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Name__________________________ Unit 4: Statistics Show all work! Date____________ Worksheet A4 (Part I) (Measures of Central Tendency Adapted from IV-16 Finite Bounded Book) Show work 1. Calculate the mean, median and mode for each of the following: a.) 2, 8, 7, 8, 5, 8, 10, 5 b.) 18, 22, 22, 17, 30, 18, 12 c.) 5, 5, 5, 5, 10 2. If each of six students scored 80 on a test, find each of the following for the set of 6 scores: a.) Mean Median Mode b.) Make up a set of 6 scores that are not all the same but that have a mean, median and mode of 80. 3. The mean score on a set of 20 tests is 75. What is the sum of the score? 4. The tram at a ski area has a capacity of 50 people with a load weight limit of 7500 lbs. What is the mean weight of the passengers if the tram is loaded to capacity? 5. The names and ages for each person in a family of five follow: Name Age Don 40 Jane 36 Kirk 8 Jean 6 Scott 2 a.) What is the mean age? b.) Find the mean in 5 years from now (everyone is 5 years older). Hint: Make a new chart which shows each person’s age 5 years from now. c.) Find the mean in 10 years from now. d.) Describe the relationship among the answers you found in parts a-c. Do you see a pattern? Describe it. 6. Suppose you own a hat shop and decide to order hats in only one size for the coming season. To decide which size to order, you look at last year’s sales figures, which are itemized according to size. Should you find the mean, median or mode for the data? Explain your answer with words (be clear). Name__________________________ Unit 4: Statistics Date____________ Worksheet A4 (Part II) (Adapted from IV-17 Finite Bounded Book) Show work (if you use a calculator, show me what you put into the calculator). 1. The following table gives the annual salaries of the 40 dancers of a certain troupe. a.) Find the mean annual salary for the troupe Hint: 2 dancers made $18,000 so multiply 2 times 18,000, do this for all the dancers Salary Number of Salary x # of Dancers Dancers $18,000 2 $36,000 $22,000 4 $26,000 4 b.) Find the median salary. $35,000 3 Hint: Is there ONE middle $38,000 12 number or TWO? $44,000 8 $50,000 4 $80,000 2 $150,000 1 c.) Find the mode. 2. If Janet traveled 45 miles in 90 minutes, what was her mean speed? 3. The youngest person at Google is 17 and the range of ages at Google is 27 years. How old is the oldest person at Google? 4. Choose the set of numbers that fits the descriptions given in each of the following: a. Choose the set that has a mean of 6 and a range of 6 Set A: 3, 5, 7, 9 Set B: 2, 4, 6, 8 Set C: 2, 3, 4, 15 b. Choose the set that has a mean of 11, a median of 11, and a mode of 11 Set A: 9, 10, 10, 11, 12, 12, 13 Set B: 10, 11, 11, 11, 11, 11, 14 Set C: 9, 11, 11, 11, 11, 12, 12 c. Choose the set that has a mean of 3, a median of 3 and has no mode Set A: 0, 2.5, 6.5 Set B: 1, 3, 3, 5 Set C: 1, 2, 4, 5 Name__________________________ Unit 4: Statistics Date____________ Worksheet B4 (Measures of VariationAdapted from IV-17 Finite Bounded Book) Show work (if you use a calculator, show me what you put into the calculator). 1. What is the standard deviation of the heights of seven trapeze artists if there heights are 175 cm, 182 cm, 190 cm, 180 cm, 192 cm, 172 cm and 190 cm? Use the table below to guide xi (heights) xi x ( xi x ) 2 For the middle column, find the mean and subtract the mean from each height. For the last column, square the middle column. Now add the last column and divide by n. Do you remember the last step? 2. If all the numbers in a set are equal, what is the standard deviation? For instance, suppose you are in Hawaii and it’s 80 degrees every day, what is the standard deviation? 3. Go on-line or watch the weather and find out the daytime high temperature for the next 4 days (starting tomorrow). List those here: ___ ____ ____ ____ a.) Find the mean_____________ c.) Find the mode____________ b.) Find the median_____________ d.) Find the standard deviation (create a table like the one – use the back or a separate sheet) Review on Measures of Center 4. To receive an A in a class, Will needs at least a mean of 90 on 5 exams. Will’s grades on the first 4 exams were 84, 95, 86 and 94. What is the minimum score he needs on the fifth exam to earn an A in the class (he needs a 90 or more – no rounding up). 5. The mean of 5 numbers is 6. If one of the 5 numbers is removed, the mean becomes 7. What is the value of the number that was removed? Try some values if you can’t figure it out. Challenge (this is very doable) 6. Ginny’s median score on 3 tests was 90. Her mean score was 92 and her range was 6. What were her 3 test scores? Name__________________________ Unit 4: Statistics Date____________ Worksheet C4 (Part I) Frequency Tables Needs to be scanned Will be given to you in class Name__________________________ Unit 4: Statistics Date____________ Worksheet C4 (Part II) (Measures of Variation Adapted from IV-17 Finite Bounded Book) Show work: graphs/charts need to be neat )use a ruler or straightedge Make a frequency table and histogram for each data set. #1. The following are the ounces in canned goods of 18 cans: 11, 15, 16, 16, 14, 15, 10, 8, 8, 12, 15, 16, 8, 15, 8, 14, 10, 10 Histogram Here (neatly) Size (ounces) Frequency 2.) Make a grouped frequency table for the following Berwyn June temperatures: 75, 78, 99, 88, 74, 89, 61, 91, 84, 78, 75, 92, 88, 67, 82, 85 Finish Table Class Frequency 60-69 70-79 Name__________________________ Unit 4: Statistics Date____________ Worksheet D4 (Part I) Stem and Leaf Plots, Histograms, and Circle Graphs Needs to be scanned Will be given to you in class Name__________________________ Unit 4: Statistics Date____________ Worksheet D4 (Part II) 3.) Make a circle graph for the following Students were asked about their favorite type of music. The responses of 500 students are recorded in the following table. HINT: Divide the number of students choosing each genre by the total number of students surveyed. Then multiply by the TOTAL number of degrees in the circle. (Round degree measures to the nearest degree). USE a PROTRACTOR to measure degree. I gave you a radius as a starting point. Classical Rock R&B Country Hip-Hop Emo 43 115 181 57 78 26 Name__________________________ Unit 4: Statistics Date____________ Worksheet E4 (Adapted from IV-17 Finite Bounded Book) 1. Construct a boxplot for the following mileages per gallon of various company cars: 22 18 14 28 30 12 38 22 30 39 20 18 14 16 10 Be sure to draw a number line with an appropriate scale. Be neat. Min:______ Q1:______ Q2(Med):______ Range:________ Q3:______ Max:______ IQR:________ 2. Following are boxplots comparing ticket prices of two performing arts theaters: a. What is the median ticket price for each theater? b. Which theater has the greatest range of prices? c. What is the highest ticket price at either theater? d. Draw 2 conclusions comparing the ticket prices at Theater A versus Theater B (Be specific.) Box Office Ticket Prices Theatre A Theatre B 0 10 20 Conclusion 1: Conclusion 2: 30 40 50 60 70 80 90 100 3. Construct a boxplot (neatly please) for the following set of test scores. Indicate outliers, if any, with asterisks. Using the 1.5 IQR, show if there are outliers. Remember to add this value to Q3 and subtract it from Q1 to help determine if you have an outlier. Data: 20 95 40 70 90 70 80 80 90 95 4. Using the following 8 daytime temperatures from Hawaii's Big Island: 80, 84, 80, 81, 84, 82, 82, 84, add a 9th temperature so there is no right whisker. What is your added temperature:___________ What 2 values must be equal so there is no right whisker:___________________ Use your 9 temperatures and draw a boxplot below (always be neat, draw a number line and show your scale). Extra Credit: Find the next 10-day temps for Tampa Bay, Florida. Using your same number line above, create a boxplot below the one you just created using your Tampa Bay temperatures. Draw 2 conclusions based on your side-by-side boxplots of Tampa Bay, Florida and Hawaii's Big Island. Name__________________________ Unit 4: Statistics Show all work! Date____________ Worksheet F4 Needs to be scanned Will be given to you in class Name__________________________ Unit 4: Statistics Date____________ Worksheet G4 For every question: Fill in z-scores, mean, and mean +/-standard deviations for each z-score on the sketch. 1. The mean IQ score for 1500 students is 100, with a standard deviation of 15. Assuming the scores have a normal curve, determine the following. a.) How many have an IQ between 85 and 115? (Hint: Find the percent first and then multiply by 1500.) b.) How many have an IQ between 70 and 130? (Hint: Find the percent first and then multiply by 1500.) c.) How many have an IQ over 145? (Hint: Find the percent that has under a 145 and then subtract.) 2. Sugar Plops boxes claim to hold 16oz. To make sure they do, the manufacturer fills the box to a mean weight of 16.1 oz, with a standard deviation of 0.05 oz. a.) If the weights have a normal curve, what percent of the boxes actually contain 16 oz. or MORE? 3. For certain workers, the mean wage is $5.00/hr, with a standard deviation of $0.50. Assuming a normal distribution, what is the probability that the worker’s wage is between $4.50 and $5.50? 4. A job applicant test consisted of three parts: verbal, quantitative, and logical reasoning. The mean and standard deviation for each part are as follows: Mean (x-bar) Stand. Dev (s) Verbal Quantitative Logical Reasoning 84 10 118 18 14 4 a.) Holly’s scores were 90 on verbal, 113 on quantitative and 18 on logical reasoning. Determine her z-score for each part. (show setup)Verbal z-score:__________ score:_________ Quant. z-score:__________ Logical z- b.) Use the answers in part a to answer the following: (i) On which part did she perform relatively the highest?_________________ (ii) On which part did she perform relatively the lowest?_________________ 5. The average phone call in a certain town lasts 4 min with a standard deviation of 2 minutes. Assume a normal distribution. a.) What percent of calls lasts fewer than 2 minutes? b.) What percent of calls lasts greater than 6 minutes? 6. According to psychologists, IQs are normally distributed with a mean of 100 and a standard deviation of 15. a.) What percent of the population have IQs between 100 and 130? (Use your normal curve with percents). b.) What percent of the population have IQs lower than 85? c.) What percent of the population have IQs greater than 85? Name__________________________ Unit 4: Statistics Date____________ Worksheet H4 Unit 4 Finite Math Jeopardy Problems Measures of Central Tendency Frequency 5 Summary Variance & Normal Tables & Values and Standard Distribution Histograms Box Plots Deviation 100: What is the mode of the following data? 5, 7, 8, 5, 6, 6 100: Make a frequency table to organize the following data. 6, 5, 6, 6, 4, 4, 6 100: Find the range of the following data. 57, 80, 63, 42, 38, 43, 34, 35, 58 100: Calculate the variance for the following set of data. 5, 7, 8, 5, 6, 6 100: If the mean age of students in a class is 16, and Molly is 16, what is her zscore? 200: What is the median of the following data? 12, 18, 13, 11, 17 200: Make a grouped frequency table to organize the following data, and use it to ESTIMATE the mean. 6, 15, 32, 12, 18, 8, 3, 4, 9 200: Find the Quartiles and inner quartile range of the following data. 57, 80, 63, 42, 38, 43, 34, 35, 58 200: Calculate the standard deviation for the following set of data. 5, 7, 8, 5, 6, 6 300: What is the mean of the following data? 24, 36, 12, 18, 26, 32, 33 300: Make a histogram using the grouped frequency table from 200. (6, 15, 32, 12, 18, 8, 3, 4, 9) 300: Make a box plot to represent the following data. 57, 80, 63, 42, 38, 43, 34, 35, 58 300: Calculate the variance and standard deviation for the following set of data. 12, 18, 13, 11, 17 200: 2500 students took the SAT’s on a given day in Chester County. The mean was a 1130 and the standard deviation was 130. How many students scored between an 870 and a 1390? 300: The mean IQ score in the US is a 100 with a standard deviation of 15. If Joe scores a 93, what percentage of people score lower than him?