Create and Interpret Stem & Leaf Plots 4

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Question 1 of 7

1. Question

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

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

`\text(Median )=` (44)

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

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

`27/2=13.5` and always round up which equals the `14`th score

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

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

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

Hence, the median is `44`, which is the two numbers combined.

`\text(Median)=44`

Question 2 of 7

2. Question

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

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

`\text(Median )=` (47)

Correct

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

Since the total number of scores is `29`, the middle score should be the `15`th score.

`29/2=14.5` and always round up which equals the `15`th score

Simply count the numbers under the Leaf column until you reach the `15`th score.

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

The `15`th number is along Stem 4, specifically Leaf 7.

Hence, the median is `47`, which is the two numbers combined.

`\text(Median)=47`

Question 3 of 7

3. Question

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

Round your answer to two decimal places

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

`\text(Mean )=` (69.89)

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Mean Formula

`\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.

`color(forestgreen)(sum x)`	`=`	`35+49+51+52+53+54+54+56+`
		`57+59+61+61+65+66+71+74+`
		`76+76+82+85+88+92+92+`
		`92+93+94+95`
	`=`	`1,887`

Next, divide the sum of all values `color(forestgreen)(sum x)` by the number of values `(color(tomato)(N))`.

`\text(Mean)`	`=`	`(color(forestgreen)(sum x))/(color(tomato)(N))`	Finding the mean

	`=`	`(color(forestgreen)(1887))/(color(tomato)(27))`	There are `27` given values

	`=`	`69.89`	Rounded to two decimal places

`\text(Mean)=69.89`

Question 4 of 7

4. Question

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

Round your answer to two decimal places

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

`\text(Mean )=` (31.74)

Correct

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Incorrect

Mean Formula

`\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.

`color(forestgreen)(sum x)`	`=`	`11+11+12+12+18+21+22+22+`
		`24+24+25+26+27+32+35+36+`
		`36+37+38+39+42+45+45`
		`+45+46+53+73`
	`=`	`857`

Next, divide the sum of all values `color(forestgreen)(sum x)` by the number of values `(color(tomato)(N))`.

`\text(Mean)`	`=`	`(color(forestgreen)(sum x))/(color(tomato)(N))`	Finding the mean

	`=`	`(color(forestgreen)(857))/(color(tomato)(27))`	There are `27` given values

	`=`	`31.74`	Rounded to two decimal places

`\text(Mean)=31.74`

Question 5 of 7

5. Question

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

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

`\text(IQR )=` (20)

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Interquartile Range

`\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`, the middle score should be the `color(darkgoldenrod)(14)`th score.

`27/2=13.5` and always round up which equals the `14`th score

Simply count the numbers under the Leaf column until you reach the `color(darkgoldenrod)(14)th` score.

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

The `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` values.

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

Stem	Leaf
Lower Half
1	1 1 2 2 8
2	1 2 2 4 4 5 6 7

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

Finally, use the formula to get the interquartile range.

`\text(IQR)`	`=`	`color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))`	Interquartile Range formula
	`=`	`color(deeppink)(42)-color(darkviolet)(22)`	Substitute values
	`=`	`20`	Evaluate

`\text(IQR)=20`

Question 6 of 7

6. Question

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

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

`\text(IQR )=` (19.5)

Correct

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Incorrect

Interquartile Range

`\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 `29`, the middle score should be the `color(darkgoldenrod)(15)`th score.

`29/2=14.5` and always round up which equals the `15`th score

Simply count the numbers under the Leaf column until you reach the `color(darkgoldenrod)(15)th` score.

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

The `color(darkgoldenrod)(15)`th number is along Stem 4, specifically Leaf 7.

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

The median divides the data set into two quartiles, each with `14` values.

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

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

Stem	Leaf
Greater Half
4	8 8 9
5	2 4 6 8 8
6	5 8 9
7	4 5
8	7

`\text(Lower Quartile)`	`=`	`(38+39)/2`

	`=`	`38.5`

`\text(Upper Quartile)`	`=`	`(58+58)/2`

	`=`	`58`

Finally, use the formula to get the interquartile range.

`\text(IQR)`	`=`	`color(deeppink)(\text(Q)_\text(Upper))-color(darkviolet)(\text(Q)_\text(Lower))`	Interquartile Range formula
	`=`	`color(deeppink)(58)-color(darkviolet)(38.5)`	Substitute values
	`=`	`19.5`	Evaluate

`\text(IQR)=19.5`

Question 7 of 7

7. Question

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

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

`\text(IQR )=` (16)

Hint

Help Video

Correct

Correct!

Incorrect

Interquartile Range

`\text(IQR )=``\text(Q)_\text(Upper)``-``\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 `21`, the middle score should be the `11`th score.

`21/2=10.5` and always round up which equals the `11`th score

Simply count the numbers under the Leaf column until you reach the `11`th score.

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

The `11`th number is along Stem 6, specifically Leaf 6.

Hence, the median is `66`, which is the two numbers combined.

The median divides the data set into two quartiles, each with `10` values.

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

Stem	Leaf
Lower Half
4	3 8
5	0 2 5 5 6
6	1 3 3
7
8

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

`\text(Lower Quartile)`	`=`	`(55+55)/2`

	`=`	`55`

`\text(Upper Quartile)`	`=`	`(70+72)/2`

	`=`	`71`

Finally, use the formula to get the interquartile range.

`\text(IQR)`	`=`	`\text(Q)_\text(Upper)``-``\text(Q)_\text(Lower)`	Interquartile Range formula
	`=`	`71``-``55`	Substitute values
	`=`	`16`	Evaluate

`\text(IQR)=16`

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