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Unit 1.1 Investigating Data 1

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Frequency and Histograms CCSS: S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). Also N.Q.1 2

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Types of Data Graphs Dot Plots Frequency Tables Histograms Box-and-whisker plots 2-way tables 3

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Dot Plots One dot represents one occurrence of the item. Sometimes an X is used instead of a dot. These plots are sometimes called line plots. 4

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Creating a Dot Plot Find the least and greatest value in a data set. Use these values to draw a number line. For each piece of data, draw a dot above the number line that corresponds to the data. 5

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Frequency Tables Frequency tables show the number of times something occurs in a given interval. From this chart, we don’t have individual data, just numbers in each group. 6

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Histograms Data is continuous numerical data (range). Bars touch each other. 7

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Histograms Bar graph used to display the frequency of data divided into equal intervals Bars must be equal width and should touch, but not overlap 8

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Steps to Make a Histogram Make a frequency table Use scale and intervals from table Draw a bar for the number in each interval Title the graph and label axes 9

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Shape of Histograms 10

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Measures of Central Tendency and Dispersion CCSS: S.ID.2 Use statistics appropriate to the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Also S.ID.3, N.Q.2 11

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Measures of Central Tendency Central tendency – where the “center” of the data is. Mean ( )– numerical average of the data Mode – most frequent number in the data Median – middle number of the data if put into numerical order from lowest to highest 12

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Measures of Dispersion Dispersion - How spread out the data is. Range – difference between the maximum value and minimum value of the data Standard deviation – measure of how values in a data set vary (deviate) from the mean. 13

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Standard Deviation Symbol: σ Calculation: 1.Find the mean of the data 2.Find the difference of each item from the mean. 3.Square the differences. 4.Find the average of the differences. 5.Take the square root. 14

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Example of Calculating Std. Dev. Data : 12.6, 15.1, 11.2, 17.9, 18.2 X X-barX – (X-bar)(X – X-bar) 2 12.6 15 15.1 15 11.2 15 17.9 15 18.2 15 Average of the difference of the squares: Square root of the averages (σ): Note: x-bar stands for the mean of data 15

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Interpreting the Standard Deviation As the data becomes more widely distributed, the standard deviation increases. A small standard deviation means that the data are clustered tightly around the mean. 16

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Box-and-Whisker Plots CCSS: S.ID.2 Use statistics appropriate to the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Also N.Q.1, S.ID.1 17

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Box-and-Whisker Plot Graph that summarizes a set of data by displaying it along a number line. It consists of a box and two whiskers. 18

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Box-and-whisker Plot Comprised of 5 numbers (sometimes called the 5-number summary): Min – minimum value (left whisker) Q1 – median of lower half of data (left side of box) Median (Q2) (middle line) Q3 – median of upper half of data (right side of box) Max – maximum value (right whisker) 19

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Quartiles Quartiles – values that divide a data set into 4 equal parts. The middle half of the data (Q3 – Q1) is called the interquartile range or IQR. (contained in the box) From Min to Q1 – 25% of data From Q1 to median – 25% of data From Median to Q3 – 25% of data From Q3 to Max – 25% of data 20

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Interpreting Box Plots Shows middle of data, range (spread) of data, extreme values. Does not show individual data or mean (average). Outlier – a data value that is much higher or much lower than other values in the data set. Percentile rank – percent of data values that are ≤ that value. 21

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Two-way Tables CCSS: S.ID.5 Summarize categorical data for two categories in two- way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). 22

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2-way Tables Way of organizing data to show data that pertain to two different categories. Can find the conditional probability of events occurring. 23

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2-way Tables (cont’d) 1.What is the probability that if a student plays a sport, he also takes a foreign language? 2.What is the probability that if a student doesn’t take a foreign language, she doesn’t play a sport? 3.What is the probability that a student doesn’t take a foreign language? 24

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More 2-way tables 1.What is the probability that a student has a MP3 player? 2.What is the probability that if a student doesn’t have an MP3 player, he has a cell phone? 3.What is the probability that if a student doesn’t have a cell phone, he has a MP3 player? 25

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