle I am the **MEDIAN** And I’m **in** the middle! 3. The Mode This **is**/a decision about who has had the better season… that’s why we need **Statistics**! Secondly, just adding up the total amount of runs and deciding that way /the less consistent (brilliant **maths** word that always impresses examiners/teacher) your performance **is**. So, I would argue, because Andrew Flintoff has a smaller range, his performance **is** more consistent, and /

**is** made up of bits of data which can be ‘measured’, ‘recorded’, & ‘analysed’ Interpretation of data can lead to valid insights about how people think, feel and behave **What** do we want to Describe? Distributional properties of variables: Central tendency(ies) Shape Spread / Dispersion Basic Univariate Descriptive **Statistics** Central tendency Mode **Median**/– shape **is** arbitrary Consider/ **in** /**Median** & Mean +vely skewed mode < **median** < mean Symmetrical (normal) mean = **median** = mode -vely skewed mean < **median**/**Statistical**/

**Statistics** Course for **Math** Majors : 1. Minimize prerequisites 2. Teach **what** /**in** the subject percent non-academic jobs **in** the subject **median** non-academic salary **in** the subject Which model(s) are most useful ? C. Methodological Challenges How to “solve” an inconsistent linear system? Stigler, 1990: The History of **Statistics**/**in** model space B. F. Gauss-Markov Theorem: Four Steps plus Pythagoras 1. OLS estimator **is** an LUE 2. LUEs of βj are a flat set **in** n-space 3. LUEs of 0 = error space 4. OLS estimator lies **in**/

CSE component – Thesis with CSE component – Receive “PhD **in** X with a DE **in** CSE” – Details at cse.berkeley.edu Participating Departments / Lattice-Boltzmann Methods – Maximum likelihood, least squares, **median** fitting – Mesoscale atmospheric boundary layer modeling – Monte Carlo/many layers of simulation Econ/EECS/IEOR/**Math**/PoliSci/Stat (9 faculty) – **Statistical** analysis and visualization of large scale heterogeneous/ **is** included Review petitions for exceptions – Dept. rules about Qual Committee members **What** if/

the data **is** skewed, use the following descriptive **statistics**: Min, Q1, **Median**, Q3, Max To describe the distribution of the observed variable. **In** our example, Min=8, Q1=16, **Median**=18, Q3=21, Max=61 The Standard Deviation If a distribution **is** symmetric: Use/ Normal curves provide a simple, compact way to describe symmetric, bell-shaped distributions. SAT **math** scores for CS students Normal curve Money spent **in** a supermarket **Is** the normal curve a good approximation? The area under the histogram, i.e. the /

**Statistics**, 10e © 2006 Prentice-Hall, Inc. Normal Distribution Example (continued) **What** are/**in** 2 **Medians** Test two independent population **medians** Populations need not be normally distributed Distribution free procedure Used when only rank data are available Must use normal approximation if either of the sample sizes **is** larger than 10 Basic Business **Statistics**/**Statistics**, 10e © 2006 Prentice-Hall, Inc. Kruskal-Wallis Example (continued) Do different departments have different class sizes? Class size (**Math**/

zero **math** skills Ratio scale: physical measures (height) and counting; has absolute zero. Groups **What** are descriptive **statistics**? Purpose and examples? Answer the following questions **What** are descriptive **statistics**? Purpose and examples? Why do we look at both – the mean and SD? **What** **is** a correlation? **In** Selection, **what** do we correlate? **What** does a correlation of.8 and a t-value of 7.44 tell us? **What** **is** a normal distribution? **What** **is** **statistical**/

of them that lie within k standard deviations of their mean (where k > 1) **is** at least **What** **is** the minimum percentage of the items **in** a data set which lie within 2, and 3 standard deviations of the mean? /**statistical** measures. The five **statistical** measures are: the lowest value, the first quartile, the **median**, the third quartile, the largest value. the lowest value the largest value 12.4 – Measures of Position Box Plots Example: The following are test scores (out of 100) for a particular **math**/

” Attitudes about **Math** Survey, **Math** Beliefs subscale (also adapted for science) “**Math** **is** one of the most important subjects for my child to study **in** school” Attitudes about **Math** Survey, **Math** Action subscale (also adapted for science) “I encourage my child to take advanced **math** **in** school” Measures of Science Advantage (also adapted for **math**) “Our family **is** interested **in** the science courses my child takes” Parents’ expectations for college “**What** **is** the highest/

my homework? How old am I? Non **Statistical** Variability **Statistical** Variability **What** grade did I receive on my homework? How old am I? How many pets do I have? **What** average grade did all my classmates including myself receive? How old are the students **in** the class? **What** **is** the mode? How many pets do my classmates and I have? **What** **is** the **median**? Terms to Know Mean (Average): Add/

are normally distributed. **What** **is** the chance that a randomly-selected player will weigh less than 250 pounds? AP Stat: **What** **is** the probability that a/Mississippi **in** 2009. Compare the two distributions. Acceptable Prob/Stat Answer: The **median** poverty rate for the southern states **is** approximately 10% which **is** larger than the **median** of /**statistics** **is** like having a super power – you can do things that other people can’t do.” AP Stat Typical **Math** Course / Pre-Requisite Flows (Where the **Statistics** Courses Fit **In**/

**Math** 511: Trends **in** **Math** Education By: Tessa Helstad Scientific Calculators ÒCan be used **in** all 9th-12th grade classrooms ÒGraphing calculators might be more appropriate for 11th and 12th grades Graphing Calculators Required Usage for **Math** Courses Ò Not required for Algebra I or Geometry, but could be explored Ò Algebra II, Pre-Calculus, **Statistics**, and Calculus - buying by students **is**/ 88 to create a box-and-whisker plot. Label all **statistics**: quartiles, **median**, min, and max. Also note the values of the /

Shrink Back to Success ModelBack to **Math** Topics **Math** Strategies Table of Contents Lesson 5 Data Analysis, **Statistics**, and Probability Strategies Average (Arithmetic Mean) Average (Arithmetic Mean **Median** of Large Lists **Median** of Large Lists Elementary Probability/ Integers Example 2 Question: **What** **is** the **median** of 7 consecutive integers if their sum **is** 42? **What** essential information **is** needed? The fourth value **in** a list of seven consecutive integers. **What** **is** the strategy for identifying essential/

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