Unit 2 Worksheet



Unit 4 –from the EOCT study guide Name____________________________

Part 1: Measurable Variables

|Measures of Central Tendency include Median, Mean, and|6.) Would having an outlier affect your |9.) Mr. Storer, the physical education teacher, |

|Mode |a.) median? Y or N |measured the height of the students in his first period|

|1.) 70, 84, 78, 90, 84, 82, 83 |b.) mean? Y or N |class. He organized his data in this chart. |

| |c.) IQR? Y or N | |

| |d.) MAD? Y or N |Height |

|Mean Median Mode | |Frequency |

| |7.) p. 131 | |

| | |42 |

| |Jack’s Tips |1 |

|Which one do we use to calculate your grade? |Jill’s Tips | |

| | |43 |

|Measures of variation/spread include Range, IQR, and |Mon |2 |

|MAD |40 | |

|2.) 70, 78, 82, 83, 84, 85, 90 |40 |44 |

|a.) Find the IQR and make a box and whisker plot | |4 |

| |Tues | |

| |20 |45 |

| |45 |5 |

| | | |

| |Wed |46 |

| |36 |4 |

|b.) What was the range of the data? |53 | |

| | |47 |

| |Thur |2 |

|c.) Find the MAD of the data |28 | |

| |41 |48 |

| | |1 |

| |Fri | |

| |31 | |

| |28 |a. Make a dot plot for the data. |

| | | |

|3.) Which measure of central tendency was the | | |

|quickest to find? |a. Who had the greatest median earnings from tips? | |

| | | |

|Which determinant of variability was the quickest to |What is the difference in the median of | |

|find? |Jack’s earnings from tips and the median of Jill’s | |

| |earnings from tips? | |

| | | |

|4a.) Which determinant of variability requires the | | |

|median? | | |

| | |b. Make a histogram for the data with 2 heights per bin|

|b.) Which determinant of variability requires the | | |

|mean? | | |

| |b. What is the difference in the interquartile range | |

| |for Jack’s earnings from tips and Jill’s earnings from | |

| |tips? | |

|5a.) Which number here is the outlier? 2, 3, 2, 3,| | |

|2, 2, 456, 3, 4 | | |

| | | |

|b.) A data value is an outlier if it is less than Q1 –| | |

|1.5 • IQR or above Q3 + 1.5 • IQR. So what numbers | | |

|would be outliers in #2? | |c. Make a box plot for the data. |

| | | |

| |8.) | |

| |[pic] | |

| | | |

| |a.) each interval is called a “bin.” How many bins | |

| |are there above? | |

| | | |

| |b.) How many kids read between 4 to 7 books over the | |

| |summer? | |

| | | |

| | | |

| | | |

| | | |

| | |d. Does the distribution of heights appear normal/bell |

| | |shaped? Explain. |

|10.) Old Faithful, a geyser in Yellowstone National |11.) Top 5 salaries at a company: |14.) 44, 49, 39, 43, 50, 44, 45, 49, 51 |

|park, is renowned for erupting fairly regularly. In |$90.4, $73, $69, $68.5, $61 Bottom 5 salaries at the |For this data, which summary statistic is NOT correct? |

|more recent times, it has become less predictable. |same company: |A. The minimum is 39. |

| |$29, $28.5, $25.6, $24.5, $22.8 |B. The lower quartile is 44. |

|[pic] | |C. The median is 45. |

|[pic] |a. Find the mean absolute deviation for each set of |D. The maximum is 51. |

| |data. Round to the nearest hundredth. | |

|[pic] | |15.) |

| | |[pic] |

|a. Does the Year-to-Date distribution seem normal, | | |

|skewed, or uniform? | |Which class had the highest pulse rates after climbing |

| | |the stairs? |

| | |A. 1 B. 2 C. 3 D. 4 |

| | | |

|b. Compare Last Week’s distribution to Last Month’s. | |16.) Peter’s Bowling Scores: |

| |b. Compare the variations of the data sets. |Week 1: 70, 70, 70, 73, 75 |

| | |Week 2: 72, 64, 73, 73, 75 |

| |12.) This table shows the average low temperature, in |What is the best explanation of why Peter’s Week 2 mean|

|c. What does the Year-to-Date distribution tell you |ºF, recorded in Macon, GA, and Charlotte, NC, over a |score was lower than his Week 1 mean score? |

|about the interval of time between Old Faithful’s |six-day period. |A. Peter received the same score three times in Week 1.|

|eruptions? |M |B. Peter had 1 very bad score in Week 2. |

| |71 |C. Peter didn’t improve as he did the first week. |

| |72 |D. Peter had 1very good score in Week 1. |

| |66 | |

| |69 |17.) What kind of distribution is shown below? |

| |71 |[pic] |

| |73 | |

| | |18) In Class 1, the median score was 70 points, and the|

| |C |IQR was 15 points. |

| |69 |In Class 2, the median score was 75 points, and IQR was|

| |64 |12 points. |

| |68 |Which range of numbers includes only third quartile of |

| |74 |scores for both classes? |

| |71 |A. 70 to 87 points B. 70 to 85 points |

| |75 |C. 75 to 87 points D. 75 to 85 points |

| | | |

| | | |

| |Which conclusion can be drawn from the data? | |

| |A. The interquartile range of the temperatures is the | |

| |same for both cities. | |

| |B. The lower quartile for the temperatures in Macon is | |

| |lower than the lower quartile for the temperatures in | |

| |Charlotte. | |

| |C. The mean and median temperatures of Macon were | |

| |higher than the mean and median temperatures of | |

| |Charlotte. | |

| |D. The upper quartile for the temperatures in Charlotte| |

| |was lower than the upper quartile for the temperatures | |

| |in Macon. | |

| | | |

| |13) A school was having a coat drive for a local | |

| |shelter. | |

| |• The freshman collected a median number of coats per | |

| |class of 10, and the | |

| |interquartile range was 6. | |

| |• The sophomores collected a median number of coats per| |

| |class of 10, and the | |

| |interquartile range was 4. | |

| | | |

| |Which range of numbers includes the third quartile of | |

| |coats collected for both classes? | |

| |A. 4 to 14 | |

| |B. 6 to 14 | |

| |C. 8 to 15 | |

| |D. 12 to 15 | |

Part 2: Bivariate Data

|Categorial data (non-numbers): Ex. Color, gender, |6.) (p. 146) Evan charted how long people studied and what grade people |#6 continued |

|ethnicity, religions, pets |made on their tests for three different classes. |Now graph the points to check to |

|Quantitative data: height, age, scores |a.) class #1 b.) class #2 c.) class #3 |see if you were right |

| |Mean study time | |

|2-Way Frequency Chart: |Mean test score |[pic] |

|[pic] | | |

| |Mean study time |[pic] |

|1.) What are the marginal frequencies? |Mean test score | |

| | |[pic] |

| |Mean study time | |

|2.) What are the joint frequencies? |Mean test score | |

| | | |

| |0.5 | |

|3.) Conditional frequencies can be calculated from |63 | |

|the table, but isn’t in the table. Example: Of the | | |

|band kids, what percentage is male? |0.5 | |

| |60 | |

| | | |

| |0.5 | |

|[pic] |71 | |

| | | |

|4.) Conditional frequency Ex2 What percentage of the|1.0 | |

|females in the school are in chorus? |67 | |

| | | |

| |1.0 | |

| |61 | |

| | | |

|5.) Melissa says that the following graph isn’t a |1.0 | |

|scatter plot because it fails the vertical line test. |94 | |

|Is she right? | | |

| |1.5 | |

|[pic] |72 | |

| | | |

| |1.5 | |

| |63 | |

| | | |

| |1.5 | |

| |87 | |

| | | |

| |2.0 | |

| |76 | |

| | | |

| |2.0 | |

| |68 | |

| | | |

| |2.0 | |

| |98 | |

| | | |

| |2.5 | |

| |80 | |

| | | |

| |2.5 | |

| |74 | |

| | | |

| |2.5 | |

| |69 | |

| | | |

| |3.0 | |

| |85 | |

| | | |

| |3.0 | |

| |82 | |

| | | |

| |3.0 | |

| |78 | |

| | | |

| |3.5 | |

| |89 | |

| | | |

| |3.5 | |

| |93 | |

| | | |

| |3.5 | |

| |91 | |

| | | |

| | | |

| |Without graphing the data, explain if the data is relatively linear, | |

| |exponential or neither and explain how you know. | |

| |a.) | |

| | | |

| | | |

| | | |

| |b.) | |

| | | |

| | | |

| | | |

| | | |

| | | |

| |c.) | |

| | | |

| | | |

| |7.) Use Eye-balling and then find the equation of the line of best fit | |

| |(i.e. trend line or regression line/curve). Is the data strongly | |

| |correlated? Use “residuals” in your answer. | |

| |A.) | |

| |[pic] | |

| | | |

| |B.) | |

| |[pic] | |

|Find the line of the best-fit for the following data points: |10.) |

|8.) (1, 48), (2, 42), (2, 50), (4, 45), (5, 69), (6, 44), (7, 82), (7, 93), (8, 96) | |

| |Spring |

|[pic] |Summer |

| |Fall |

| |Total |

| | |

| |Small |

| |24 |

| |22 |

| |18 |

| |64 |

| | |

| |Medium |

| |23 |

| |28 |

| |19 |

|9.) The Environment Club is doing research about recycling. They collected data on |70 |

|how many soda cans were sold at the vending machine and how many soda cans were found | |

|in the recycling receptacle. |Large |

|Sold |18 |

|18 |27 |

|15 |29 |

|19 |74 |

|8 | |

|10 |Jumbo |

|13 |16 |

|9 |21 |

|14 |33 |

| |70 |

|Recycled | |

|8 |Total |

|6 |81 |

|10 |98 |

|6 |99 |

|3 |278 |

|7 | |

|5 | |

|4 |a. In which season did the most customers prefer jumbo drinks? |

| | |

| |b. What percent of those surveyed purchased the small drinks? |

|What’s the equation for the line of best-fit? | |

| |c. What percent of those surveyed purchased medium drinks in the summer? |

|[pic] | |

| |d. What do you think the fast-food restaurant learned from their survey? |

| | |

| | |

| | |

| |11.) Easiest question ever! Which graph displays a set of data for which a |

| |linear function is the model of best fit? |

| |A. B. C. |

| | |

| |[pic] [pic] [pic] |

| | |

| |[pic] |

| | |

| |12.) Which is the equation of the line of best-fit? |

| | |

| | |

| | |

| | |

| |13.) If the linear regression model for these data were |

| |y = 1.10x – 2.29, what would be the predicted number of 2011 wins for a team |

| |that won 5 games in 2010? |

| |A.) 3 B.) 4 C.) 5 D.) 6 |

Part 3: Interpreting Linear Models

|1.) Remember Even? We put his data for the first class (the one that ended up |Back to Old Faithful: Short eruptions meant you didn’t have to wait long before |

|linear) into a computer program that yields regression curves. Apparently the |you could see the next one. |

|line of best-fit is |I = 10×D + 30. Visitors to Yellowstone literally could multiply the duration of |

|y = 8.8x + 58.4. |the eruption by 10, add 30 min, and that would tell them when the next eruption |

|With such a perfect (computer generated) equation, the residuals should add up to |was going to happen. Those were the good ol’days. |

|zero. | |

|Fill in the chart below. |Duration |

|Mean study time |Today’s Interval |

|Mean test score |Used to be Interval |

|Predicted Score |Residual |

|Residual | |

| |1.5 |

|0.5 |51 |

|63 | |

| | |

| | |

| |2.0 |

|1.0 |58 |

|67 | |

| | |

| | |

| |2.5 |

|1.5 |65 |

|72 | |

| | |

| | |

| |3.0 |

|2.0 |71 |

|76 | |

| | |

| | |

| |3.5 |

|2.5 |76 |

|80 | |

| | |

| | |

| |4.0 |

|3.0 |82 |

|85 | |

| | |

| | |

| |4.5 |

|3.5 |89 |

|89 | |

| | |

| | |

| |5.0 |

| |95 |

|2.) There is such thing as a “residual plot.” What is one? | |

| | |

|[pic] | |

| | |

| |4.) Fill in the last 2 coloumns of the table with a.) what the interval (how |

|The correlation coefficient is a number between –1 and + 1 |long ppl had to wait) for the next eruption and with b.) the residuals |

|[pic] [pic] |(difference from old to new) |

|[pic] | |

| |5.) Use your calculator’s “data” button to find the following: |

| |a.) Correlation Coefficient |

| | |

| |b.) Line of best fit with today’s data |

| | |

| |c.) Find the line of best fit with Evan’s data in #1, and see if the TI-30XS |

| |Multiview agrees with the computer prgm. |

| | |

| | |

| | |

| |6a) What type of a relationship is suggested by the scatter plot |

| |(positive/negative, |

| |weak/strong)? |

| | |

| | |

| |b.) What is the domain of ages considered by the researchers? |

| | |

| |c.) What is the range? |

| | |

| | |

| |d.) Do you think age causes income level to increase? Why or why not? |

| | |

| | |

|7.) Income in Singapore: |10.) How would you describe the correlation of the two variables based on the |

|[pic] |scatter plot? [pic] |

|[pic] | |

| |Alan’s points per basketball game: 8, 15, 10, 9, 10, 12, 12, 7, 8, 10, 12, 11, |

|a. Does there appear to be a relationship between age and income? |7, 8, 8, 13, 11, 9, 9 |

| |11a.) Could you compute Alan’s Five Summary Statistics? min, Q1, median, Q3, |

|b. Do all three types of employees appear to share the same benefit of aging when |max |

|it comes to income? |b.) Could you compute his range, the IQR, the standard deviation, the MAD, and |

| |what kind of scores would be outliers for him? |

| |c.) Could you take this data and draw a dot plot, a histogram, and a box (and |

|c. Does a linear model appear to fit the data for any of the employee types? |whisker) plot? |

| | |

| |12.) Given two histograms, could you tell which had more spread? |

|d. Does the effect of age vary over a person’s lifetime? | |

| |13.) Could you draw the following distribution types? |

| |a.) a symmetric, unimodal, bell-shaped |

| |b.) skewed right |

|8.) Check out the residual plot below. Was the regression line used a good |c.) slightly skewed left |

|predictor of weight? |d.) uniform |

|Was the regression line better at predicting weight for shorter people or taller |e.) symmetric bimodal |

|people? |f.) non-symmetric, bimodal |

|[pic] |g.) a distribution with a gap |

| |h.) a histogram with an outlier |

|9.) Beth, a highly intelligent student, wants to find out what percentage of | |

|students at AHS is going to UGA. She is obviously not going to ask every single |14.) Do you know off-hand what marginal frequencies, joint frequencies, and |

|student. |conditional frequencies are in a 2-way frequency table? |

|What would be a stupid idea for her to get a sample? | |

| |15a.) Given a scatter plot, could you determine a line of best fit using |

| |eyeballing, the calculator, and median-median? |

|What would be a good idea for her to get a sample? |b.) Could you examine the residuals and make a residual plot to analyze the |

| |error? |

| | |

| |16.) Would the correlation between skipping school & getting good grades be |

| |positive/negative/strong/weak? |

| | |

| |17.) Do you know the difference between when something is correlated and when |

| |something causes another? |

-----------------------

A. bimodal

B. uniform

C. multi-outliers

D. skewed to the right

The correlation between two variables is related to the slope and the goodness of the fit of

a regression line.

3.) Try guessing at some

[pic]

[pic]

A. positive, strong linear

B. negative, weak linear

C. negative, fairly strong linear

D. little or no correlation

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