Name: ___________________________ Date: __________________ AIM: SWBAT find the measures of center for a set of data and determine which is the most appropriate to use in a given situation. Students will also understand Random Samples Statistics is the study of collecting, organizing and interpreting information, or data. Mean, median and mode are called measures of center because they are statistics that describe the center of a set of data.
Mean is the sum of the data divided by the number of items in the data set.
Median is the middle number of the data when the numbers are in order from least to greatest. *If the set has 2 middle numbers, the median is the mean of those 2 numbers.
Mode is the number or numbers that occur the most often.
*Not every set of data has a mode. Sometimes there is more than one mode.*
Range is the difference between the greatest number and the least number in the data set.
***REMEMBER ALWAYS PUT YOUR DATA IN ORDER FROM
LEAST TO GREATEST***
1) Find the mean, median, mode, and range for the following set of data. Ages of Math Teachers at FFMS
25, 33, 39, 37, 42, 51, 25 Line the number up from least to greatest first!
MEAN (add them and then divide the sum by the number of addends you have)
MODE (which number occurs the Most)
2) Use the following set of data to find the mean, median, mode and range: 70, 62, 61, 60, 62, 57
Line the number up from least to greatest first!
MEAN (add them and then divide the sum by the number of addends you have)
MODE (which number occurs the Most)
MEDIAN (which number is in the Middle) RANGE (subtract the smallest from the largest number)
3) The table below shows the number of people in the House of Representatives. Find the mean, median, mode, and range of the data.
Line up the numbers from least to greatest first!
MEAN (add them and then divide the sum by the number of addends you have)
MODE (which number occurs the Most)
*MEDIAN *If the set has 2 middle
numbers, the median is the mean of those 2 numbers*
RANGE (subtract the smallest from the largest number)
RANDOM SAMPLES
A food service company supplies meals for 12 different schools. How might the company get information about students’ favorite lunches? Surveying every student in every school would take a lot of time and effort. It would be more efficient to survey a random sample that represents the whole group, or population.
In order for a sample to be considered random, every object or event has to have an equal chance of being selected. Suppose you fill a jar with slips of paper that contain the names of all students in a school. Suppose you pick ten slips of paper from the top of the jar. Do all names have an equal chance of being selected? Maybe the slips at the top belong to the last class that put their names in the jar. This would be a biased sample because it does not represent the whole population.
Suppose, instead, you put your hand in and mix the slips all around. You do this each time you pick a name. With this method, all names get an equal chance of being selected. This would be a random sample.
Here are some ways to select a REPRESENTATIVE RANDOM SAMPLE:
Use a pattern, such as selecting every fourth period who enters the cafeteria
Use a method, such as drawing names out of a hat, where everyone has an equal chance of being selected.
Divide the population into groups, such as by grade level, and randomly select people from each group.
Here are some ways of selecting a sample that might result in a BIASED SURVEY: Let people volunteer to take a survey.
Choose people who are easy to reach, such as the students who happen to be in the cafeteria when you are available to give surveys.
Choose people as a group, such as students on the honor roll.
Carla has a list of all 720 students in her middle school. She writes the names of each student on a slip of paper and puts each slip in a box. She then pulls 30 names from the box to decide who she will survey about the upcoming election.
How many students are in Carla’s sample? _____ How many students are in Carla’s population? _____
Decide if the methods for selecting a sample are FAIR or BIASED. Give reasons for your answers.
1) A store owner wants to survey customers about the products he sells. He programs the computer to select 100 customers from the mailing list and sends them each a survey.
_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 2) The events committee wants to survey students about a school dance. The committee is meeting in the gym, where the girls’ basketball team is practicing. They survey the players on the girls’ basketball team.
_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 3) Roberto wants to know the favorite sport of adults in his hometown. He surveys 50 adults at a baseball game.
_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 4) Paula wants to know the favorite type of music for students at her school. She surveys the first 60 people who enter the school doors in the morning.
_______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 5) Dallas wants to know what elective subjects the students at his school like best. He surveys students who are leaving band class.
Name: _______________________________ Date: _________________
HOMEWORK – MEASURES OF CENTER Period 7
Find the mean, median and mode for each set of data. If necessary, round to the nearest whole number.
1) The minutes spent biking each day in one week: 45, 30, 65, 90, 74, 60, 35 Remember to put the numbers in order first!
Mean: _____________ Median: _____________
Mode: ____________ Range: _____________
2) Last week, Sarah spent 34, 30, 45, 30, 40 and 28 minutes exercising.
Mean: _____________ Median: _____________
Mode: ____________ Range: _____________
3) Paula wants to know the favorite type of music for students at her school. She surveys the first 60 people who enter the school doors in the morning. (circle the correct choice below)
FAIR or BIASED
5) Dallas wants to know what elective subjects the students at his school like best. He surveys students who are leaving band class.
