Create and Interpret Stem & Leaf Plots 1

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Question 1 of 7

1. Question
The data shows the number of hours worked in a week by a group of $20$ $20$ employees. Arrange the data in a stem & leaf plot.

$12$ $12$ $28$ $28$ $14$ $14$ $13$ $13$ $19$ $19$ $21$ $21$ $32$ $32$ $34$ $34$

$33$ $33$ $28$ $28$ $18$ $18$ $29$ $29$ $24$ $24$ $23$ $23$ $32$ $32$ $17$ $17$

$19$ $19$ $34$ $34$ $38$ $38$ $16$ $16$

Enter the value for each respective column in the table below
- Stem Leaf
  
  (1) (2) (3) (4) (6) (7) (8) (9) (9)
  
  (2) (1) (3) (4) (8) (8) (9)
  
  (3) (2) (2) (3) (4) (4) (8)
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A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

First, identify all the possible first digits of the scores and list them in the Stem column.

Stem Leaf

1

2

3

Next, read across the data while listing them to their corresponding stem.

List the scores’ last digit to the Leaf column.

$12$ $12$ $28$ $28$ $14$ $14$ $13$ $13$ $19$ $19$ $21$ $21$ $32$ $32$ $34$ $34$

$33$ $33$ $28$ $28$ $18$ $18$ $29$ $29$ $24$ $24$ $23$ $23$ $32$ $32$ $17$ $17$

$19$ $19$ $34$ $34$ $38$ $38$ $16$ $16$

Stem Leaf

1 2    4

2 8

3

Continue doing this until all scores are listed.

Stem Leaf

1 2    4    3    9    8    7    9    6

2 8    1    8    9    4    3

3 2    4    3    2    4    8

Finally, arrange the values on the Leaf column in ascending order.

Stem Leaf

1 2    3    4    6    7    8    9    9

2 1    3    4    8    8    9

3 2    2    3    4    4    8

Stem Leaf

1 2    3    4    6    7    8    9    9

2 1    3    4    8    8    9

3 2    2    3    4    4    8

Stem	Leaf
(1)	(2) (3) (4) (6) (7) (8) (9) (9)
(2)	(1) (3) (4) (8) (8) (9)
(3)	(2) (2) (3) (4) (4) (8)

Stem	Leaf
1
2
3

Stem	Leaf
1	2 4
2	8
3

Stem	Leaf
1	2 4 3 9 8 7 9 6
2	8 1 8 9 4 3
3	2 4 3 2 4 8

Stem	Leaf
1	2 3 4 6 7 8 9 9
2	1 3 4 8 8 9
3	2 2 3 4 4 8

Stem	Leaf
1	2 3 4 6 7 8 9 9
2	1 3 4 8 8 9
3	2 2 3 4 4 8

Question 2 of 7

This stem & leaf plot shows the marks of

23

$23$ students in a science quiz. Find the mode.

Stem	Leaf
$4$ $4$	$5 1 0$ $5 1 0$
$5$ $5$	$3 2 6 8 4$ $3 2 6 8 4$
$6$ $6$	$8 3 4 3 3$ $8 3 4 3 3$
$7$ $7$	$9 1 6 5 8$ $9 1 6 5 8$
$8$ $8$	$7 2 8$ $7 2 8$
$9$ $9$	$5 1$ $5 1$

$Mode =$ $\text(Mode )=$ (63)

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The mode is the most frequent score in a data set.

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

To view repeating numbers easier, arrange the values on the Leaf column in ascending order.

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9	1 5

Next, find the score that repeats the most under the Leaf column.

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9	1 5

Notice that in Stem 6, the Leaf 3 appears thrice.

Hence, the mode is 63, which is the two numbers combined.

Mode = 63

$\text(Mode)=63$

Question 3 of 7

This stem & leaf plot shows the marks of

23

$23$ students in a science quiz. Find the range.

Stem	Leaf
$4$ $4$	$5 1 0$ $5 1 0$
$5$ $5$	$3 2 6 8 4$ $3 2 6 8 4$
$6$ $6$	$8 3 4 3 3$ $8 3 4 3 3$
$7$ $7$	$9 1 6 5 8$ $9 1 6 5 8$
$8$ $8$	$7 2 8$ $7 2 8$
$9$ $9$	$5 1$ $5 1$

$Range =$ $\text(Range )=$ (55)

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Range Formula

$Highest Score$ $\text(Highest Score)$

-

$-$ $Lowest Score$ $\text(Lowest Score)$

Remember

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

First, arrange the values on the Leaf column in ascending order.

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9	1 5

Next, find the highest and the lowest score. This will be the numbers at the bottom and top columns.

1 5

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$95$ $95$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$40$ $40$

Finally, subtract the lowest score from the highest score to get the range

$Range$ $\text(Range)$	$=$ $=$	$Highest Score$ $\text(Highest Score)$ $-$ $-$ $Lowest Score$ $\text(Lowest Score)$	Finding the range
	$=$ $=$	$95$ $95$ $-$ $-$ $40$ $40$	Substitute values
	$=$ $=$	$55$ $55$	Evaluate

Range = 55

$\text(Range)=55$

Question 4 of 7

This stem & leaf plot shows the marks of

23

$23$ students in a science quiz. Find the median.

Stem	Leaf
$4$ $4$	$5 1 0$ $5 1 0$
$5$ $5$	$3 2 6 8 4$ $3 2 6 8 4$
$6$ $6$	$8 3 4 3 3$ $8 3 4 3 3$
$7$ $7$	$9 1 6 5 8$ $9 1 6 5 8$
$8$ $8$	$7 2 8$ $7 2 8$
$9$ $9$	$5 1$ $5 1$

$Median =$ $\text(Median )=$ (64)

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The median is the middle score in a data set.

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

First, arrange the values on the Leaf column in ascending order.

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9	1 5

Since the total number of scores is

23

$23$ , the middle score should be the $12$ $12$ th score.

\frac{23}{2} = 11.5

$23/2=11.5$ and always round up which equals the

12

$12$ th score

Simply count the numbers under the Leaf column until you reach the $12$ $12$ th score.

Stem	Leaf
4	0 1 5
5	2 3 4 6 8
6	3 3 3 4 8
7	1 5 6 8 9
8	2 7 8
9	1 5

The $12$ $12$ th number is along Stem 6, specifically Leaf 4.

Hence, the median is $64$ $64$ , which is the two numbers combined.

Range = 64

$\text(Range)=64$

Question 5 of 7

Find the interquartile range of the stem and leaf plot below.

Stem	Leaf
$5$ $5$	$6 7$ $6 7$
$6$ $6$
$7$ $7$	$2 3 5 5 6 6 8$ $2 3 5 5 6 6 8$
$8$ $8$	$3 4$ $3 4$

$IQR =$ $\text(IQR )=$ (6)

Incorrect

Interquartile Range

IQR =

$\text(IQR )=$ $Q_{Upper}$ $\text(Q)_\text(Upper)$

-

$-$ $Q_{Lower}$ $\text(Q)_\text(Lower)$

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

First, since the total number of scores is

11

$11$ , the middle score should be the $6$ $6$ th score.

\frac{11}{2} = 5.5

$11/2=5.5$ and always round up which equals the

6

$6$ th score

Simply count the numbers under the Leaf column until you reach the $6$ $6$ th score.

Stem	Leaf
5	6 7
6
7	2 3 5 5 6 6 8
8	1 3

The $6$ $6$ th number is along Stem 7, specifically Leaf 5.

Hence, the median is $75$ $75$ , which is the two numbers combined.

The median divides the data set into two quartiles, each with

5

$5$ values.

Find the median of both quartiles to get the lower and upper quartiles

Stem	Leaf
Lower Half
5	6 7
6
7	2 3 5
8

Stem	Leaf
Greater Half
5
6
7	6 6 8
8	1 3

$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$72$ $72$
$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$78$ $78$

Finally, use the formula to get the interquartile range.

$IQR$ $\text(IQR)$	$=$ $=$	$Q_{Upper}$ $\text(Q)_\text(Upper)$ $-$ $-$ $Q_{Lower}$ $\text(Q)_\text(Lower)$	Interquartile Range formula
	$=$ $=$	$78$ $78$ $-$ $-$ $72$ $72$	Substitute values
	$=$ $=$	$6$ $6$	Evaluate

IQR = 6

$\text(IQR)=6$

Question 6 of 7

This stem & leaf plot shows the marks of $27$ $27$ students in a science quiz. Find the mode.

Stem	Leaf
3	9
4	9
5	1 2 3 4 4 6 7 9
6	1 1 5 6
7	1 4 6 6
8	2 5 8
9	2 2 2 3 4 5

$Mode =$ $\text(Mode )=$ (92)

Incorrect

The mode is the most frequent score in a data set.

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

To view repeating numbers easier, arrange the values on the Leaf column in ascending order.

Stem	Leaf
3	9
4	9
5	1 2 3 4 4 6 7 9
6	1 1 5 6
7	1 4 6 6
8	2 5 8
9	2 2 2 3 4 5

Next, find the score that repeats the most under the Leaf column.

Stem	Leaf
3	9
4	9
5	1 2 3 4 4 6 7 9
6	1 1 5 6
7	1 4 6 6
8	2 5 8
9	2 2 2 3 4 5

Notice that in Stem 9, the Leaf 2 appears thrice.

Hence, the mode is 92, which is the two numbers combined.

Mode = 92

$\text(Mode)=92$

Question 7 of 7

This stem & leaf plot shows the marks of $29$ $29$ students in a science quiz. Find the range.

Stem	Leaf
2	3 5 6
3	3 5 6 8 9
4	2 2 5 6 7 7 7 8 8 9
5	2 4 6 8 8
6	5 8 9
7	4 5
8	7

$Range =$ $\text(Range )=$ (64)

Incorrect

Range Formula

$Highest Score$ $\text(Highest Score)$

-

$-$ $Lowest Score$ $\text(Lowest Score)$

Remember

A stem and leaf plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit).

First, arrange the values on the Leaf column in ascending order.

Stem	Leaf
2	3 5 6
3	3 5 6 8 9
4	2 2 5 6 7 7 7 8 8 9
5	2 4 6 8 8
6	5 8 9
7	4 5
8	7

Next, find the highest and the lowest score. This will be the numbers at the bottom and columns.

Stem	Leaf
2	3 5 6
3	3 5 6 8 9
4	2 2 5 6 7 7 7 8 8 9
5	2 4 6 8 8
6	5 8 9
7	4 5
8	7

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$87$ $87$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$23$ $23$

Finally, subtract the lowest score from the highest score to get the range

$Range$ $\text(Range)$	$=$ $=$	$Highest Score - Lowest Score$ $color(deeppink)(\text(Highest Score))-color(darkviolet)(\text(Lowest Score))$	Finding the range
	$=$ $=$	$87 - 23$ $color(deeppink)(87)-color(darkviolet)(23)$	Substitute values
	$=$ $=$	$64$ $64$	Evaluate

Range = 64

$\text(Range)=64$

Create and Interpret Stem & Leaf Plots 1

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Quiz summary

Information

1. Question

Hint

Great Work!

2. Question

Hint

Fantastic!

3. Question

Hint

Excellent!

Range Formula

Remember

4. Question

Hint

Nice Job!

5. Question

Excellent!

Interquartile Range

6. Question

Keep Going!

7. Question

Keep Going!

Range Formula

Remember

Quizzes

$12$ $12$	$28$ $28$	$14$ $14$	$13$ $13$	$19$ $19$	$21$ $21$	$32$ $32$	$34$ $34$
$33$ $33$	$28$ $28$	$18$ $18$	$29$ $29$	$24$ $24$	$23$ $23$	$32$ $32$	$17$ $17$
$19$ $19$	$34$ $34$	$38$ $38$	$16$ $16$

$12$ $12$	$28$ $28$	$14$ $14$	$13$ $13$	$19$ $19$	$21$ $21$	$32$ $32$	$34$ $34$
$33$ $33$	$28$ $28$	$18$ $18$	$29$ $29$	$24$ $24$	$23$ $23$	$32$ $32$	$17$ $17$
$19$ $19$	$34$ $34$	$38$ $38$	$16$ $16$