4th Grade - Mode, Median And Outliers Of Data

 
     
 
     
 
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4th
Graphs and Charts
Mode, Median and Outliers of Data
Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.
Find the modes (the number that appears the most), the median (the middle number of data that has been put in order from least to greatest), and outliers (the number that does not belong to the data set because it is too large are too small) for sets of numbers.
 

Sample Problems

(1)

Find the median of the data:

87 70 57 43 88 47 17 93 87


(70)

(2)

Find the mode of the data:

193 182 130 187 229 210 187 182 187 229


(187)

(3)

Identify the median and mode of the decimals:

55.48 94.58 75.13 75.31 55.18 94.58 94.9


(Median: 75.31 Mode: 94.8)

(4)

Use the line plot to identify the mode, range, and outlier for the data:

After summer vacation, my teacher took a survey to see how many times we went to the movies during our break.

x

x x

x x x x

x x x x x

x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

0 1 2 3 4 5 6 7 8 9


Mode: ______

Outlier: ______

Range: ________


(Mode: 5; Outlier: 9; Range: 7)

(5)

Use the table to find the median, mode, and outlier for the data:


School Fundraiser for Playground Equipment

Grade Level

Money Raised

Kindergarten

$220.00

First Grade

$187.00

Second Grade

$219.00

Third Grade

$220.00

Fourth Grade

$225.00

Fifth Grade

$643.00


Mode: ______

Median: ______

Outlier: ______


(Mode: $220; Median: $220; Outlier: $643.00)

Learning Tips

(1)

Order numbers from least to greatest:

Practice ordering small and large numbers, including decimals from least to greatest. Reviewing the skill will help the child in finding the median of the data because they have to place the numbers in order from least to greatest before they determine the median number.

(2)

Place numbers on cards and practice with mode, median and outlier by allowing the child to have a hands-on experience with the data.


For example, you can use some index cards and write numbers on 6-10 cards. First, have the child move the number and order them from least to greatest. Once the cards are in order, you can ask them questions about the mode (which number appears the most), median (what is the number placed in the middle), range (what is the difference of the greatest and least number), and outlier (which number is not close in value with the other numbers).

(3)

Math vocabulary

Median- The middle number in a set of numbers ordered from least to greatest

12 64 71 88 88 95 98

Mode- The number (or item) that occurs the most often in a set of data

12 64 71 88 88 95 98


Outlier- A value separated from the rest of the data

12 64 71 88 88 95 98


Line plot- A graph with a number line that shows how often something occurs (frequency)


Range- The difference between the greatest and least values in a set of data.

12 64 71 88 88 95 98


98 – 12 = 86


(4)

Strategy to find median:

27 39 28 27 25 32 31

1. List the data in order from least to greatest

25 27 27 28 31 32 39

2. Cross out one number from each end until you reach the middle:

25 27 27 28 31 32 39

25 27 27 28 31 32 39

25 27 27 28 31 32 39

3. The median is 28


If there data set has an even amount of numbers, you add the two middle numbers and divide by 2 to find the median (does not occur too often in 4th grade).


For example: 25 27 27 28 30 31 32 39

Add: 28 + 30 = 58

Divide: 58 ÷ 2 = 29

The median = 29



(5)


Use a reality situation to find median and mode:

Have your child look in the newspaper or on the internet to find the weather temperatures for the week (7 days). Have them write the numbers in order from least to greatest. Then, find median and mode.


This will allow them to make a connection on why we may need to find the median and mode of data, which will allow the skill to be meaningful and will be remembered for later lessons.

Extra Help Problems

(1)

Find the median of the data:

29 21 28 29 21 21 24 30 32


(28)

(2)

Find the median of the data:

151 139 152 147 156 151 172 141 150


(151)

(3)

Find the median of the data:

72 74 71 70 76 72 74 89 80


(74)

(4)

Find the median of the data:

1,732 1,718 1,987 1,893 1,342 1,722 1,673


(1,722)

(5)

Find the median of the data:

627 621 726 813 623 613 672 635 532


(627)

(6)

Find the mode of the data:

2 2 3 4 5 3 3 7 4 6 1 1 0


(3)

(7)

Find the mode of the data:

  1. 543 294 435 543 249 924


(none)

(8)

Find the mode of the data:

83 98 92 56 27 30 30 92 44 23


(30 and 92)

(9)

Find the mode of the data:

□□□○ □□ ○○□□ □□□○ ○○□


(□□□○)

(10)

Find the mode of the data:

7,223 7,332 7,323 7,232 7,230 7,233 7,331 7,223


(7,223)

(11)

Identify the median and mode of the decimals:

38.79 37.74 34.61 34.6 38.97 36.42 47.16 37.74 36.4


(Median: 37.74 Mode: 37.74)

(12)

Identify the median and mode of the decimals:

42.97 54.25 45.27 57.21 42.97 54.52 54.25


(Median: 54.25 Mode: 54.25)

(13)

Identify the median and mode of the decimals:

32.62 34.92 35.9 28.49 34.92 32.9 32.09


(Median: 32.9 Mode: 34.92)

(14)

What is the range of the decimals:

55.84 94.85 75.31 97.61 45.77 58.94 94.58


(41.77)

(15)

Which decimal is an outlier:

39.44 16.64 32.69 45.21 37.09 41.98


(16.64)

(16)

Use the line plot to identify the mode and range for the data:

How many rides did you get on at the fair?

x

x x x

x x x x x

x x x x x x x

x x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

0 1 2 3 4 5 6 7 8 9


Mode: ______

Range: ________


(Mode: 0 Range:6)

(17)

Use the line plot to identify the mode, range, and outlier for the data:

We had a bake sale that sold 5 cookies for $1.00. How many cookies did your class sell?

x

x x

x x x x x

x x x x x x

x x x x x x x x

--׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀--------׀---

10 15 20 25 30 35 40 45 50 55


Mode: ______

Outlier: ______

Range: ________


(Mode: 35; Outlier: 55; Range: 35)

(18)

Use the table to find the median, mode, and range for the data:


Number of free-throws made by the basketball teams

Teams

Free-throws made

Team 1

\\\\ \\\\ \\\\

Team 2

\\\\

Team 3

\\\\ \\\

Team 4

\\\\ \\\\ \\\

Team 5

\\\\ \\\\ \\\\

Team 6

\\\

Team 7

\\


Mode: ______

Median: ______

Range: ______


(Mode: 14; Median:8; Range: 12)

(19)

Use the table to find the median and mode for the data:


Who has the most pencils?

Groups

Number of Pencils

Red group

12

Yellow Group

15

Blue Group

11

Green Group

10

Purple Group

12


Mode: ______

Median: ______


(Mode: 12; Median: 12)


(20)

Use the table to find the mode and range for the data:


Age Groups for Summer Camp

Age

Number of kids

7

20

8

23

9

27

10

23


Mode: ______

Range: ______


(Mode: 23; Range: 7)

(21)

Find the mode for the sentence:

Most of the families in our neighborhood have dogs. Five families have 1 dog, two families have 3 dogs, four families have 2 dogs, and three families have 4 dogs.


(1 dog)

(22)

Find the median:

The temperatures in the San Fernando Valley this week were 90, 91, 89, 100, 101, 99, and 91.


(91)  

(23)

Order the numbers from least to greatest:


82, 83, 80, 90, 91, 97, 84


(80, 82, 83, 84, 90, 91, 97)

(24)

Order the numbers form least to greatest:

14.5 14.50 14.05 15.4 15.04


(14.05, 14.5, 14.50, 15.04, 15.4)

(25)

How can you identify an outlier?

  1. it is the largest number

  2. It is the number that appears the most

  3. It does not relate to the data in its set


(c)

 

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