Create and Interpret Bar & Line Graphs (Histograms)

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Question 1 of 6

1. Question
From the frequency histogram shown below, find the mode of the scores.
- $\text(Mode )=$ (4)
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A histogram is a bar graph version of the frequency distribution table.

The mode is the value that appears most often in a set of data.

First, convert the histogram into a frequency table.

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

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

Score $(x)$ Frequency $(f)$

1 2

2 8

3 16

4 20

5 12

6 4

7 2

Notice that the highest value in the Frequency column is $20$ and it corresponds to $4$ .

Score $(x)$ Frequency $(f)$

1 2

2 8

3 16

4 20

5 12

6 4

7 2

In other words, the score $4$ occurs the most frequently, and is therefore the mode.

$\text(Mode)=4$

Score $(x)$	Frequency $(f)$
1	2
2	8
3	16
4	20
5	12
6	4
7	2

Score $(x)$	Frequency $(f)$
1	2
2	8
3	16
4	20
5	12
6	4
7	2

Question 2 of 6

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

Round your answer to two decimal places

$\text(Mean )=$ (3.81)

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Mean Formula

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

Remember

A histogram is a bar graph version of the frequency distribution table.

First, convert the histogram into a frequency table.

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

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

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

Score $(x)$	Frequency $(f)$	$f⋅x$
1	2	2
2	8	16
3	16	48
4	20	80
5	12	60
6	4	24
7	2	14

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

$sum f$	$=$	$2+8+16+20+12+4+2$
	$=$	$64$

$sum f⋅x$	$=$	$2+16+48+80+60+24+14$
	$=$	$244$

Score $(x)$	Frequency $(f)$	$f⋅x$
1	2	2
2	8	16
3	16	48
4	20	80
5	12	60
6	4	24
7	2	14
	$\text(Total) =64$	$\text(Total) =244$

Use the formula to compute for the mean.

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

$\text(Mean)$	$=$	$\frac{\color{#314EC4}{244}}{\color{#9202AA}{64}}$	Substitute values

$\text(Mean)$	$=$	$3.81$	Rounded to two decimal places

$\text(Mean)=3.81$

Question 3 of 6

From the frequency histogram shown below, find the median of the scores.

$\text(Median )=$ (4)

Question 4 of 6

4. Question
A group of $17$ students were surveyed as to how many phone calls they made on the weekend. Draw a frequency distribution table and then a histogram.

$10$ $8$ $12$ $9$ $10$ $6$ $10$ $9$ $9$

$11$ $7$ $9$ $6$ $9$ $11$ $8$ $10$
- 1.
- 2.
- 3.
- 4.
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A frequency distribution table displays how many times a particular score has occurred in a set of data.

A histogram is a bar graph version of the frequency distribution table.

First, fill in the Score column with the range of all possible scores, in ascending order.

Score $(x)$ Tally Frequency $(f)$

6

7

8

9

10

11

12

$\text(Total) =$

Next, read across the data while placing a stroke in the Tally column for each corresponding score.
To reduce the chance of mistakes, cross off each score as they are tallied.

$10$ $8$ $12$ $9$ $10$ $6$ $10$ $9$ $9$

$11$ $7$ $9$ $6$ $9$ $11$ $8$ $10$

Score $(x)$ Tally Frequency $(f)$

6

7

8

9

10

11

12

$\text(Total) =$

Continue doing this until all scores are tallied.

Score $(x)$ Tally Frequency $(f)$

6

7

8

9

10

11

12

$\text(Total) =$

Count the tallies per score and note it under the Frequency column.

Score $(x)$ Tally Frequency $(f)$

6 2

7 1

8 2

9 5

10 4

11 2

12 1

$\text(Total) =$

To check, count the total frequency and make sure it is equal to the number of given scores.

Score $(x)$ Tally Frequency $(f)$

6 2

7 1

8 2

9 5

10 4

11 2

12 1

$\text(Total) =17$

From the given data, we know that $N=17$

Therefore, all scores have been accounted for.

Now, for the histogram, prepare a bar graph with the scores listed at the bottom, and the frequency listed at the left side.

For each score, draw a bar with height corresponding to the frequency of that score.

Score $(x)$	Frequency $(f)$
1	2
2	8
3	16
4	20
5	12
6	4
7	2

Score $(x)$	Frequency $(f)$
1	2
2	8
3	16
4	20
5	12
6	4
7	2
	$\text(Total) =64$

Score $(x)$	Tally	Frequency $(f)$
6		2
7		1
8		2
9		5
10		4
11		2
12		1
		$\text(Total) =$

Score $(x)$	Tally	Frequency $(f)$
6		2
7		1
8		2
9		5
10		4
11		2
12		1
		$\text(Total) =17$

Question 5 of 6

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

Round your answer to one decimal place

$\text(Mean )=$ (5.6)

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Mean Formula

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

Remember

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

First, convert the frequency polygon into a frequency table.

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

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

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

Score $(x)$	Frequency $(f)$	$f⋅x$
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 $f.x$ columns.

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

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

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

Use the formula to compute for the mean.

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

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

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

$\text(Mean)=5.6$

Question 6 of 6

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

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

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

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

2

3

4

5

6

7

8

$\text(Total) =$

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

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$\text(Total) =$

Lastly, count the total frequency.

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

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$\text(Total) =40$

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

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$\text(Total) =40$

$1$	$1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$3$	$3$	$3$	$3$	$3$
$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$4$	$4$	$4$	$4$
$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$
$4$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$6$	$6$
$6$	$6$	$7$	$7$

Create and Interpret Bar & Line Graphs (Histograms)

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Quiz summary

Information

1. Question

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Great Work!

2. Question

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Correct!

Mean Formula

Remember

3. Question

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Fantastic!

4. Question

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Correct!

5. Question

Hint

Keep Going!

Mean Formula

Remember

6. Question

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Nice Job!

Quizzes

$1$	$1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$3$	$3$	$3$	$3$	$3$
$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$4$	$4$	$4$	$4$
$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$
$4$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$6$	$6$
$6$	$6$	$7$	$7$

$10$	$8$	$12$	$9$	$10$	$6$	$10$	$9$	$9$
$11$	$7$	$9$	$6$	$9$	$11$	$8$	$10$

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

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

$1$	$1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$3$	$3$	$3$	$3$	$3$
$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$4$	$4$	$4$	$4$
$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$
$4$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$6$	$6$
$6$	$6$	$7$	$7$

$1$	$1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$3$	$3$	$3$	$3$	$3$
$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$3$	$4$	$4$	$4$	$4$
$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$	$4$
$4$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$5$	$6$	$6$
$6$	$6$	$7$	$7$