Create and Interpret Stem & Leaf Plots 2

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Question 1 of 7

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

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

$Mode =$ $\text(Mode )=$ (47)

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
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 score that repeats the most under the Leaf column.

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

Notice that in Stem 4, the Leaf 7 appears thrice.

Hence, the mode is 47, which is the two numbers combined.

Mode = 47

$\text(Mode)=47$

Question 2 of 7

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

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

$Mode =$ $\text(Mode )=$ (45)

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

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

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

Notice that in Stem 4, the Leaf 5 appears thrice.

Hence, the mode is 45, which is the two numbers combined.

Mode = 45

$\text(Mode)=45$

Question 3 of 7

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

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

$Range =$ $\text(Range )=$ (68)

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
1	1 2 5 7 7
2	1 1 2 4 5 7 9
3	1 2 2 4 7
4	2 5 6 6 6
5	2 2
6	4
7	5 9

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

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

$Highest Score$ $\text(Highest Score)$	$=$ $=$	$79$ $79$
$Lowest Score$ $\text(Lowest Score)$	$=$ $=$	$11$ $11$

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
	$=$ $=$	$79 - 11$ $color(deeppink)(79)-color(darkviolet)(11)$	Substitute values
	$=$ $=$	$68$ $68$	Evaluate

Range = 68

$\text(Range)=68$

Question 4 of 7

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

Stem Leaf

2 1

3 1 2 2 4 4 5 6 6 7

4 5

5 2 3 4 5 6 6 6 7

6 9

7 3

8 2 5 8

9 2 2 5
- $Median =$ $\text(Median )=$ (54)
Correct

Keep Going!

Incorrect

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

2 1

3 1 2 2 4 4 5 6 6 7

4 5

5 2 3 4 5 6 6 6 7

6 9

7 3

8 2 5 8

9 2 2 5

Since the total number of scores is $27$ $27$ , the middle score should be the $14$ $14$ th score.

$\frac{27}{2} = 13.5$ $27/2=13.5$ and always round up which equals the $14$ $14$ th score

Simply count the numbers under the Leaf column until you reach the $14$ $14$ th score.

Stem Leaf

2 1

3 1 2 2 4 4 5 6 6 7

4 5

5 2 3 4 5 6 6 6 7

6 9

7 3

8 2 5 8

9 2 2 5

The $14$ $14$ th number is along Stem 5, specifically Leaf 4.

Hence, the median is $54$ $54$ , which is the two numbers combined.

$Range = 54$ $\text(Range)=54$

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

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

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

Question 5 of 7

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

Round your answer to two decimal places

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

$Mean =$ $\text(Mean )=$ (42.59)

Incorrect

Mean Formula

Mean = \frac{\sum x}{N}

$\text(Mean)=(color(forestgreen)(sum x))/(color(tomato)(N))$

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, solve for the sum of the given values.

$\sum x$ $color(forestgreen)(sum x)$	$=$ $=$	$11 + 12 + 13 + 13 + 16 + 21 + 22 + 24 +$ $11+12+13+13+16+21+22+24+$
		$31 + 32 + 34 + 35 + 39 + 41 + 45 + 45 +$ $31+32+34+35+39+41+45+45+$
		$46 + 46 + 58 + 61 + 62 + 64 + 71 +$ $46+46+58+61+62+64+71+$
		$72 + 75 + 79 + 82$ $72+75+79+82$
	$=$ $=$	$1, 150$ $1,150$

Next, divide the sum of all values

\sum x

$color(forestgreen)(sum x)$ by the number of values

(N)

$(color(tomato)(N))$ .

$Mean$ $\text(Mean)$	$=$ $=$	$\frac{\sum x}{N}$ $(color(forestgreen)(sum x))/(color(tomato)(N))$	Finding the mean

	$=$ $=$	$\frac{1150}{27}$ $(color(forestgreen)(1150))/(color(tomato)(27))$	There are $27$ $27$ given values

	$=$ $=$	$42.59$ $42.59$	Rounded to two decimal places

Mean = 42.59

$\text(Mean)=42.59$

Question 6 of 7

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

Stem Leaf

3 1 2 2 9

4 1 4 6 8

5 2 2 7 9

6 1 5 6

7 1 1 2 2 3 4 5 6

8 3

9 1 3 4
- $Median =$ $\text(Median )=$ (65)
Correct

Keep Going!

Incorrect

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

3 1 2 2 9

4 1 4 6 8

5 2 2 7 9

6 1 5 6

7 1 1 2 2 3 4 5 6

8 3

9 1 3 4

Since the total number of scores is $27$ $27$ , the middle score should be the $14$ $14$ th score.

$\frac{27}{2} = 13.5$ $27/2=13.5$ and always round up which equals the $14$ $14$ th score

Simply count the numbers under the Leaf column until you reach the $14$ $14$ th score.

Stem Leaf

3 1 2 2 9

4 1 4 6 8

5 2 2 7 9

6 1 5 6

7 1 1 2 2 3 4 5 6

8 3

9 1 3 4

The $14$ $14$ th number is along Stem 6, specifically Leaf 5.

Hence, the median is $65$ $65$ , which is the two numbers combined.

$Range = 65$ $\text(Range)=65$

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

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

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

Question 7 of 7

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

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

$IQR =$ $\text(IQR )=$ (25)

Incorrect

Interquartile Range

IQR = Q_{Upper} - Q_{Lower}

$\text(IQR )=color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))$

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

27

$27$ , the middle score should be the

14

$color(darkgoldenrod)(14)$ th score.

\frac{27}{2} = 13.5

$27/2=13.5$ and always round up which equals the

14

$14$ th score

Simply count the numbers under the Leaf column until you reach the

14 t h

$color(darkgoldenrod)(14)th$ score.

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

The

14

$color(darkgoldenrod)(14)$ th number is along Stem 3, specifically Leaf 2.

Hence, the median is 32, which is the two numbers combined.

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

13

$13$ values.

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

Stem	Leaf
Lower Half
1	1 2 5 7 7
2	1 1 2 4 5 7 9
3	1

Stem	Leaf
Greater Half
3	2 4 7
4	2 5 6 6 6
5	2 2
6	4
7	5 9

Finally, use the formula to get the interquartile range.

$IQR$ $\text(IQR)$	$=$ $=$	$Q_{Upper} - Q_{Lower}$ $color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))$	Interquartile Range formula
	$=$ $=$	$46 - 21$ $color(deeppink)(46)-color(darkviolet)(21)$	Substitute values
	$=$ $=$	$25$ $25$	Evaluate

IQR = 25

$\text(IQR)=25$

Create and Interpret Stem & Leaf Plots 2

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Quiz summary

Information

1. Question

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2. Question

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3. Question

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Range Formula

Remember

4. Question

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5. Question

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Mean Formula

6. Question

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7. Question

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Interquartile Range

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