Interpret Cumulative Frequency Tables and Charts

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Question 1 of 11

1. Question
Find the median score.

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

0 6

1 10

2 6

3 4

4 3

5 0

6 1

$Total = 30$ $\text(Total)=30$
- $Median =$ $\text(Median )=$ (1)
Hint

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Correct

Excellent!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

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

0 6 6

1 10 6+10=16

2 6 16+6=22

3 4 22+4=26

4 3 26+3=29

5 0 29+0=29

6 1 29+1=30

$Total = 30$ $\text(Total)=30$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $30$ $30$ , the middle score should be the average of the $15$ $15$ th and $16$ $16$ th score.

Find the row that includes the $15$ $15$ th and $16$ $16$ th scores.

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

0 6 6

1 10 6+10=16

2 6 10+6=16

3 4 6+4=10

4 3 4+3=7

5 0 3+0=3

6 1 0+1=1

$Total = 30$ $\text(Total)=30$

The second row covers all scores between the $6$ $6$ th and $16$ $16$ th position — this includes the $15$ $15$ th and $16$ $16$ th.

Hence, the median is $1$ $1$ .

$Median = 1$ $\text(Median)=1$
Question 2 of 11

2. Question
Find the median score.

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

5 4

6 8

7 10

8 6

9 3

10 2
- $Median =$ $\text(Median )=$ (7)
Hint

Help Video

Correct

Nice Job!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

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

5 4

6 8

7 10

8 6

9 3

10 2

$Total = 33$ $\text(Total)=33$

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

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

5 4 4

6 8 4+8=12

7 10 12+10=22

8 6 22+6=28

9 3 28+3=31

10 2 31+2=33

$Total = 33$ $\text(Total)=33$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $33$ $33$ , the middle score should be the $17$ $17$ th score.

Find the row that includes the $17$ $17$ th score.

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

5 4 4

6 8 4+8=12

7 10 12+10=22

8 6 22+6=28

9 3 28+3=31

10 2 31+2=33

$Total = 33$ $\text(Total)=33$

The third row covers all scores between the $12$ $12$ th and $22$ $22$ nd position — this includes the $17$ $17$ th.

Hence, the median is $7$ $7$ .

$Median = 7$ $\text(Median)=7$
Question 3 of 11

3. Question
Find the median score.

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

2 2

3 5

4 10

5 12

6 8

7 5
- $Median =$ $\text(Median )=$ (5)
Hint

Help Video

Correct

Well Done!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

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

2 2

3 5

4 10

5 12

6 8

7 5

$Total = 42$ $\text(Total)=42$

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

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

2 2 2

3 5 2+5=7

4 10 7+10=17

5 12 17+12=29

6 8 29+8=37

7 5 37+5=42

$Total = 42$ $\text(Total)=42$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $42$ $42$ , the middle score should be the average of the $21$ $21$ st and $22$ $22$ nd score.

Find the row that includes the $21$ $21$ st and $22$ $22$ nd score.

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

2 2 2

3 5 2+5=7

4 10 7+10=17

5 12 17+12=29

6 8 29+8=37

7 5 37+5=42

$Total = 42$ $\text(Total)=42$

The fourth row covers all scores between the $17$ $17$ th and $29$ $29$ th position — this includes the $21$ $21$ st and $22$ $22$ nd.

Get the average of the two scores to get the median.

$Median$ $\text(Median)$ $=$ $=$ $\frac{5 + 5}{2}$ $(5+5)/2$

$=$ $=$ $\frac{10}{2}$ $10/2$

$=$ $=$ $5$ $5$

$Median = 5$ $\text(Median)=5$
Question 4 of 11

4. Question
Find the median score.

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

1 1

2 3

3 6

4 7

5 2

6 1
- $Median =$ $\text(Median )=$ (3.5)
Hint

Help Video

Correct

Correct!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

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

1 1

2 3

3 6

4 7

5 2

6 1

$Total = 20$ $\text(Total)=20$

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

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

1 1 1

2 3 1+3=4

3 6 4+6=10

4 7 10+7=17

5 2 17+2=19

6 1 19+1=20

$Total = 20$ $\text(Total)=20$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $20$ $20$ , the middle score should be the average of the $10$ $10$ th and $11$ $11$ th score.

Find the row that includes the $10$ $10$ th and $11$ $11$ th score.

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

1 1 1

2 3 1+3=4

3 6 4+6=10

4 7 10+7=17

5 2 17+2=19

6 1 19+1=20

$Total = 20$ $\text(Total)=20$

The third row covers all scores between the $5$ $5$ th and $10$ $10$ th position, which includes the $10$ $10$ th, and the fourth row covers all scores between the $11$ $11$ th and $17$ $17$ th position, which includes the $11$ $11$ th.

Get the average of the two scores to get the median.

$Median$ $\text(Median)$ $=$ $=$ $\frac{3 + 4}{2}$ $(3+4)/2$

$=$ $=$ $\frac{7}{2}$ $7/2$

$=$ $=$ $3.5$ $3.5$

$Median = 3.5$ $\text(Median)=3.5$
Question 5 of 11

5. Question
Find the median score.

Games per World Series

Games $(x)$ $(x)$ Frequency $(f)$ $(f)$

4 2

5 2

6 3

7 4
- $Median =$ $\text(Median )=$ (6)
Correct

Fantastic!

Incorrect

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

Games $(x)$ $(x)$ Frequency $(f)$ $(f)$

4 2

5 2

6 3

7 4

$Total = 11$ $\text(Total)=11$

Next, add a Cumulative Frequency column to the table.

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

Game $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

4 2 2

5 2 2+2=4

6 3 4+3=7

7 4 7+4=11

$Total = 11$ $\text(Total)=11$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $11$ $11$ , the middle score should be the $6$ $6$ th score.

Find the row that includes the $6$ $6$ th score.

Game $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

4 2 2

5 2 2+2=4

6 3 4+3=7

7 4 7+4=11

$Total = 11$ $\text(Total)=11$

The third row covers all scores between the $5$ $5$ th and $7$ $7$ th position — this includes the $6$ $6$ th.

Hence, the median is $6$ $6$ .

$Median = 6$ $\text(Median)=6$
Question 6 of 11

6. Question
Find the median score.

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

7 4 4

8 2 6

9 3 9

10 2 11
- $Median =$ $\text(Median )=$ (8)
Correct

Nice Job!

Incorrect

The median is the middle value in an ordered set of data.

Since the total number of scores is $11$ $11$ , the middle score should be the $6$ $6$ th score.

Find the row that includes the $6$ $6$ th score.

Game $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

7 4 4

8 2 6

9 3 9

10 2 11

The second row covers all scores between the $5$ $5$ th and $6$ $6$ th position — this includes the $6$ $6$ th.

Hence, the median is $8$ $8$ .

$Median = 8$ $\text(Median)=8$
Question 7 of 11

7. Question
Find the median score.

Academy Awards Won by Movie

No. of Awards $(x)$ $(x)$ Frequency $(f)$ $(f)$

2 1

3 3

4 4

5 3

7 1

8 2

9 1
- $Median =$ $\text(Median )=$ (4)
Correct

Great Work!

Incorrect

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

No. of Awards $(x)$ $(x)$ Frequency $(f)$ $(f)$

2 1

3 3

4 4

5 3

7 1

8 2

9 1

$Total = 15$ $\text(Total)=15$

Next, add a Cumulative Frequency column to the table.

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

No. of Awards $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

2 1 1

3 3 1+3=4

4 4 4+4=8

5 3 8+3=11

7 1 11+1=12

8 2 12+2=14

9 1 14+1=15

$Total = 15$ $\text(Total)=15$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $15$ $15$ , the middle score should be the $8$ $8$ th score.

Find the row that includes the $8$ $8$ th score.

No. of Awards $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

2 1 1

3 3 1+3=4

4 4 4+4=8

5 3 8+3=11

7 1 11+1=12

8 2 12+2=14

9 1 14+1=15

$Total = 15$ $\text(Total)=15$

The third row covers all scores between the $5$ $5$ th and $8$ $8$ th position — this includes the $8$ $8$ th.

Hence, the median is $4$ $4$ .

$Median = 4$ $\text(Median)=4$
Question 8 of 11

8. Question
Find the median score.

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

12 1 1

13 2 3

16 2 5

17 4 9

22 1 10
- $Median =$ $\text(Median )=$ (16.5)
Correct

Keep Going!

Incorrect

The median is the middle value in an ordered set of data.

Since the total number of scores is $10$ $10$ , the middle score should be the average of the $5$ $5$ th and
$6$ $6$ th scores.

Find the row that includes the $5$ $5$ th and $6$ $6$ th scores.

Game $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

12 1 1

13 2 3

16 2 5

17 4 9

22 1 10

The third row covers all scores between the $4$ $4$ th and $5$ $5$ th position and the fourth row covers all scores between the $6$ $6$ th and $9$ $9$ th position.

Get the average of the two scores to get the median.

$Median$ $\text(Median)$ $=$ $=$ $\frac{16 + 17}{2}$ $(16+17)/2$

$=$ $=$ $\frac{33}{2}$ $33/2$

$=$ $=$ $16.5$ $16.5$

$Median = 16.5$ $\text(Median)=16.5$
Question 9 of 11

9. Question
Find the median score.

Age at First Job

Age $(x)$ $(x)$ Frequency $(f)$ $(f)$

12 1

13 3

14 2

15 2

16 2

17 5

18 1
- $Median =$ $\text(Median )=$ (15.5)
Correct

Excellent!

Incorrect

The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

Age $(x)$ $(x)$ Frequency $(f)$ $(f)$

12 1

13 3

14 2

15 2

16 2

17 5

18 1

$Total = 16$ $\text(Total)=16$

Next, add a Cumulative Frequency column to the table.

To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.

Age $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

12 1 1

13 3 1+3=4

14 2 4+2=6

15 2 6+2=8

16 2 8+2=10

17 5 10+5=15

18 1 15+1=16

$Total = 16$ $\text(Total)=16$

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Since the total number of scores is $16$ $16$ , the middle score should be the average of the $8$ $8$ th and
$9$ $9$ th scores.

Find the row that includes the $8$ $8$ th and $9$ $9$ th scores.

Age $(x)$ $(x)$ Frequency $(f)$ $(f)$ Cumulative Frequency

12 1 1

13 3 1+3=4

14 2 4+2=6

15 2 6+2=8

16 2 8+2=10

17 5 10+5=15

18 1 15+1=16

$Total = 16$ $\text(Total)=16$

The fourth row covers all scores between the $7$ $7$ th and $8$ $8$ th position and the fifth row covers all scores between the $9$ $9$ th and $10$ $10$ th position.

Get the average of the two scores to get the median.

$Median$ $\text(Median)$ $=$ $=$ $\frac{15 + 16}{2}$ $(15+16)/2$

$=$ $=$ $\frac{31}{2}$ $31/2$

$=$ $=$ $15.5$ $15.5$

$Median = 15.5$ $\text(Median)=15.5$
Question 10 of 11

10. Question
Use this cumulative frequency histogram to find the median.
- $Median =$ $\text(Median )=$ (15)
Hint

Help Video

Correct

Well Done!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

Create a cumulative frequency polygon by connecting the top-right corners of each bar using straight lines, as shown here.

Find the middle value in the cumulative frequency axis (left side).

Since the highest value is $60$ $60$ , simply divide it by $2$ $2$ .

$\frac{60}{2}$ $60/2$ $=$ $=$ $30$ $30$

Trace a horizontal line from $30$ $30$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the score $15$ $15$ .

Hence, the median is $15$ $15$ .

$Median = 15$ $\text(Median)=15$
Question 11 of 11

11. Question
Complete the following cumulative frequency table and draw a polygon and histogram. Then, find the median.

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

2 3

3 2

4 5

5 6

6 9

7 12

8 3

$Total = 40$ $\text(Total)=40$
- $Median =$ $\text(Median )=$ (6)
Hint

Help Video

Correct

Exceptional!

Incorrect

Help Video

The median is the middle value in an ordered set of data.

First, fill in the Cumulative Frequency column by adding the frequency, as seen below.

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

2 3 3

3 2 3+2=5

4 5 5+5=10

5 6 10+6=16

6 9 16+9=25

7 12 25+12=37

8 3 37+3=40

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

To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.

Next, create a graph with the Score $(x)$ $(x)$ values on the bottom side and the Cumulative Frequency values on the left side.

Next, add bars to the graph corresponding to the cumulative frequency per score.

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

2 3 3

3 2 3+2=5

4 5 5+5=10

5 6 10+6=16

6 9 16+9=25

7 12 25+12=37

8 3 37+3=40

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

Continue adding bars until all the scores are accounted for.

Next, create a cumulative frequency polygon by connecting the top-right corners of each bar using straight lines, as shown here.

Find the middle value in the cumulative frequency axis (left side).

Since the highest value is $40$ $40$ , simply divide it by $2$ $2$ .

$\frac{40}{2}$ $40/2$ $=$ $=$ $20$ $20$

Trace a horizontal line from $20$ $20$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the score $6$ $6$ .

Hence, the median is $6$ $6$ .

$Median = 6$ $\text(Median)=6$

Interpret Cumulative Frequency Tables and Charts

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Quiz summary

Information

1. Question

Hint

Excellent!

2. Question

Hint

Nice Job!

3. Question

Hint

Well Done!

4. Question

Hint

Correct!

5. Question

Fantastic!

6. Question

Nice Job!

7. Question

Great Work!

8. Question

Keep Going!

9. Question

Excellent!

10. Question

Hint

Well Done!

11. Question

Hint

Exceptional!

Quizzes

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
0	6	6
1	10	6+10=16
2	6	16+6=22
3	4	22+4=26
4	3	26+3=29
5	0	29+0=29
6	1	29+1=30
	$Total = 30$ $\text(Total)=30$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
0	6	6
1	10	6+10=16
2	6	10+6=16
3	4	6+4=10
4	3	4+3=7
5	0	3+0=3
6	1	0+1=1
	$Total = 30$ $\text(Total)=30$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
5	4	4
6	8	4+8=12
7	10	12+10=22
8	6	22+6=28
9	3	28+3=31
10	2	31+2=33
	$Total = 33$ $\text(Total)=33$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
2	2	2
3	5	2+5=7
4	10	7+10=17
5	12	17+12=29
6	8	29+8=37
7	5	37+5=42
	$Total = 42$ $\text(Total)=42$

$Median$ $\text(Median)$	$=$ $=$	$\frac{5 + 5}{2}$ $(5+5)/2$

	$=$ $=$	$\frac{10}{2}$ $10/2$

	$=$ $=$	$5$ $5$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
1	1	1
2	3	1+3=4
3	6	4+6=10
4	7	10+7=17
5	2	17+2=19
6	1	19+1=20
	$Total = 20$ $\text(Total)=20$

$Median$ $\text(Median)$	$=$ $=$	$\frac{3 + 4}{2}$ $(3+4)/2$

	$=$ $=$	$\frac{7}{2}$ $7/2$

	$=$ $=$	$3.5$ $3.5$

No. of Awards $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
2	1	1
3	3	1+3=4
4	4	4+4=8
5	3	8+3=11
7	1	11+1=12
8	2	12+2=14
9	1	14+1=15
	$Total = 15$ $\text(Total)=15$

$Median$ $\text(Median)$	$=$ $=$	$\frac{16 + 17}{2}$ $(16+17)/2$

	$=$ $=$	$\frac{33}{2}$ $33/2$

	$=$ $=$	$16.5$ $16.5$

Age $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
12	1	1
13	3	1+3=4
14	2	4+2=6
15	2	6+2=8
16	2	8+2=10
17	5	10+5=15
18	1	15+1=16
	$Total = 16$ $\text(Total)=16$

Games $(x)$ $(x)$	Frequency $(f)$ $(f)$
Games per World Series
4	2
5	2
6	3
7	4

$Median$ $\text(Median)$	$=$ $=$	$\frac{15 + 16}{2}$ $(15+16)/2$

	$=$ $=$	$\frac{31}{2}$ $31/2$

	$=$ $=$	$15.5$ $15.5$

Score $(x)$ $(x)$	Frequency $(f)$ $(f)$	Cumulative Frequency
2	3	3
3	2	3+2=5
4	5	5+5=10
5	6	10+6=16
6	9	16+9=25
7	12	25+12=37
8	3	37+3=40
	$Total = 40$ $\text(Total)=40$