Unit 6
Statistics
Name ______Color ______
Drawing Inferences
Use a proportion to solve for the unknown quantity.
1. Use the table to predict the number of students out of 528 that would say each of the
following was their least favorite chore.
a. clean my room b. wash dishes
c. walk the dog d. take out the garbage
2. The results of a survey asking teens their favorite type of book to read is shown.
Out of 250 teens, predict how many would choose:
a. mystery b. adventure
c. romance
Samples
Random
Simple Random Sample - Each student’s name is written on a piece of paper. The names are placed in a bowl, and names are picked without looking.
Why?
Stratified Random Sample - Students are picked at random from each grade level at a school?
Why?
Systematic Random Sample - Every 20thperson is chosen from an alphabetical list of all students attending a school.
Why?
Biased
Convenience Sample - To represent all the students attending a school, the principal surveys the students in one math class.
Why?
Voluntary Response Sample - Students at a school who wish to express their opinions complete an online survey.
Why?
Independent Practice
1. Max wants to find out the exercise habits of local children. He plans to survey every third child he sees coming out of a sporting goods store. Max says his sample is not biased (not unfair). Do you agree? Explain your answer.
2. The school board wants to study computer literacy among teachers. Which would represent a random sample of teachers?
A) All high school math teachers
B) Teachers from the middle school whose name begins with N
C) All male teachers
D) Every eighth teacher on an alphabetical list
3. Ms. Constantine is choosing among three field trips for her two classes. She wants to determine which trip her students prefer. Should she survey the entire population or use a sample? Explain.
4. A researcher catches 60 fish from different locations in a lake. He then tags the fish and puts them back in the lake. Two weeks later, the researcher catches 40 fish from the same locations. 8 of these 40 fish are tagged. Predict the number of fish in the lake.
5. A middle school has 1,800 students. A random sample of 80 shows that 24 have cell phones. Predict the number of students in the middle school who have cell phones.
6. In a random sample, 3 of 400 computer chips are found to be defective. Based on the sample, about how many chips out of 100,000 would you expect to be defective?
7. You survey customers at a mall. You want to know which stores they shop at the most. You walk around a computer shop and choose 20 customers there for your survey. (Biased or Unbiased)
8. A country radio station wants to know what the most popular type of music is, so they ask their listeners to call in to say their favorite type.
Measures of Central Tendency
Measures of central tendency show what the ______of a data set looks like.
The measures of central tendency are the ______, ______, and ______.
The ______is NOT a measure of central tendency.
Find the mean, median, mode, and range of 8, 3, 5, 4, 1, and 3.
Mean ______Range ______
______
1 + 3 + 3 + 4 + 5 + 8 = 24 8 – 1 = 7
246 = 4 The mean is 4. The range is 7
List in order: 1, 3, 3, 4, 5, 8
Mode ______Median ______
______
There can be several modes or no mode. The middle two numbers are 3 and 4
The mode in this example is 3. 3 + 4 = 7 72 = 3.5
The median is 3.5
Find the median, mode, mean and range of each data set.
1. 6, 5, 3, 6, 8 2. 12, 15, 17, 9, 17
3. 7, 6, 13, 16, 15, 9 4. 51, 62, 68, 55, 68, 62
An outlier is an extreme value – either ______
Use the data set to answer the questions.
4, 6, 3, 6, 25, 3, 2
5. Is there an outlier? ______If so, what is it? ______
6. How does the outlier affect the mean and the median?
7. Which measure of central tendency best describes the data? Explain your answer.
Mean Absolute Deviation
Mean Absolute Deviation ______
______
Step 1. Find the mean.
Step 2. Find the absolute value of the difference
between each data value and the mean.
Step 3. Find the average of those differences.
1. 52 + 48 + 60 + 55 + 59 + 54 + 58 + 62 = 448 4488 = 56
2. 56 – 52 = 56 – 48 = 56 – 60 = 56 – 55 =
56 – 59 = 56 – 54 = 56 – 58 = 56 – 62 =
3.
Try one on your own!
Practice Problems
1. The table shows the running time in minutes for two kinds of movies. Find the mean absolute deviation for each set of data. Round to the nearest tenth. Then write a few sentences comparing their variation.
2. The table shows the height of waterslides at two different water parks. Find the mean absolute deviation for each set of data. Round to the nearest whole number. Then write a few sentences comparing their variation.
Box and Whisker Plot
A box-and-whisker plot uses ______
To make a box-and-whisker plot, first divide the data into four equal parts using ______.
The ______, or ______, divides the data into a lower half and an upper half. The median of the lower half is the ______, and the median of the upper half is the ______.
Example
Use the data to make a box-and-whisker plot.
73 67 75 81 67 75 85 69
Step 1: Order the data from least to greatest.
Lowest Value ______
Lower Quartile _____ Median _____
Upper Quartile _____
Greatest Value _____
Draw a box from the lower to the upper quartile.
Inside the box, draw a vertical line through the median.
Then draw the “whiskers” from the box to the least and greatest values.
Try one on your own!
42 22 31 27 24 38 35
Practice
1) Use the data to make a box-and-whisker plot.
19, 46, 37, 16, 24, 47, 23, 19, 31, 25, 42
16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
2) Make a box-and-whisker plot of the data:
38, 42, 26, 32, 40, 28, 36, 27, 29, 30
26 28 30 32 34 36 38 40 42
Measures of Variability
Measures of Variability ______
The length of the plot corresponds to the measure of variation of the data set. The smaller it is the less is the variation!
The ______can be used to describe the variability of a set of data.
The ______is another way to describe the variability.
Determining the Best Measure
1. Ian surveyed a different group of students in his science and math classes. The double box plot shows the results for both classes. Compare their centers and variations. Write an inference you can draw bout the two populations.
· What does the does the double box plot show?
· Is either plot symmetric?
· Which measure of center should you use to compare the data?
· Which class posts more blogs?
· Which measure of variation should you use to compare the data?
· Which class has a greater spread of data around the median?
2. The double dot plot shows the daily high temperatures for two cities for thirteen days. Compare the centers and variations for the two populations. Write an inference you can draw about the two populations.
3. Mrs. Ferguson, your school librarian, asks you to conduct a survey of how many books students read during the year. You get the following results:
12, 22, 10, 12, 4, 10, 8, 12, 15, 20, 18, 24, 21, and 9.
a) Make a box plot of the data.
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
b) Make a line plot of the data
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
c) Is the data symmetric or skewed?
Are there any outliers?
What is the IQR?
What is the Range?
4. Ms. Carpenter asked each of her students to record how much time it takes them toget from school to home this afternoon. The next day, students came back with thisdata, in minutes:
15, 12, 5, 55, 6, 9, 47, 8, 35, 3, 22, 26, 46, 54, 17, 42, 43, 42, 15, 5
a) Create a stem-and-leaf plot
b) Find the median and range.
5) 24, 20, 18, 25, 22, 32, 30, 29, 35, 30, 28, 24, 38
a. Create a stem-and-leaf plot for the data.
b. What is the range?
c. What is the median?
d. What percentage of data falls between 10 and 30?
`
Reading Box-and-Whisker Plots
1)
a. Which group has a larger interquartile range?
b. Which group of players has more predictability in their height?
2)
a. Which shoe store has a greater median?
b. Which shoe store has a greater interquartile range?
c. Which shoe store appears to be more predictable in the number of shoes sold per week?
Line Plots
Example 1
Number of sibling per student in Ms. Stojo’s class
1. How many students are in the class?
2. How many students have more than one sibling?
3. How many students are an only child? 4. How many students have 3 or more
siblings?
5. How many students have less than 3 sibling? 6. How many students have more than
3 siblings?
Example 2
The nature club as Westville Middle School went on a field trip to the seashore. Eachmember collected seashells to put on display at the school. The line plot below showshow many shells each club member collected.
a) What is the mode? b) What is the median?
c) What is the range? d) What is the mean?
Example 3
a) Which number/s are the outliers? b) What is the mode?
c) What is the median? d) What is the range?
Example 4
Create a line plot for the Number of Goals Scored by 24 Hockey Players.
a) What is the mode? b) What is the median?
c) What is the range? d) What is the mean?
Frequency Histogram
Example 1
Example 2
During a car trip, Antoine counted the number of red, black,blue, and green cars he passed on the highway. He recordedthe results in the box below.
Number of Cars
Test Review
1. The table below shows the golf scores for two people.
Make two box and whisker plots of the data on the same number line.
a) Which golfer has the lower median score?
b) Which golfer has the smaller interquartile range of scores?
c) Which golfer appears to be more consistent?
2. Find the mean absolute deviation for the following quiz scores: 6, 9, 6, 9, 8, and 10.
3. Box-and-whisker plots can sometimes compare two sets of data. What conclusion can be drawn from the box-and-whisker plot below?
4. The following table shows the annual salaries for two different companies.
Company A / $12,000 / $15,000 / $27,500 / $28,000 / $80,000Company B / $27,000 / $27,500 / $27,500 / $40,000 / $45,000
a. Find the mean, median, and mode of the two companies.
b. Which company would you rather work for? Justify your answer.
5. Create a box and whisker plot for the following set of data.
16, 14, 13, 13, 18, 12, 11, 12, 12
7. Create a line plot for the following set of data.
52, 54, 57, 59, 55, 54, 55, 51, 53, 52 , 50, 56