Unit 1.1 Investigating Data 1. Frequency and Histograms CCSS: S.ID.1 Represent data with plots on...
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Transcript of Unit 1.1 Investigating Data 1. Frequency and Histograms CCSS: S.ID.1 Represent data with plots on...
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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
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Types of Data Graphs
• Dot Plots• Frequency Tables• Histograms• Box-and-whisker plots• 2-way tables
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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.
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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.
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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.
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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
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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
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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
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Measures of Central Tendency
Central tendency – where the “center” of the data is.
Mean ( )– numerical average of the dataMode – most frequent number in the dataMedian – middle number of the data if put into
numerical order from lowest to highest
x
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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.
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Standard Deviation
• Symbol: σ • Calculation:1. Find the mean of the data2. 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.
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Example of Calculating Std. Dev.Data : 12.6, 15.1, 11.2, 17.9, 18.2
X X-bar X – (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
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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.
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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
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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.
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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)
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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
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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.
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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).
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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.
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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?