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Using the State Curriculum: Mathematics, Grade 4

Algebra | Geometry | Measurement | Statistics | Probability | Number | Processes
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 4.0 Knowledge of Statistics

Topic B. Data Analysis

Indicator 2. Describe a set of data

Objective a. Determine median, mode, and range

  • Use no more than 8 pieces of data and whole numbers (0 – 100)

Clarification

The mean, median and mode of a data set are its measures of central tendency and each can represent an "average". Many people equate the average with the mean. All means are averages but NOT all averages are means.

The mean of a data set is obtained by adding all the data values and dividing by the number of values.

The median is the number that falls exactly in the middle of a set of data when the data is arranged in order from least to greatest. Half the values lie at or above the median and half below. When there is an odd number of data, the median is the middle number. When there is an even number of data points, the median is the mean of the two middle numbers. For sets of data with values that are much higher or lower then most of the other values, the median may be a good choice for measuring central tendency.

The mode is the number in a data set that occurs most often. Sometimes a set of data can have two modes. The data is said to be bi-modal at this level. If there are more than two modes, then the set of data contains no mode, since there are too many values that occur with the same frequency.

The range of a data set is the difference between the greatest and least numbers in a set of data. Knowing the range can help decide whether the differences among the data are important and which measure of central tendency should be used to describe the "average" of the set. For example, in the set 2, 3, 4, 5, 20, the range is 18. The difference between the first four sets of values is 1 and the difference between the last two values is 15. Is the range equally distributed between the values of the data set? Which measure of central tendency should be used to describe the "average" of the data? The mean is about 7 and the median is 4. The median in this case is a better describer of the average of the set of data because the range is not distributed evenly between the members of the set.

Students need to be able to describe and summarize data using range, mean, median and mode so they can draw conclusions based on the data.

Classroom Example 1

The following data set shows the number of customers served at Main Street Ice Cream Store during a Wednesday afternoon.

HOURS 11-12 12-1 1-2 2-3 3-4 4-5 5-6
# OF CUSTOMERS 52 99 65 64 60 62 63

The median is 63, because when we arrange the data from least to greatest

52, 60, 62, 63, 64, 65, 99

the middle value is 63.

You can also find the median by removing a data point from each side of the values.
For example,

  • 52 and 99 would be removed because they are the least and greatest value points.
  • Then, 60 and 65 would be removed because they are the next data points that are the least and greatest.
  • Next, 62 and 64 would be removed as the remaining least and greatest values.
  • Finally, only 63 remains.

Classroom Example 2

The chart below shows the number of jumping jacks some third-graders did in one minute.

Student Total Jumping Jacks
Sue 89
Jimmy 88
Natashia 94
Jose 56
Jordyn 58
Robert 86
Desmond 84
Rebeka 100

The range of the data is 100 - 56 = 44 jumping jacks in one minute. Because we find the greatest value and least value data point and find the difference between these values.

100 jumping jacks was the greatest amount jumped (Rebeka).
56 jumping jacks was the least amount jumped (Jose).

Is there a significant amount between the least value and greatest value? Yes! So a student knows that there are large variations in the data.

  • The median of the data is 87 jumping jacks. First arrange the data points from least to greatest: 56, 58, 84, 86, 88, 89, 94, 100.
  • Begin by removing or crossing out the least and greatest values, 56 and 100. Next remove the next least and greatest values, 58 and 94.
  • Then remove or cross out the next least and greatest value 84 and 89.
  • There are two values remaining, 86 and 88. The value between these two data values, or the average of 86 and 88, is 87.

The median value must be computed, because there is an even number of data.

Classroom Example 3

The table below shows the shoe sizes of a group of students in 4th grade.

Student 1 4
Student 2 5
Student 3 6
Student 4 4
Student 5 3
Student 6 4
Student 7 7
Student 8 4
Student 9 4
Student 10 4
Student 11 5
Student 12 5
Student 13 3
Student 14 4
Student 15 3

What is the mode of the set of data? [4] Does it describe the average size of this group of 4th graders? [Yes it describes the average size of this group of 4th graders because besides being the Mode, it is also the Median of the data set and the Range of the data set. It is the most named data point, the middle data point, and the difference between the smallest and largest shoe size.]

Classroom Example 4

The following chart shows data obtained from the American Trucking Association's website. It shows the maximum speed limits and the number of states that have those maximum speed limits.

Maximum Speed Limits Number of States
55 mph 9
60 mph 3
65 mph 21
70 mph 8
75 mph 10

The mode of the data set is 65 miles per hour because 65 miles per hour occurred 21 times, most often, compared to the other speed limits.

Classroom Example 5

The following were scores obtained from a cumulative test given to eight 4th graders.

92, 89, 89, 89, 92, 100, 92, 98

The mode is 89 and 92 because both the scores of 89 and 92 occur most often (3 times each). This is an example of a bi-modal data set.
/toolkit/vsc/clarification/mathematics/grade4/4B2a.xml
Resources for Objective 4.B.2.a:
CLARIFICATIONS | Lesson Seeds | Sample Assessments | Public Release Items |