displaying and analyzing data...

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Displaying and Analyzing Data (S.ID.1,3) Is the given scenario observational or experiments? 1. You measure bean plants on a farm and record their heights to know how tall plants grow in sunlight. 2. You grow some bean plants on your windowsill and some others in a dark closet and record their heights to study the height of plants in given environments. Types of Distribution: Create a histogram for the given test scores. 1. 2 . 3. Compare and contrast the histograms for the biology classes in histograms above. 4. Create a dot plot for the given data. Describe the shape of the data.

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Page 1: Displaying and Analyzing Data (S.ID.1,3)mrslexismith.weebly.com/uploads/8/4/0/9/84092548/unit_1... · 2018-08-31 · Displaying and Analyzing Data (S.ID.1,3) Is the given scenario

Displaying and Analyzing Data (S.ID.1,3) Is the given scenario observational or experiments? 1. You measure bean plants on a farm and record their heights to know how tall plants grow in sunlight. 2. You grow some bean plants on your windowsill and some others in a dark closet and record their heights to study the height of plants in given environments. Types of Distribution: Create a histogram for the given test scores. 1.

2

.

3. Compare and contrast the histograms for the biology classes in histograms above.

4. Create a dot plot for the given data. Describe the shape of the data.

Page 2: Displaying and Analyzing Data (S.ID.1,3)mrslexismith.weebly.com/uploads/8/4/0/9/84092548/unit_1... · 2018-08-31 · Displaying and Analyzing Data (S.ID.1,3) Is the given scenario

5.

6.

7.

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Investigating Measures of Center (S.ID.2,3) Measure of Center: represents the average of a set of data and can be used to describe the set Mean: Median: Mode: Outliers: 1. What measure of central tendency is affected most by an outlier? What measure of central tendency is best when there is an outlier? Find the mean and median for each data set. 2. 5, 25, 10, 15, 20 3. 1, 7, 3, 2, 6 4. 10, 90, 10, 60, 40, 30 5. Find the median for each data set.

6. Find the mean for each data set.

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7. 8. 9.

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Investigating Spread (S.ID.2,3) Spread (or variability): describes how closely the data points are grouped Standard Deviation: measure of spread, which describes how much individual data points vary from the mean

Compare the variability of the data sets shown by each pair of graphs. 1.

2.

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Find the mean and standard deviation for each data set. Round to the nearest tenth. 3. 1, 2, 2, 4, 6 4. 39, 42, 45, 47, 52 5. -15, 5, 20, 50 6.

7.

8. Keitaro competes in the long jump. The distance, in meters, that he jumped during his most recent meet is shown below. 4.8, 4.8, 4.9, 5.0, 5.1, 5.4 a) Keitaro wants to know how variable his jumps were during the recent meet. Calculate the mean and standard deviation, to the nearest tenth, for Keitaro’s jumps. b) Keitaro’s final jump of 5.4 meters is declared to be a foul at the last minute. The length is not recorded, and he does not get another attempt. Keitaro records this distance as 0.0 meters. Calculate the mean and standard deviation, to the nearest tenth, for the new set. Compare the mean and standard deviation of the new data set with those of the original data set.

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Constructing and Analyzing Box Plots (S.ID.1-3)

Interquartile Range (IQR): measure of spread – middle 50% of data set (Q3-Q1) - better used when data set is skewed First Quartile (Q1): median (M) of first half of data Second Quartile (Q3): median (M) of second half of data Lower Extreme: smallest data value Upper Extreme: largest data value Box-and-Whisker Plot - Box = 50% of data and each whisker = 25% of data

1. Use the box plot to answer the questions.

a) What is the median? b) What is the lower extreme? c) What is the upper extreme?

d) What is the first quartile? e) What is the third quartile? f) What is the IQR?

2. Biologists are studying the weight of Albacore tuna caught off the coast of Washington State. A sample of tuna is taken and their weights, in pounds, are given below. Create a box plot. 36, 22, 41, 18, 36, 27, 31, 38, 25, 29, 22, 34, 48, 20, 12, 19, 35, 32, 41, 50

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3. Music festival A and music festival B each had 100 volunteers. The box plots show the ages of the volunteers at each festival. a) Compare the median ages of the volunteers at the two festivals. b) At which festival do the ages of the volunteers have more variability? Explain. 4. A zoologist recently gathered data on the birth weights of African elephants in various nature preserves. The data show a symmetric distribution. Which measure of variability is likely to describe the zoologist’s data better; standard deviation or IQR? Why? 5. Identify the median price and the IQR of sandwich prices at each shop. If you wanted to buy a sandwich but not spend much money, which shop would you try first? Why?

6. Mrs. Heath visited her aunt in Alaska for the first 10 days of January. She recorded the daily low temperature in degrees Fahrenheit each day: -27, -27, -31, -33, -34, -33, -34, -25, -29, -26 a) Organize the data by displaying them in a box plot. b) Mrs. Heath said, “The weather was very, very cold and did not vary much during the trip.” Is her statement accurate?

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Constructing and Analyzing Two-Way Frequency Tables (S.ID.5) Quantitative Data: involves numbers (temperature, height, cost, population, etc) Categorical Data: values that are names or labels (gender, profession, nationality, etc)

1. Twenty students were asked which type of music they like best. Three boys said hip-hop, four boys said jazz, and two boys said rock. Six girls said hip-hop, one girl said jazz, and four girls sad rock. Use the grid below to create a two-way frequency table for the data.

2. Erika asked ten high school seniors if they owned a car and if they had an after-school job. Her results are shown in the table. Car yes yes no no yes no no yes no yes Job yes no yes yes yes no no yes no yes a) Use Erika’s results to complete the two-way frequency table below.

Car No Car Total

Job

No Job

Total

b) Complete the table below to show relative frequencies for each column in the table you created. Express the frequencies as percentages.

Car No Car Total

Job

No Job

Total

c) Does the two-way relative frequency table show a possible association between owning a car and having an after-school job? Explain. d) Does the two-way relative frequency table show a possible association between not owning a car and having an after-school job? Explain.

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7. The table shows results of a poll of 50 randomly selected students who were asked whethter they prefer to watch hockey or football. a) Probability that a student prefers football,

given they are a boy. b) Probability that a student is a boy,

given they prefer hockey. 8. The table shows the results of a poll of 150 randomly selected middle school students who were asked if they take French or Spanish. a) Probability a student is a 7th grader,

given they take French. b) Probability a student is an 8th grader, given they take Spanish. c) Probability a student takes French, given they are a 6th grader. 9. The table shows the results of a poll of randomly selected juniors and seniors who were asked if they attended prom. a) Probability a student is a junior, given they did not attend prom. b) Probability a student did not attend prom, given they are a senior. c) Probability a student is a junior, given they attended prom. 10. The table shows the fate of the first, second, and third class passengers on the Titanic. a) Probability of being 1st class, given they died. b) Probability of surviving, given being 2nd class. c) Probability of being 1st or 3rd class, given they survived.

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Constructing & Analyzing Scatter Plots, Best Fit, & Correlation (S.ID.6-9) Describe the relationship shown in each scatter plot. 1. The table shows T-shirt sales data for a store one weekend. Create a scatter plot on desmos (enter table). Find the line of best fit (𝑦1~𝑚𝑥1 + 𝑏 𝑂𝑅 𝑦1~𝑎 ∙ 𝑏𝑥1). What is the slope? What does it represent? 2. The lines of fit in the scatter plots are identical. Which line better fits the data in the scatter plot? Correlation Coefficient (r): describes the strength and direction of the relationship between two variables

The value of r is always in the range −1 ≤ 𝑟 ≤ 1 If r is close to 1, the data shows a strong positive correlation If r is close to -1, the data show a strong negative correlation If r=0, the data do not show a linear correlation

3. Describe what each correlation coefficient tells you about the data set. a) r = 0 b) r = 0.250 c) r = -0.895 4. Can a line of best fit help you predict values for variables? 5. How do you know when to use 𝑦1~𝑚𝑥1 + 𝑏 or 𝑦1~𝑎 ∙ 𝑏𝑥1?

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6. The information in the table below shows average temperature in Northern Latitudes. a) Find the line of best fit. b) Estimate the average temperature for a city with a latitude of 25°. c) Find the correlation coefficient. What does this tell us? 7. The information in the table shows the Olympic 500-meter Men’s Gold Medal Speed Skating times since 1980. a) Find the line of best fit. b) Estimate the 500-meter time for the 2012 Olympics. c) Find the correlation coefficient. What does this tell us? 8. The information in the table shows sales for a certain retail department store (in billions of dollars). a) Find the line of best fit. b) Estimate the store sales for the year 2008. c) Find the correlation coefficient. What does this tell us? 9. The scatter plot below shows the number of dollars (in billions) spent on books and maps in the US from 1990 through 1995. a) Find the line of best fit. b) Estimate the amount spent on books in 2005. c) Find the correlation coefficient. What does this tell us?