Create and Interpret Line Graphs (Frequency Polygon)

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Question 1 of 2

1. Question
From the frequency polygon shown below, construct a frequency distribution table and determine how many fishermen are in the group.

Enter the frequency for each respective score in the table below
- Score $(x)$ $(x)$ Frequency $(f)$ $(f)$
  
  2 (3)
  
  3 (2)
  
  4 (5)
  
  5 (6)
  
  6 (9)
  
  7 (12)
  
  8 (3)
  
  $Total =$ $\text(Total) =$
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A frequency distribution table displays how many times a particular score has occurred in a set of data.

This frequency polygon can be expressed as:

Hours fishing $=$ $=$ Score $(x)$ $(x)$

No. of fishermen $=$ $=$ Frequency $(f)$ $(f)$

Name the table accordingly, then fill in the Hours fishing column with the values at the bottom of the polygon.

Hours fishing $(x)$ $(x)$ No. of fishermen $(f)$ $(f)$

2

3

4

5

6

7

8

$Total =$ $\text(Total) =$

Next, check the points on the polygon and note the corresponding No. of fishermen for each Hours fishing under the No. of fishermen column.

Hours fishing $(x)$ $(x)$ No. of fishermen $(f)$ $(f)$

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$Total =$ $\text(Total) =$

Lastly, count the total frequency.

Hours fishing $(x)$ $(x)$ No. of fishermen $(f)$ $(f)$

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$Total = 40$ $\text(Total) =40$

Hours fishing $(x)$ $(x)$ No. of fishermen $(f)$ $(f)$

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$Total = 40$ $\text(Total) =40$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$
2	(3)
3	(2)
4	(5)
5	(6)
6	(9)
7	(12)
8	(3)
	$Total =$ $\text(Total) =$

Hours fishing $(x)$ $(x)$	No. of fishermen $(f)$ $(f)$
2
3
4
5
6
7
8
	$Total =$ $\text(Total) =$

Hours fishing $(x)$ $(x)$	No. of fishermen $(f)$ $(f)$
2	3
3	2
4	5
5	6
6	9
7	12
8	3
	$Total =$ $\text(Total) =$

Hours fishing $(x)$ $(x)$	No. of fishermen $(f)$ $(f)$
2	3
3	2
4	5
5	6
6	9
7	12
8	3
	$Total = 40$ $\text(Total) =40$

Hours fishing $(x)$ $(x)$	No. of fishermen $(f)$ $(f)$
2	3
3	2
4	5
5	6
6	9
7	12
8	3
	$Total = 40$ $\text(Total) =40$

Question 2 of 2

From the frequency polygon shown below, find the mean of the scores.

Round your answer to one decimal place

$Mean =$ $\text(Mean )=$ (5.6)

Incorrect

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Mean Formula

Mean = \frac{\sum f \cdot x}{\sum f}

$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$

Remember

A frequency polygon is a line graph version of the frequency distribution table.

First, convert the frequency polygon into a frequency table.

Score $(x)$ $(x)$ – values at the bottom of the histogram

Frequency $(f)$ $(f)$ – height of each bar on the histogram

$f \cdot x$ $f⋅x$ – sum of $x$ $x$ and $f$ $f$ on each row in the newly created frequency table.

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	$f \cdot x$ $f⋅x$
2	3	6
3	2	6
4	5	20
5	6	30
6	9	54
7	12	84
8	3	24

Find the sum of both the Frequency and $f . x$ $f.x$ columns.

$\sum f$ $sum f$	$=$ $=$	$3 + 2 + 5 + 6 + 9 + 12 + 3$ $3+2+5+6+9+12+3$
	$=$ $=$	$40$ $40$

$\sum f \cdot x$ $sum f⋅x$	$=$ $=$	$6 + 6 + 20 + 30 + 54 + 84 + 24$ $6+6+20+30+54+84+24$
	$=$ $=$	$224$ $224$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	$f \cdot x$ $f⋅x$
2	3	6
3	2	6
4	5	20
5	6	30
6	9	54
7	12	84
8	3	24
	$Total = 40$ $\text(Total) =40$	$Total = 224$ $\text(Total) =224$

Use the formula to compute for the mean.

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$	Mean Formula

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\color{#314EC4}{224}}{\color{#9202AA}{40}}$	Substitute values

$Mean$ $\text(Mean)$	$=$ $=$	$5.6$ $5.6$	Evaluate

Mean = 5.6

$\text(Mean)=5.6$

Create and Interpret Line Graphs (Frequency Polygon)

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Quiz summary

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1. Question

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2. Question

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Mean Formula

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Quizzes

Hours fishing	$=$ $=$	Score $(x)$ $(x)$
No. of fishermen	$=$ $=$	Frequency $(f)$ $(f)$