1. 4th Grade Math Mini-Lesson 9
Median, Mode, and Range
MA.E.1.2.2

2. MA.E.1.2.2
The student determines range, mean, median, and mode from sets of data.

3. Part 1
Explicit Instruction

4. Explicit Instruction (about 15 minutes)
For this Mini-Lesson, we are going to review median, mode, and range.

5. Explicit Instruction (about 15 minutes)
What is Median ?
Median is the middle number when you list a group of numbers or set of data in order from least to greatest.

6. Explicit Instruction (about 15 minutes)
Let’s find the median of the seven
Fourth Grade Classes at Jefferson Elementary School.
Mrs. Kay has 28 students.
Ms. Rowe has 35 students.
Mrs. Little has 18 students.
Mr. Erie has 25 students.
Mr. Bell has 25 students.
Mrs. Moore has 31 students.
Ms. Wright has 22 students.

7. Explicit Instruction (about 15 minutes)
To find the median or middle number for this set of data, we have to make sure the data is in order from least to greatest. Is our data in order from least to greatest?
Explicit Instruction (about 15 minutes)
No, our data is not in order from least to greatest.
First let’s take the data from our problem, and put it into a list.
Mrs. Kay has students.
Ms. Rowe has students.
Mrs. Little has students.
Mr. Erie has students.
Mr. Bell has students.
Mrs. Moore has students.
Ms. Wright has students. 28 35 18 25 25 31 22
28,
35,
18,
25,
25,
31, 22

8. Explicit Instruction (about 15 minutes)
Since the data is not in order from least to greatest, let’s fix that.
Much better!
28,
35,
18,
25,
25,
31,
22,

9. Explicit Instruction (about 15 minutes)
Since the number 25 is right in the middle of our set of data, 25 is the median.
Now that the data is in order, let’s find our median. Start by eliminating numbers at each end of the set of data. X
18,
22,
25,
25,
28,
31, 35 X X

10. Explicit Instruction (about 15 minutes)
What is Mode?
Mode is the value that occurs most often in a group of numbers or set of data.

11. Explicit Instruction (about 15 minutes)
Let’s find the mode of the same seven
Fourth Grade Classes at Jefferson Elementary School.
Mrs. Kay has 28 students.
Ms. Rowe has 35 students.
Mrs. Little has 18 students.
Mr. Erie has 25 students.
Mr. Bell has 25 students.
Mrs. Moore has 31 students.
Ms. Wright has 22 students.

12. Explicit Instruction (about 15 minutes)
First let’s take the data from our problem, and put it into a list.
Mrs. Kay has students.
Ms. Rowe has students.
Mrs. Little has students.
Mr. Erie has students.
Mr. Bell has students.
Mrs. Moore has students.
Ms. Wright has students. 28 35 18 25 25 31 22
28,
35,
18,
25,
25,
31, 22

13. Explicit Instruction (about 15 minutes)
The data is not in order from least to greatest, so let’s fix that.
Even though the numbers don’t need to be in order from least to greatest to find the mode, it is COOL to be organized!
28,
35,
18,
25,
25,
31,
22,

14. Explicit Instruction (about 15 minutes)
We can see that 25 appears the most in the set, so 25 is our mode.
Now that the data is in order, let’s find our mode. Start by looking for the value that appears the most often.
18,
22,
25,
28,
31, 35

15. Explicit Instruction (about 15 minutes)
What is Range?
Range is the difference between the greatest value and the least value in a group of numbers or set of data.

16. Explicit Instruction (about 15 minutes)
Let’s find the range of the same seven
Fourth Grade Classes at Jefferson Elementary School.
Mrs. Kay has 28 students.
Ms. Rowe has 35 students.
Mrs. Little has 18 students.
Mr. Erie has 25 students.
Mr. Bell has 25 students.
Mrs. Moore has 31 students.
Ms. Wright has 22 students.

17. Explicit Instruction (about 15 minutes)
Let’s use our list, and put the data in order from least to greatest.
Much better!
28,
35,
18,
25,
25,
31,
22,

18. Explicit Instruction (about 15 minutes)
Now that the data is in order, let’s find our range. Start by finding the greatest number in the set.
The greatest number is 35.
18,
22,
25,
28,
31, 35

19. Explicit Instruction (about 15 minutes)
17 students is the range of the number of students in fourth grade classes at Jefferson Elementary.
Explicit Instruction (about 15 minutes)
= 17
The difference between 35 and 18 is 17.
We can use an open number line to find the difference between 18 and 35.
Now find the least or lowest number.
18,
22,
25,
28,
31, 2 10 5 20 30 18 35

20. Explicit Instruction (about 15 minutes)
For the seven Fourth Grade Classes at Jefferson Elementary School…
Mrs. Kay has 28 students.
Ms. Rowe has 35 students.
Mrs. Little has 18 students.
Mr. Erie has 25 students.
Mr. Bell has 25 students.
Mrs. Moore has 31 students.
Ms. Wright has 22 students.
The median class size is 25.
The mode class size is 25.
The range of class sizes is 17.

21. Explicit Instruction (about 15 minutes)
We can also use a line graph to find the range. Here is a line graph that shows the temperatures in New York City over 6 days.

22. Explicit Instruction (about 15 minutes)
The difference between 67 and 43 is 24.
67 – 43 = 24
The range is 24.
= 24
Explicit Instruction (about 15 minutes)
The range is the difference between the greatest value and the least value.
We can use an open number line to find the difference between 43 and 67.
Let’s find the range of temperatures in New York City.
First, let’s put the temperatures in order from greatest to least.
43,
50,
53,
57,
59, 67 7 10 7 50 60 43 67

23. Part 2
Guided Practice

24. Guided Practice (5 – 7 minutes)
Let’s review: Median is the middle number when you list a group of numbers or set of data in order from least to greatest. Mode is the number that occurs most often in a group of numbers or set of data. Range is the difference between the greatest value and the least value in a group of numbers or set of data.

25. Guided Practice (5 – 7 minutes)
Using this problem, let’s find the median, mode, and range.
The list below shows how the students in Mr. Lee’s class did on the Form A Mini-Assessment. Find the median, mode, and range assessment scores.
Form A Scores 40 80
100 60

26. Guided Practice (5 – 7 minutes)
Remember that we must put our data in order from least to greatest.
Let’s find the median first.
Form A Scores 40 80
100 60 40 80
100 60 80

27. Guided Practice (5 – 7 minutes)
Now with our numbers in order we can find the median or middle number.
So for Mr. Lee’s class, the median number of assessment scores is 40 X 60 X 80 80 X
100 X

28. Guided Practice (5 – 7 minutes)
Even though the numbers don’t need to be in order from least to greatest to find the mode, it is COOL to be organized! Plus, they are already in order from when we found our median.
Now let’s find the mode. Remember mode is the number that appears the most often in a set of data.
Form A Scores 40 80
100 60 40 80
100 60 80

29. Guided Practice (5 – 7 minutes)
Now with our numbers in order we can find the mode or the number that appears the most. 40 60 80
100
Two students scored an 80 on the assessment.
So for Mr. Lee’s class, the mode of assessment scores is 80.

30. Guided Practice (5 – 7 minutes)
Remember that we must put our data in order from least to greatest.
Now let’s find the range. Remember range is the distance between the greatest number in the set of data and the least or lowest number.
Form A Scores 40 80
100 60 40 80
100 60 80

31. Guided Practice (5 – 7 minutes)
The range of assessment scores is 60.
Having our numbers in order from least to greatest really saves time for median and range!
I didn’t even need an open number line for this problem.
In my head I started at 100 and counted down by 10s.
90, 80, 70, 60.
With our numbers in order we can take the greatest number and subtract the lowest number to find our range. 40 60 80
100
= 60

32. Guided Practice (5 – 7 minutes)
To find the range, find the difference between the greatest number and the least number.
The greatest number of people fishing is The least number of people fishing is 313.
We can also find the range on a line graph.
Guided Practice (5 – 7 minutes)
Here are some fishing statistics from the San Diego area for one week in March What is the range of the data?

33. Guided Practice (5 – 7 minutes)
Here are some fishing statistics from the San Diego area for one week in March What is the range of the data?
I see a total of The difference between 625 and 313 is
312!
There are a few different ways we can find the difference between 625 and 313.
Let’s look at an open number line.
100
100
100 12
413
513
613
313
625

34. Guided Practice (5 – 7 minutes)
Here are some fishing statistics from the San Diego area for one week in March What is the range of the data?
Either way we solve it, the range is 312!
So, if the difference between 600 and 300 is 300, and the difference between 25 and 13 is 12, the total difference is 312.
We can decompose, or break apart, each number and then subtract.
There are a few different ways we can find the difference between 625 and 313.
625
313
600 25
300 13
= 300
= 12

35. Part 3
Independent Practice

36. Independent Practice (5 - 7 minutes)
Year
Home Runs
2003 18
2004 23
2005
2006 14
2007 12
2008 11
2009 17
1. The chart to the right shows how many home runs Derek Jeter hit over the last 7 years. What is median and mode of Derek Jeter’s home runs?
2. What is the range of home runs over the last 7 years for Derek Jeter?
3. Use the musical instruments below to determine the instrument that is the mode.

37. Independent Practice (5 - 7 minutes)
Player
Goals Scored
Abby Wambach
107
Cindy Parlow 60
Kristine Lilly
129
Mia Hamm
158
Michelle Akers
113
Shannon MacMillan
Tiffany Milbrett
105
4. The United States Women’s Soccer team has some great goal scorers. The chart to the right shows the top goal scorers in the team’s history. What is the median and mode of the goals scored?

38. Independent Practice (5 - 7 minutes)
5. The United States Women’s Soccer team has some great goal scorers. The line graph to the right shows the top goal scorers in the team’s history. What is the range of the goals scored?

39. Independent Practice (5 - 7 minutes)
The answers to the Independent Practice questions appear on the next 3 slides.

40. Independent Practice (5 - 7 minutes)
1. The chart to the right shows how many home runs Derek Jeter hit over the last 7 years. What is median and mode of Derek Jeter’s home runs? Median = 17 Mode = 18
Year
Home Runs
2003 18
2004 23
2005
2006 14
2007 12
2008 11
2009 17
2. What is the range of home runs over the last 7 years for Derek Jeter? Range = 12
3. Use the musical instruments below to determine the instrument that is the mode.

41. Independent Practice (5 - 7 minutes)
Player
Goals Scored
Abby Wambach
107
Cindy Parlow 60
Kristine Lilly
129
Mia Hamm
158
Michelle Akers
113
Shannon MacMillan
Tiffany Milbrett
105
4. The United States Women’s Soccer team has some great goal scorers. The chart to the right shows the top goal scorers in the team’s history. What is the median and mode of the goals scored? Median = 107 Mode = 60

42. Independent Practice (5 - 7 minutes)
5. The United States Women’s Soccer team has some great goal scorers. The line graph to the right shows the top goal scorers in the team’s history. What is the range of the goals scored?
Range = 98

43. Mini-Assessment Form A
Part 4
Mini-Assessment Form A

44. Mini-Assessment Form A (5 - 7 minutes)
Test ID #8977

45. Mini-Assessment Form A (5 - 7 minutes)
The amount of money seven students earned selling candy bars for the school fundraiser is listed in the following table.
What is the median amount of money raised among the seven students?
A.  $15.99       
B.  $26.28
C.  $35.40
D.  $63.81

46. Mini-Assessment Form A (5 - 7 minutes)
The fourth grade is having a competition to see who can read the most books. According to the chart below, what is the mode for the number of books read?
A.  1       
B.  2       
C.  3       
D.  4

47. Mini-Assessment Form A (5 - 7 minutes)
3. Kelly made a chart of all the dogs’ ages in her neighborhood. What is the range of the dogs’ ages?
A.  3       
B.  7       
C.  10       
D.  11

48. Mini-Assessment Form A (5 - 7 minutes)
Mrs. Moore’s chart showed a group of science quiz scores. What was the median score on the quiz?
A.  80      
B.  85       
C.  86       
D.  88

49. Mini-Assessment Form A (5 - 7 minutes)
What is the range of the temperatures?
A.  15 degrees       
B.  20 degrees       
C.  25 degrees       
D.  30 degrees

50. Mini-Assessment Form A (5 - 7 minutes)
The answers to the Mini- Assessment appear on the following slide.

51. Mini-Assessment Form A (5 - 7 minutes)C D B

52. Mini-Assessment Form A (5 - 7 minutes)
Provide reteaching to students who do not receive 60% or better on the Mini- Assessment.

53. Part 5
Reteach/ Enrich

54. Mini-Assessment Form B

55. Mini-Assessment Form B (5 - 7 minutes)
Test ID #8978

56. Mini-Assessment Form B (5 - 7 minutes)
Each member of the bird watching club keeps a record of the number of cardinals spotted over the weekend. What is the median number of cardinals spotted by the members of the bird watching club?
A.  3       
B.  5       
C.  7       
D.  8

57. Mini-Assessment Form B (5 - 7 minutes)
The local police station used their radar devices to track speeds of cars traveling down a major road and listed the speeds in the following table. What is the mode of the speeds listed?
A.  40 mph      
B.  55 mph      
C.  65 mph     
D.  72 mph

58. Mini-Assessment Form B (5 - 7 minutes)
Ms. Taylor’s fourth grade class took a math test, and the test scores of seven students are displayed in the following table. What is the range of the scores from Ms. Taylor’s class?
A.  48       
B.  50       
C.  71       
D.  95

59. Mini-Assessment Form B (5 - 7 minutes)
4. The track team practices running the 50-yard dash twice per week. What is the median time in seconds recorded for the 50-yard dash?
A. 5       
B.  7       
C.  8       
D.  11       

60. Mini-Assessment Form B (5 - 7 minutes)
What is the range of the quiz scores?
A.  10       
B.  32       
C.  34       
D.  64

61. Mini-Assessment Form B (5 - 7 minutes)
The answers to the Mini- Assessment appear on the following slide.

62. Mini-Assessment Form B (5 - 7 minutes)C