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
$4$ $4$	$510$ $5 1 0$
$5$ $5$	$32684$ $3 2 6 8 4$
$6$ $6$	$83433$ $8 3 4 3 3$
$7$ $7$	$91658$ $9 1 6 5 8$
$8$ $8$	$728$ $7 2 8$
$9$ $9$	$51$ $5 1$

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

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

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

Question 3 of 7

This stem & leaf plot shows the marks of

23

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

Stem	Leaf
$4$ $4$	$510$ $5 1 0$
$5$ $5$	$32684$ $3 2 6 8 4$
$6$ $6$	$83433$ $8 3 4 3 3$
$7$ $7$	$91658$ $9 1 6 5 8$
$8$ $8$	$728$ $7 2 8$
$9$ $9$	$51$ $5 1$

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

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

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

Question 4 of 7

This stem & leaf plot shows the marks of

23

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

Stem	Leaf
$4$ $4$	$510$ $5 1 0$
$5$ $5$	$32684$ $3 2 6 8 4$
$6$ $6$	$83433$ $8 3 4 3 3$
$7$ $7$	$91658$ $9 1 6 5 8$
$8$ $8$	$728$ $7 2 8$
$9$ $9$	$51$ $5 1$

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

Question 5 of 7

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

Stem Leaf

$5$ $5$ $67$ $6    7$

$6$ $6$
$7$ $7$ $2355668$ $2    3    5    5    6    6    8$

$8$ $8$ $34$ $3    4$
- $IQR =$ $\text(IQR )=$ (6)
Correct

Excellent!

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

Lower Half

Stem Leaf

5 6    7

6

7 2    3    5

8

Greater Half

Stem Leaf

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

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

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

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

Stem	Leaf
$5$ $5$	$67$ $6 7$
$6$ $6$
$7$ $7$	$2355668$ $2 3 5 5 6 6 8$
$8$ $8$	$34$ $3 4$

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

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

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

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)

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)

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

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

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

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

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

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

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

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

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

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