Interpret Cumulative Frequency Tables and Charts 2

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Question 1 of 8

1. 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)
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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 2 of 8

2. Question
Use this cumulative frequency histogram to find the median.

Rankings of a TV show
- $Median =$ $\text(Median )=$ (3)
Correct

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Incorrect

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

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

Since the highest value is $25$ $25$ , simply divide it by $2$ $2$ .

$\frac{25}{2}$ $25/2$ $=$ $=$ $12.5$ $12.5$

Trace a horizontal line from $12.5$ $color(darkgoldenrod)(12.5)$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the score $3$ $3$ .

Hence, the median is $3$ $3$ .

$Median = 3$ $\text(Median)=3$
Question 3 of 8

3. 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 4 of 8

4. 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 5 of 8

5. Question
Use this cumulative frequency histogram to find the median.

Number of phones in a household
- $Median =$ $\text(Median )=$ (4)
Correct

Keep Going!

Incorrect

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

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

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

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

Trace a horizontal line from $color(darkgoldenrod)(20)$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the score $4$ .

Hence, the median is $4$ .

$\text(Median)=4$
Question 6 of 8

6. Question
Find the median score.

Age at First Job

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

12 1

13 3

14 2

15 2

16 2

17 5

18 1
- $\text(Median )=$ (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 $(x)$ Frequency $(f)$

12 1

13 3

14 2

15 2

16 2

17 5

18 1

$\text(Total)=16$

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 $(x)$ Frequency $(f)$ 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

$\text(Total)=16$

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

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

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

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

$\text(Total)=16$

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

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

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

$=$ $31/2$

$=$ $15.5$

$\text(Median)=15.5$
Question 7 of 8

7. Question
Find the median score.

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

1 1

2 3

3 6

4 7

5 2

6 1
- $\text(Median )=$ (3.5)
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The median is the middle value in an ordered set of data.

First, get the sum of the Frequency column.

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

1 1

2 3

3 6

4 7

5 2

6 1

$\text(Total)=20$

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

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

$\text(Total)=20$

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

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

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

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

$\text(Total)=20$

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

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

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

$=$ $7/2$

$=$ $3.5$

$\text(Median)=3.5$
Question 8 of 8

8. Question
Use this cumulative frequency histogram to find the median.

Attendance at soccer matches
- $\text(Median )=$ (102)
Correct

Keep Going!

Incorrect

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

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

Since the highest value is $35$ , simply divide it by $2$ .

$35/2$ $=$ $17.5$

Trace a horizontal line from $color(darkgoldenrod)(17.5)$ until it touches part of the polygon.

Notice that it touches the polygon across the bar for the score $102$ .

Hence, the median is $102$ .

$\text(Median)=102$

Interpret Cumulative Frequency Tables and Charts 2

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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6. Question

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7. Question

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8. Question

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Quizzes

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

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

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

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

Age $(x)$	Frequency $(f)$	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
	$\text(Total)=16$

Score $(x)$	Frequency $(f)$	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
	$\text(Total)=20$