6DASP.1 – Describe and compare data sets using the concepts of median, mean, mode , maximum, and range.
SWBAT find the median of a data set.
· The median is the middle number of a data set – there an equal number of data points less than the median as there are greater than the median
· If there is an even amount of data points – the median is the average (mean) of the two middle data points
· The median is generally not as easily affected by “outliers”
Look at the data set below.
11, 14, 18, 21, 21
Which of these data sets has the same median as the given set?
A. 14, 16, 17, 18, 20
B. 11, 13, 19, 20, 21
C. 13, 16, 18, 20, 25
D. 13, 16, 20, 21, 21
Reon practiced playing the piano four times this week. The number of minutes he practiced are listed below.
18, 31, 25, 21
What is the median number of minutes that Reon practiced the piano this week?
The chart below shows the amount of prep dollars Ebony earned each day this week.
What is the median number of prep dollars Ebony earned this week?
Warm Up: (5 mins)
· Put the following numbers in order from least to greatest. Put your answer in the grid paper with one number per square
Ex: 3,1, 4, 5, 2 à
o 96, 87, 76, 90, and 76.
o 90, 44, 23, 83, and 23.
o 74, 80, 74, 92
o 87, 57, 67, 77
· Ask students to cut each group out into a single strip of numbers (show a model)
· One Inch - Grid paper
· Scissors for each student (pair of students)
Opening: (5 mins)
· Review the ordering of the numbers from the warm up
· Ask students to follow your directions as you model taking each strip and folding it exactly in half.
· Start by folding the strips that have 5 numbers and then with the strips that have four numbers.
o Which of these strips have and even amount of numbers?
o Which of these strips have an odd amount of numbers?
o What do you notice happens when you fold a strip of paper that has an odd amount of numbers? Where is the fold?
o Do you think the same thing will happen if you had 9 numbers? 15 numbers? 10 numbers?
o Where is the fold when you fold a strip that has an even amount of numbers?
o Do you think the same thing will happen with 8 numbers? 20 numbers? 11 numbers?
Intro/Direct Instruction: (10 mins)
· Over the past couple of days we have been working on describing data by analyzing it
· More specifically we have worked on describing statistics about a data set. So far we know we can find the mean of a data set by distributing all of the parts equally among the groups or by using the procedure of adding and dividing.
· We have also learned that we can describe a set based on which number or numbers come up most common which is called the mode. We also remember that sometimes a set doesn’t have a mode and sometimes a data set has many modes.
· Well today we are going to learn about another statistic or way to analyze data.
· Today we are going to learn about the median of a data set
Direct Students to Notes:
· Define median as the middle number of a data set. This means that there are an equal number of data points less than the median as there are that are more than the median.
· Just like the past two days we have a chant that will help us to remember the procedure for finding the median
· Students and teacher should practice the chant together
· “median’s the middle, so put them in order”
· Review that today for our warm up – we were finding the median for each set of numbers.
· Model that the first step is to count the number of data points and write that number in the box.
· Model that the second step of finding the median is to put the numbers in order no matter what format they are displayed in.
· As modeling highlight the importance of taking time and making sure that all data points are accounted for. After ordering the numbers, count the number of data points and make sure it matches the number placed in the box.
· Model that the second step is to find the middle number – one way to do this is to simply cross out the first number and then the last number and the first number and last number until you reach the middle.
· Tell/Model for students that if there is an odd number of data points there will be just one middle number – when we look back to our strips from the warm up, we see that in the strips with an odd number of data, the fold fell exactly on one number. That number is our median
· Tell/model for students that if there are an even number of data there will be two middle numbers – refer back to the strips of paper where the fold was on the line between two numbers.
Guided Practice: (10mins)
· Students will complete the problems on notes page / or on slate boards
· Problem 1 – odd number of data
· Problem 2 – odd number of data within a table (check to see if students pick the middle value of the table or if they first order the data) – point out as a common mistake
· Problem 3 – even number of data
· Problem 4 – even number of data – ask students what data point could be added to the data set that would keep the median the same.
Independent Practice: (15 mins)
· Students complete worksheet – teacher circulates to monitor understanding/practice – or pull a small group of students who struggled during the guided practice
Closing: (8 mins)
· Review the chant
· Ask students for the steps of finding the median.
· Give students exit ticket - a data set in a chart – ask students to come up with multiple choice answers – tell students 3 answers have to be incorrect and one answer should be correct. Ask students to explain or show why they came up with each answer choice – remind students that the wrong answers should be mistakes that you think students commonly make.
|CW Median Classwork||
|Notes Median Notes||