Math 391: Statistics
Mrs. Chen's class shares how much allowance they earn each week for doing chores at home. Eight of the nine students receive the following amounts: $15, $12, $13, $18, $20, $8, $14, $6 If the median of the data set is $13 and the range of the data set is $14. Which of the following could be the missing student's allowance? $14 $5 $19 $11
$11 If $11 is added, the data set becomes: $6, $8, $11, $12, $13, $14, $15, $18, $20. The median, the middle number when placed in ascending order, is $13$. The range is $20-$6=$14.
Miss Austin gives her class 6 sets of data and asks them to identify which data set can most accurately be summarized by the mean. What topic is she covering? reading data tables finding averages choosing measures of central tendency addition and division skills
choosing measures of central tendency Students need to understand when to use the mean, median, and mode to identify data summaries.
Which of the following are statistical experiments? Select all answers that apply. flipping a coin 12 times rolling two dice until you get doubles counting the desks in a classroom rolling a die 6 times in a row
flipping a coin 12 times rolling two dice until you get doubles rolling a die 6 times in a row A statistical experiment is a repeatable trial whose outcome is determined by chance and flipping a coin leads to heads or tails which is not controlled by the flipper. A statistical experiment is a repeatable trial whose outcome is determined by chance rolling dice leads to 12 possible outcomes which are not controlled by the roller. A statistical experiment is a repeatable trial whose outcome is determined by chance and rolling a die leads to 6 possible outcomes which are not controlled by the roller.
What is the mode of the data set below? 1.8, 1.5, 2.4, 2.1, 1.5, 2.1, 1.7, 1.5, 1.8 1.5 1.8 2.4 2.1
1.5 The mode is the number that appears the most in the data set. 1.5 appears 3 times, more than any other.
Use the table below to answer the question that follows. Jan. 10 Feb. 3 Mar. 8 Apr. 23 May 10 June 8 July 7 Aug. 7 Sept. 9 Oct. 13 Nov. 14 Dec. 20 The table above shows the total precipitation each month. What is the average amount of precipitation in a month? 20 11 10 7
11 To find the average, sum all of the values and divide by 12 (the number of months in the dataset). 132/12 = 11
The debate team has averaged 108 points in the last 5 tournaments. If they scored 120, 98, 92, and 108 in the first 4 tournaments, how many points were scored in the fifth tournament? 120 122 108 124
122 If the average is 108 for 5 tournaments, then the total number of points scored is 540: (5 tournaments x 108 points) = 540 points. So, 540 - 120 - 98 - 92 - 108 = 122 points.
Zuri has scored 16, 22, 18, 10, and 22 points in her first 5 basketball games. How many points does she need to score in her next game so that her average points per game is 17? 2 8 14 20
14 A mean (or average) score of 17 means Zuri had scores totaling 17×6=102 points. Since the scores of her first five games are given, we can use the equation 16+22+18+10+22+x=102. Solving for x yields 14.
Approximately what fraction of the population is within one standard deviation of the mean in a dataset with a normal distribution? 2/3 1/5 1/4 1/3
2/3 68.2% of the population will be within one standard deviation of the mean. The closest benchmark fraction to this percentage is ⅔.
The test scores in Mrs. Marsala's math class are as follows: 72, 75, 78, 84, 88, 89, 91, 92, 93, 94, 97 What is the range of scores? 89 87 72 25
25 The range is the difference between the highest and lowest value in the set. This data is already organized from lowest to highest. Therefore, the range is found by 97-72 = 25.
A journalist in a town with a population of 15,200 takes a random sample of 200 people and finds that 60 of them read the local newspaper. Based on this sample, which of the following is the best estimate for the number of people in the town that read the local newspaper? 4500 45 5 450
4500 Of the 200 people sampled, 60/200 or 30% read the paper. To find 30% of the town's population: (0.30)(15200)=4560. Therefore about 4500 people read the local paper.
What is the mean of the data set below? 15, 18, 19, 54, 74, 94, 67, 82, 48, 31, 15 40 42 52 47
47 To find the mean, or average, of a data set simply add all the values together and then divide by the total number of values. The total value of the data set is 517 and there are 11 numbers. 517 / 11 = 47.
What is the median of the data set below? 15, 18, 19, 54, 74, 94, 67, 82, 48, 31, 15 54 44 48 47
48 The median is the middle value of the data set, once the data set is arranged from the lowest to the highest value. The median of the data set is 48. To find the median, simply arrange the data set from least to greatest and find the middle value: 15, 15, 18, 19, 31, 48, 54, 67, 74, 82, 94. Since there are 11 values, the 6th value - or middle value - is the median.
Which number could be added to the data set below so that the range stays the same? 23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26 0 2 55 103
55 The range of the data set is 100−5=95100−5=95. By adding 55 to the data set, the minimum and maximum are unchanged, leaving the range at 95.
The number of inches of snowfall in Selbyville is graphed in the bar chart below. What is the mean number of inches of snowfall per month from November to March? 6 8 30 7
6 To find the mean (average) of inches of snowfall that fell in a month, add each month's amount of snowfall and divide by 5 months, 5+7+9+8+1/5=30/5=6. The mean snowfall is 6 inches.
The Blueville Bears golf team has 6 members. In their last tournament, the players averaged a score of 79. The first five players on the roster had scores of 72, 76, 102, 70, and 80. What was the score of the sixth player? 74 80 75 70
74 A mean (or average) score of 79 means the team had scores totaling 79×6=474 strokes. Since the scores of the first five players are given, we can use the equation 72+76+102+70+80+x=474. Solving for x yields 74.
Ben needs to make a statistical question for his class. Which of the following is an appropriate statistical question? Does Mr. Adams run faster than Mrs. Adams? How tall is Mr. Adams? Do males run faster than females? Is Mr. Adams taller than Mrs. Adams?
Do males run faster than females? Statistical questions involve groups of people, not just one or two individuals.
Mr. Schmidt is teaching statistics and the data lists are long. Finding the mean would take a long time so he has decided students may bring a calculator from home to use on the unit test. What can he do to ensure that all students have a device? Allow students to share devices during the test. Give advance notice to bring calculators and provide devices for those who do not have one. Require students to borrow from a friend or rent one for the test. Only allow students with their own device to use it.
Give advance notice to bring calculators and provide devices for those who do not have one. Give students an opportunity to bring their own and allow them to borrow one if they forget or do not have one.
Mrs. McCauley is asking students about statistical experiments. Most students are giving brief answers and justifications. What can she do to increase student participation? Tell them there will be a pop quiz if they do not give longer answers. Give a worksheet to assess understanding. Have students write answers and end the verbal discussion. Give sentence stems and time to think before calling on someone.
Give sentence stems and time to think before calling on someone. Give students an opportunity to think through an answer prior to giving it may allow for more thorough explanations. The sentence stems will allow them to know they are providing a complete answer.
Mrs. John's class is struggling with statistical questions. What activity can best help them master this concept? Give them a list of non-statistical questions and guide them to reword the questions to become statistical. Move on to the next concept and revisit this during the test review. Give them 2 lists with examples of non-statistical questions in one column and statistical questions in the other.. Spend a day reteaching the concept using the same materials in the first lesson.
Give them a list of non-statistical questions and guide them to reword the questions to become statistical. Guiding them through this practice allows students to ask questions and recognize misunderstandings.
A mathematics teacher determines that the median score for the most recent test was 80 percent. Which of the following is the most accurate interpretation of the result? The most common score on the test is 80 percent. The highest score on the test was 80 percent. Half the students scored an 80 percent or below. The average score on the test is 80 percent.
Half the students scored an 80 percent or below. Median is the middle number in a data set. It is calculated by arranging the numbers from least to greatest and finding the number in the middle; if there is not one middle number, then the median is the average of the two numbers. For example, in the data set 1, 2, 3, 4 the median is 2.5 because 2.5 is the average of 2 and 3. If the median score is 80, then it can be assumed half the students scored below 80 and half the students scored above 80.
Which of the following is a non-statistical question? How tall is the Empire State Building? What is the typical length of a giraffe's neck? How tall are students at Central High School? How many acorns does an average squirrel eat in a day?
How tall is the Empire State Building? This is a non-statistical question because it has one correct answer that does not require data collection.
The stem & leaf plot below shows the results of college & high school students surveyed about how many books they read the past school year. High school College 2,4,8 [0] 1,1,2 3,6 [1] 2 1,2 [2] 4 3,5 [3] 3,5 1,8 [4] 2,3,9 4,7,9 [5] 7 1 [6] 2,8 [7] 1,3 Which of the following statements are true? I. 70 high school students did not read any books. II. The college median is greater than the high school median. III. The mean is less than the median in both groups. I, II, III II, III only II only I,
II, III only The median is the middle number of the data when the data is listed from least to greatest. The median of the college students is 42 and the median of the high school students is 33. The mean is the average of each data set. Find the sum of the data set then divide by 15 (the number of data in the set). The mean of the high school books read is 31.6 and the mean of the college books read is 38.2. For each set, the mean is less than the median.
Which of the following is true of a statistical experiment? The possible outcomes are not known beforehand. It can have more than one outcome at a time. Its outcome is determined by chance. Its outcome is predetermined.
Its outcome is determined by chance. The outcome of a statistical experiment is determined at random. Only one outcome will occur for each statistical experiment and all possible outcomes are known beforehand, but which outcome will occur is not predetermined.
Boxed Juice Apple 12 Orange 8 Grape 12 Cranberry 8 Mixed Fruit 15 Julia buys a box of juice boxes containing the types and amounts listed in the table. All the juices are placed in a big bucket covered with ice. Micah reaches in and pulls out a juice box without looking. Which of the following statements is true? Micah is equally likely to pick apple or grape juice. Micah is more likely to pick orange juice than apple juice. Micah will not pick cranberry juice. Micah is certain to pick mixed fruit juice.
Micah is equally likely to pick apple or grape juice. There are an equal number of grape juice boxes and apple juice boxes; each has a probability of being chosen 23.1%. Choosing an apple juice box or a grape juice box is equally likely, therefore, this is a true statement.
Jesse surveys 20 people about her new ice cream flavor that she plans to start selling in her ice cream shop. She asks her customers to rate a sample of the new ice cream on a scale of 1-10, 1 meaning they dislike the ice cream and 10 meaning they really like the new ice cream flavor. The data below represents her results 10, 10, 10, 10, 10, 10, 10, 10, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1 Jesse concludes she will not sell the new flavor in her shop because the average of her responses is 5, meaning there was not a strong preference for this flavor. Which measure of central tendency would provide a better indicator for her to base her decision? Median Range Mean Mode
Mode If Jesse considered the mode of her data set, she would see her data has two modes, 10 and 2. The customers that tried her ice cream either really liked it or really disliked it which is different than her conclusion that no one had a strong preference either way.
Mr. Thomas is teaching measures of central tendency to his class that is mostly comprised of English Language Learners (ELL). What is the best support for teaching the new vocabulary words? Put the words on a Word Wall with the word, picture, and definition. Teach the class as if all students are fluent in English so the students don't feel different. Give the words and definitions to the students in English and Spanish. Say the words and their definitions slowly, loudly, and repeatedly throughout the lesson.
Put the words on a Word Wall with the word, picture, and definition. Word Walls give students something to reference when thinking of vocabulary.
List A (not shown) consists of integers that are greater than 60, and may appear more than once in the list. List B consists of the integers in list A and 3 additional integers that are each less than 60. Which of the following statements about the centers or spreads of lists A and B must be true? The mode in list B is less than the mode in list A The mean in list B is less than the mean in list A. The median in list B is less than the median in list B. The range in list B is less than the range in list A.
The mean in list B is less than the mean in list A. The mean in list B will be less than list A since the numbers introduced in list B will bring the mean, or average, down from the original list A.
Señora Gomez teaches Spanish at Bill Cline Preparatory School. The number of students in each of her classes is shown in the bar chart. 1st period 18 2nd period 24 3rd period 32 4th period 28 5th period 28 6th period 22 7th period 29 Which of the following statements is true? The range is 32. The mean is less than 25. The mode is 26. The median is 28.
The median is 28. Arrange the class data in order by the number of students from least to greatest: 18 22 24 28 28 29 32 The median is the middle number, which is 28.
Median
The median is the middle number of the data when the data is listed from least to greatest.
Mode
The mode is the number that appears the most in the data set.
A teacher tells the students the mode of the scores on the most recent exam was 85. Which of the following is the most accurate interpretation of the result? The highest score on the test was 85 percent. The average score on the test is 85 percent. The most common score on the test is 85 percent. Half the students scored below 85 percent.
The most common score on the test is 85 percent. Mode is the number that appears the most in a data set.
Rachel is thinking about buying her first house. The data below represents the houses sold in her city in the last month. $90k, $120k, $200k, $350k, $459k, $750k, $775k, $800k, $990k Rachel concludes she can't buy a house because the median home price is $459k and her budget is only $200k. Why is the use of the median misleading in this situation? The outliers of the data set are making the median higher than normal. The small amount of data might be skewing the median higher than normal. The outliers of the data set are making the median lower than normal. Based on the median there are no houses in her price range.
The small amount of data might be skewing the median higher than normal. This is a small sample and may be a month in which more expensive homes sold compared to less expensive homes. She should look at the data from the last 3-6 months in order to make a better decision. In addition, the data set shows there are still homes in her price range.
Which of the following is a statistical question? How many students are absent today? When do students have gym class? What time is 6th grade lunch? How tall is Mrs. Hill?
When do students have gym class? A statistical question has a variety of answers and students may have gym at a variety of times during the day. This is a statistical question.
The test scores of 10 students are listed below. An 11th student makes up the test and earns a 77. Which of the following will definitely increase? 56, 61, 68, 72, 72, 81, 82, 92, 93, 95 mode median range mean
median The median, or middle number when the scores are in order least to greatest, of the first 10 scores was 76.5. When 77 is added, the median becomes 77.
What is the median and mean of the data set below? 10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3 median: 7.0; mean: 5.05 median: 4.5; mean: 4.5 median: 4.5; mean: 5.05 median: 3.5; mean: 5.05
median: 4.5; mean: 5.05 Remember that before you can find the median, the data must be arranged in order from least to greatest or greatest to least. 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10 Since there is an even number of terms (20) the median is the average of the two middle scores: (4+5)÷2=4.5 The mean is the sum of all of the numbers in the data set divided by 20, the number of items in the data set: 101÷20=5.05
Mrs. Azul had each of her first graders separate a small bag of M&Ms into groups by color, arrange the groups into side by side bars, and determine which color they had the most of. What concept is Mrs. Azul introducing to her first-grade class? range mode median mean
mode Mrs. Azul is having her students arrange their data (M&Ms) into bars in order to compare the heights or lengths of the bars. This is a visual representation of the bar that is the longest or has the most M&Ms - the mode. A good way for students to remember mode is to think about the word most. The mode is the piece of data (M&Ms in this case) that occurs the most frequently.
What is the range and mode of the data set below? 10, 8, 5, 3, 7, 4, 5, 9, 2, 3, 7, 3, 8, 6, 4, 1, 2, 1, 10, 3 range: 9; mode: 3 range: 10; mode: None range: 9; mode: 3 and 4 range: 10; mode: 3 and 4
range: 9; mode: 3 The largest piece of data in this set is 10, and the smallest piece of data is 1. Therefore, the range = 10 - 1 = 9. The mode is 3 because there are more 3's (there are 4 of them) than any other number in the data.
