# Psst … you should have started the Do Now!

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STATISTICS REVIEW copy down this data : heights of Ms. Gs homeroom students: 65676063 6563 6364 65737166 69607465. Psst you should have started the Do Now!. Column graphs, frequency tableS , Frequency histograms. 10 min lesson, 5 min exit slip. - PowerPoint PPT Presentation

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STATISTICS REVIEW

Psst you should have started the Do Now!STATISTICS REVIEW

copy down this data: heights of Ms. Gs homeroom students:

6567606365636364657371666960746510 min lesson,5 min exit slipColumn graphs,frequency tableS,Frequency histogramsSTEP 1: FREQUENCY TABLE (variable x, freq. y)HeightFrequency602633641654661671691711731741Column graphs measure discrete data!STEP 2: COLUMN GRAPHColumn graphs measure discrete data!ProsSuper easy to make

Easy to readEven for middle schoolers!

Abundantly clearConsCan take a long time

Hard to see trends for groups of data (for example, is it coincidence or important that only 1 person is 64?)PROS and CONS of column graphsSTEP 1: Make a Frequency Table with IntervalsFrequency histograms measure continuous OR GROUPED data!Height Interval (inches)Frequency60 - 62263 - 65866 - 68269 - 71272 - 7425 is the ideal number of intervals!The intervals have to be equal in size!

(Here, I have five intervals with 3 in. each!)STEP 2: Make a Frequency Histogram with IntervalsFrequency histograms measure continuous OR GROUPED data!The bars have to be equal width and touch each other!Column GraphsStart with freq. tableList every answerWrite down frequency

Draw the column graphBars do NOT touchBars have equal widthFrequency HistogramsStart with freq. table5 intervals of equal widthFrequency is per group

Draw the histogramBars touch (covers all possible data)Bars have equal widthRECAP and Compare/contrastMisty asked Mr. Caines homeroom how many hours they typically slept on a Friday night. Here were their responses:

445666778899910101012

Make a frequency table for this data.

Sketch a column graph for this data.

Make a frequency table with intervals of 2 hours each (e.g., 4-5 hours) for this data.

Sketch a frequency histogram for this data.

EXIT SLIP: COLUMN GRAPHS & HISTOGRAMSAnswers are on the next slide!! (No room here)Make a Frequency TableSketch a Column GraphEXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMS(c) And (d) are on the next slide ran out of room!Sleep (Hours)Frequency425163728293103121Make a Frequency Table with Intervals (group)Sketch a Frequency HistogramEXIT SLIP ANSWERS: COLUMN GRAPHS & HISTOGRAMSSleep Time (hours)Frequency4 536 758 9510 11312 - 1318 min lesson,3 min exit slipMEAN,Median,Mode,standard deviationMean measures the expected value.

Add them up!All the answers times the frequency of each answer.Called x-bar shows up as the mean on your calculator in One-Var StatsNumber of terms/answersTRY OUT MEAN with the formula!_______

Height in inches (xi)FrequencyProduct (fixi)60212063318964164654260661666716769169711717317374174SUM1610531053/16 = 65.8 (5 5.8)But what about MEAN for groups?? ___

1054/16 = 65.9 (5 5.9)Thats Easy! Just pick the middle of the interval as xi!Height (in.)Frequencyxi (interval) fixi60 - 6226112263 - 6586451266 - 6826713469 - 7127014072 - 74273146SUM16n/a1054STEP 1 of 1: Find the one that happens most often!MODE is the most common! ( la mode)The mode height for the homeroom is 65 (5 5).STEP 1/1: Find the modal class (happens most often).What about mode in groups?The modal class for homeroom height is 63 65.STEP 1: Put all the data in order.Median tells us the middle!We have two: (65 + 65)/2. Our mode is 65!6060636363646565656566676971737460606363636465656565666769717374STEP 2: Find the one in the middle. If you have two, average them.STEP 1: Enter height data into list 1.STANDARD DEVIATIONSelect STAT -> CALC -> ONE-VAR STATS(if you had a frequency list, you could actually put it into list 2, then put frequency = L2 on the stats screen)

Standard Deviation is the one thats baby sigma x: 65676063656363646573716669607465

Use the calculator! X = L1, Frequency = L2!HeightFrequency602633641654661671691711731741Try it all quickly with the Freq table!Mean ( )= 65.8, Median= 65, Mode= 65, SD ( )= 3.99

Misty asked Mr. Caines homeroom how many hours they typically slept on a Friday night. Here were their responses:

445666778899910101012

Find the mean.

Find the median.

Find the mode.

Find the standard deviation.

EXIT SLIP: mean, median, mode and standard deviationMean = 7.65 hoursMedian = 8 hoursTechnically no mode: 6, 7 and 10 all happen the most.Standard Deviation = 2.22 hours5 min lesson,7 min exit slipCumulative frequencyCumulative frequency shows data you have accumulated thus far!HeightFrequencyCumulative Frequency60226335641665410661116711269113711147311574116Add a new column: In it, add up the frequencies so far.Cumulative frequency shows data you have accumulated thus far!Plot the variable as x, and cumulative frequency as y.Connect the dots with a smooth curve.Cumulative frequency shows data you have accumulated thus far!Use the graph to find the 75th percentile height.

67Answer:75% of students in Ms. Griffiths homeroom are 67 (5 7) or shorter.Misty asked Mr. Caines homeroom how many hours they typically slept on a Friday night. Here were their responses in a frequency table:

445666778899910101012

Make a cumulative frequency table.

Sketch a cumulative frequency graph.

What is the 25th percentile for # hours of sleep?

Complete this sentence using (c): 25% of students in Mr. Caines homeroom typically sleep ___ hours or fewer on Friday nights.

EXIT SLIP: Cumulative frequencyCumulative Frequency TableHrs SleptFreq.Cum. Freq.422513636728821093131031612117EXIT SLIP: Cumulative frequency25th percentile means 0.25 * 17 = 4.25 students. Follow the line!

25% of students in Mr. Caines homeroom typically sleep 5.5 hours or fewer on Fri. nights.Misty asked Mr. Caines homeroom how many hours they typically slept on a Friday night. Here were their responses in a frequency table:

445666778899910101012

Make a cumulative frequency table.

Sketch a cumulative frequency graph.

What is the 25th percentile for # hours of sleep?

Complete this sentence using (c): 25% of students in Mr. Caines homeroom typically sleep ___ hours or fewer on Friday nights.

EXIT SLIP: Cumulative frequency2 min lesson,3 min exit slipFlash Section 1:Statistics vocabDiscrete Data you count, or data that has been roundedExamples: Shoe size, number of people, number of trees, clothes size

Continuous Measured data, can take more decimal placesExamples: Height, weight, length, distance, speed

Outlier Data far away from the main body of data.Formal definition: data more than 3 std dev away from the meanExample: Sheldon in Big Bang Theory in terms of IQ

Parameter The variable when were talking about populationExample: Average height of IDEA Donna seniors, average income of US

Statistic The variable when were talking about the sampleExample: Average height of the 15 people I happened to askMain vocab words missedPossible answer choices:A OutlierC StatisticE DiscreteB ParameterD Continuous

Height is an example of a continuous (D) variable because I measure to get the data.An outlier (A) is a datum that lies outside the standard, middle group of data.If I asked every single US resident his or her age and found the mean, I would have a parameter (B) .Shoe size is a discrete (E) variable because only certain sizes exist.If I asked a sample of Texas residents their income and found the average, I would have a statistic (C) .FLASH EXIT SLIP - VOCAB!!! 3 min lesson,3 min exit slipFlash Section 2:Box plotsSTEP 1: Enter data into calculator (L1) and find the quarters!(0%, 25%, 50%, 75%, 100% aka min, Q1, med, Q3, max)Boxplots 10160606363636465656565666769717374Min = 60, Q1 = 63, Med = 65, Q3 = 68, Max = 74STEP 2: Make the Boxplot: Scale, Dots, Box, Connect!

Misty asked Mr. Caines homeroom how many hours they typically slept on a Friday night. Here were their responses in a frequency table:

445666778899910101012

Find the following:Min = 4Q1 = 6Med = 8Q3 = 9.5Max = 12

EXIT SLIP: Box plots

I got to go to the moon because I did my stats study guide! It made me smarter!