ccgps advanced algebra unit question: how do we use data to draw conclusions about populations?...
TRANSCRIPT
![Page 1: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/1.jpg)
CCGPS Advanced AlgebraCCGPS Advanced Algebra
UNIT QUESTION: How do we use data to draw conclusions about populations?Standard: MCC9-12.S.ID.1-3, 5-9, SP.5
Today’s Question:How do I represent and compare univariate data?Standard: MCC9-12.S.ID.1
![Page 2: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/2.jpg)
Unit 4Unit 4Day 1 Vocabulary and Day 1 Vocabulary and
Graphs ReviewGraphs ReviewStandards
MCC9-12.S.1D.2 and MCC9-12.S.ID.3
![Page 3: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/3.jpg)
VocabularyVocabulary• Quantitative Data – Data that can be
measured and is reported in a numerical form.
• Categorical/Qualitative Data – Data that can be observed but not measured and is sorted by categories.
![Page 4: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/4.jpg)
VocabularyVocabulary• Center – the middle of your set of data;
represented by mean, median, and/or mode.• Spread – the variability of your set of data;
represented by range, IQR, MAD, and standard deviation.
• Outlier – a piece of data that does not fit with the rest of the data. It is more than 1.5IQRs from the lower or upper quartile, or it is more than 3 standard deviations from the mean.
![Page 5: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/5.jpg)
MeanMeanThe average value of a data set,
found by summing all values and dividing by the number of data points
Example:
5 + 4 + 2 + 6 + 3 = 20
45
20
The Mean is 4
![Page 6: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/6.jpg)
MedianMedianThe middle-most value of a data
set; 50% of the data is less than this value, and 50% is greater than it
Example:
2Q
![Page 7: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/7.jpg)
First and Third First and Third QuartilesQuartiles
The value that identifies the lower and upper 25% of the data; the median of each half.
Example:
1Q 3Q
![Page 8: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/8.jpg)
Interquartile RangeInterquartile Range
The difference between the third and first quartiles; 50% of the data is contained within this range
Example:
3Q 1QSubtract Third Quartile ( ) – First Quartile ( ) = IQR
![Page 9: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/9.jpg)
OutlierOutlier A data value that is much greater than or
much less than the rest of the data in a data set; mathematically, any data less than
or greater than is an outlier
Example:
)(5.11 IQRQ
)(5.13 IQRQ
![Page 10: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/10.jpg)
5-Number Summary5-Number Summary
• A 5-Number Summary is composed of the minimum, the lower quartile (Q1), the median (Q2), the upper quartile (Q3), and the maximum.
• These numbers discuss the spread of the data and divide the data into 4 equal parts.
![Page 11: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/11.jpg)
Box PlotBox Plot
• From a five-number summary, I can create a box plot on a graph with a scale.
• Minimum – left whiskerLower Quartile – left side of boxMedian – middle of boxUpper Quartile – right of boxMaximum – right whisker
• Each portion of the box plot represents 25% of the data.
![Page 12: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/12.jpg)
Box Plot - ExampleBox Plot - Example
2, 4, 4, 5, 6, 8, 8, 8, 9, 10, 11, 11, 12, 15, 17Min: Q1: Med: Q3: Max: Range: IQR:
2 5 8 11 17 17 – 2 = 15 11 – 5 = 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
![Page 13: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/13.jpg)
Box PlotBox PlotA plot for quantitative data showing
the minimum, maximum, first quartile, median, and third quartile of a data set; the middle 50% of the data is indicated by a box.
Example:
![Page 14: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/14.jpg)
Box Plot: Pros Box Plot: Pros and Consand Cons
Advantages:•Shows 5-point summary and outliers •Easily compares two or more data sets •Handles extremely large data sets easily Disadvantages:•Not as visually appealing as other graphs •Exact values not retained
![Page 15: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/15.jpg)
Dot PlotDot PlotA frequency plot for quantitative
data that shows the number of times a response occurred in a data set, where each data value is represented by a dot.
Example:
![Page 16: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/16.jpg)
Dot Plot: Pros Dot Plot: Pros and Consand Cons
Advantages:•Simple to make•Shows each individual data pointDisadvantages:•Can be time consuming with lots of data points to make•Have to count to get exact total. Fractions of units are hard to display.
![Page 17: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/17.jpg)
HistogramHistogramA frequency plot for quantitative
data that shows the number of times a response or range of responses occurred in a data set. Ranges should not have overlapping values.
Example:
![Page 18: CCGPS Advanced Algebra UNIT QUESTION: How do we use data to draw conclusions about populations? Standard: MCC9-12.S.ID.1-3, 5-9, SP.5 Today’s Question:](https://reader035.vdocuments.net/reader035/viewer/2022081501/5697bfee1a28abf838cb9415/html5/thumbnails/18.jpg)
Histogram: Pros and Histogram: Pros and ConsCons
Advantages:•Visually strong•Good for determining the shape of the dataDisadvantages:•Cannot read exact values because data is grouped into categories •More difficult to compare two data sets