Finding the Interquartile Range 2

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Question 1 of 6

1. Question
Find the interquartile range of the dot plot.
- $IQR =$ $\text(IQR )=$ (2)
Correct

Well Done!

Incorrect

Interquartile Range

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, take note that there is a total of $12$ $12$ scores on the dot plot, which is an even number.

Therefore, the median of the data set will be the average of the scores on the $6 t h$ $6th$ and $7 t h$ $7th$ position.

$Median$ $\text(Median)$ $=$ $=$ $\frac{4 + 4}{2}$ $(4+4)/2$

$=$ $=$ $\frac{8}{2}$ $8/2$

$=$ $=$ $4$ $4$

The median divides the data set into two quartiles, each with $6$ $6$ values.

To find the lower and upper quartiles, find the median of both the lower and greater halves.

$Lower Quartile$ $\text(Lower Quartile)$ $=$ $=$ $3$ $3$

$Upper Quartile$ $\text(Upper Quartile)$ $=$ $=$ $5$ $5$

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

$=$ $=$ $5$ $5$ $-$ $-$ $3$ $3$ Substitute values

$=$ $=$ $2$ $2$

$IQR = 2$ $\text(IQR)=2$
Question 2 of 6

2. Question
Find the interquartile range from the data set below.

$13$ $13$ $16$ $16$ $6$ $6$ $14$ $14$ $20$ $20$ $7$ $7$ $10$ $10$ $18$ $18$ $13$ $13$ $8$ $8$ $9$ $9$ $12$ $12$ $9$ $9$
- $IQR =$ $\text(IQR )=$ (6.5)
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Interquartile Range

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$6$ $6$ $7$ $7$ $8$ $8$ $9$ $9$ $9$ $9$ $10$ $10$ $12$ $12$ $13$ $13$ $13$ $13$ $14$ $14$ $16$ $16$ $18$ $18$ $20$ $20$

We can see that the value $12$ $12$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$6$ $6$ $7$ $7$ $8$ $8$ $9$ $9$ $9$ $9$ $10$ $10$ $=$ $=$ $Lower Half$ $\text(Lower Half)$

$13$ $13$ $13$ $13$ $14$ $14$ $16$ $16$ $18$ $18$ $20$ $20$ $=$ $=$ $Greater Half$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$6$ $6$ $7$ $7$ $8$ $8$ $9$ $9$ $9$ $9$ $10$ $10$

$13$ $13$ $13$ $13$ $14$ $14$ $16$ $16$ $18$ $18$ $20$ $20$

$Lower Quartile$ $\text(Lower Quartile)$ $=$ $=$ $\frac{8 + 9}{2}$ $(8+9)/2$

$=$ $=$ $8.5$ $8.5$

$Upper Quartile$ $\text(Upper Quartile)$ $=$ $=$ $\frac{14 + 16}{2}$ $(14+16)/2$

$=$ $=$ $15$ $15$

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

$=$ $=$ $15$ $15$ $-$ $-$ $8.5$ $8.5$ Substitute values

$=$ $=$ $6.5$ $6.5$

$IQR = 6.5$ $\text(IQR)=6.5$
Question 3 of 6

3. Question
Find the interquartile range from the data set below.

$17$ $17$ $29$ $29$ $21$ $21$ $23$ $23$ $42$ $42$ $17$ $17$ $22$ $22$ $13$ $13$ $4$ $4$ $21$ $21$
- $IQR =$ $\text(IQR )=$ (6)
Correct

Correct!

Incorrect

Interquartile Range

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$4$ $4$ $13$ $13$ $17$ $17$ $17$ $17$ $21$ $21$ $21$ $21$ $22$ $22$ $23$ $23$ $29$ $29$ $42$ $42$

We can see that the value $21$ $21$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$4$ $4$ $13$ $13$ $17$ $17$ $17$ $17$ $21$ $21$ $=$ $=$ $Lower Half$ $\text(Lower Half)$

$21$ $21$ $22$ $22$ $23$ $23$ $29$ $29$ $42$ $42$ $=$ $=$ $Greater Half$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$4$ $4$ $13$ $13$ $17$ $17$ $17$ $17$ $21$ $21$

$21$ $21$ $22$ $22$ $23$ $23$ $29$ $29$ $42$ $42$

$Lower Quartile$ $\text(Lower Quartile)$ $=$ $=$ $17$ $17$

$Upper Quartile$ $\text(Upper Quartile)$ $=$ $=$ $23$ $23$

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

$=$ $=$ $23$ $23$ $-$ $-$ $17$ $17$ Substitute values

$=$ $=$ $6$ $6$

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

Question 4 of 6

Find the interquartile range from the data set below.

$74$ $74$	$66$ $66$	$71$ $71$	$62$ $62$	$64$ $64$	$76$ $76$
$72$ $72$	$82$ $82$	$80$ $80$	$70$ $70$	$73$ $73$	$76$ $76$
$73$ $73$	$77$ $77$	$75$ $75$	$69$ $69$	$59$ $59$

$IQR =$ $\text(IQR )=$ (8.5)

Incorrect

Interquartile Range

IQR =

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

-

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$59$ $59$	$62$ $62$	$64$ $64$	$66$ $66$	$69$ $69$	$70$ $70$
$71$ $71$	$72$ $72$	$73$ $73$	$73$ $73$	$74$ $74$	$75$ $75$
$76$ $76$	$76$ $76$	$77$ $77$	$80$ $80$	$82$ $82$

We can see that the value $73$ $73$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$59$ $59$	$62$ $62$	$64$ $64$	$66$ $66$	$69$ $69$	$70$ $70$	$71$ $71$	$72$ $72$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$73$ $73$	$74$ $74$	$75$ $75$	$76$ $76$	$76$ $76$	$77$ $77$	$80$ $80$	$82$ $82$	$=$ $=$	$Greater Half$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$59$ $59$	$62$ $62$	$64$ $64$	$66$ $66$	$69$ $69$	$70$ $70$	$71$ $71$	$72$ $72$
$73$ $73$	$74$ $74$	$75$ $75$	$76$ $76$	$76$ $76$	$77$ $77$	$80$ $80$	$82$ $82$

$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$\frac{66 + 69}{2}$ $(66+69)/2$

	$=$ $=$	$67.5$ $67.5$

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$\frac{76 + 76}{2}$ $(76+76)/2$

	$=$ $=$	$76$ $76$

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
	$=$ $=$	$76$ $76$ $-$ $-$ $67.5$ $67.5$	Substitute values
	$=$ $=$	$8.5$ $8.5$

IQR = 8.5

$\text(IQR)=8.5$

Question 5 of 6

5. Question
Find the interquartile range of the dot plot.
- $IQR =$ $\text(IQR )=$ (7.5)
Correct

Keep Going!

Incorrect

Interquartile Range

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, take note that there is a total of $17$ $17$ scores on the dot plot, which is an odd number.

Therefore, the median of the data set will be the score on the $9 t h$ $9th$ position.

$Median$ $\text(Median)$ $=$ $=$ $71$ $71$

The median divides the data set into two quartiles, each with $8$ $8$ values.

To find the lower and upper quartiles, find the median of both the lower and greater halves.

$Lower Quartile$ $\text(Lower Quartile)$ $=$ $=$ $66$ $66$

$Upper Quartile$ $\text(Upper Quartile)$ $=$ $=$ $\frac{73 + 74}{2}$ $(73+74)/2$

$Upper Quartile$ $\text(Upper Quartile)$ $=$ $=$ $73.5$ $73.5$

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

$=$ $=$ $73.5$ $73.5$ $-$ $-$ $66$ $66$ Substitute values

$=$ $=$ $7.5$ $7.5$

$IQR = 7.5$ $\text(IQR)=7.5$

Question 6 of 6

Find the interquartile range from the data set below.

Plant	Days	Plant	Days
Average Time to Maturity
Soy Bean	70	Tomatillo	100
Arugula	35	Sweet Banana Pepper	72
Asparagus	730	Honeydew	80
Jersey Tomato	74	Endive	47
Shallots	115	Okra	55
Mesclun	40	Sugar Baby Watermelon	75
Celery	95	Bell Pepper	75
Cherry Tomato	65

$IQR =$ $\text(IQR )=$ (40)

Incorrect

Interquartile Range

IQR =

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

-

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

Remember

The lower quartile is the median of the lower half of the data set, while the upper quartile is the median of the greater half of the data set.

First, arrange the values of the data set in ascending order

$35$ $35$	$40$ $40$	$47$ $47$	$55$ $55$	$65$ $65$
$70$ $70$	$72$ $72$	$74$ $74$	$75$ $75$	$75$ $75$
$80$ $80$	$95$ $95$	$100$ $100$	$115$ $115$	$730$ $730$

We can see that the value $74$ $74$ is the middle value of the data set, and is the median of the data set.

This also divides the data set into two quartiles

$35$ $35$	$40$ $40$	$47$ $47$	$55$ $55$	$65$ $65$	$70$ $70$	$72$ $72$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$75$ $75$	$75$ $75$	$80$ $80$	$95$ $95$	$100$ $100$	$115$ $115$	$730$ $730$	$=$ $=$	$Greater Half$ $\text(Greater Half)$

Now, find the median of both quartiles to get the lower and upper quartiles

$35$ $35$	$40$ $40$	$47$ $47$	$55$ $55$	$65$ $65$	$70$ $70$	$72$ $72$
$75$ $75$	$75$ $75$	$80$ $80$	$95$ $95$	$100$ $100$	$115$ $115$	$730$ $730$

$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$55$ $55$
$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$95$ $95$

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
	$=$ $=$	$95$ $95$ $-$ $-$ $55$ $55$	Substitute values
	$=$ $=$	$40$ $40$

IQR = 40

$\text(IQR)=40$

Finding the Interquartile Range 2

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Quiz summary

Information

1. Question

Well Done!

Interquartile Range

Remember

2. Question

Hint

Correct!

Interquartile Range

Remember

3. Question

Correct!

Interquartile Range

Remember

4. Question

Fantastic!

Interquartile Range

Remember

5. Question

Keep Going!

Interquartile Range

Remember

6. Question

Nice Job!

Interquartile Range

Remember

Quizzes

$Median$ $\text(Median)$	$=$ $=$	$\frac{4 + 4}{2}$ $(4+4)/2$

	$=$ $=$	$\frac{8}{2}$ $8/2$

	$=$ $=$	$4$ $4$

$6$ $6$	$7$ $7$	$8$ $8$	$9$ $9$	$9$ $9$	$10$ $10$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$13$ $13$	$13$ $13$	$14$ $14$	$16$ $16$	$18$ $18$	$20$ $20$	$=$ $=$	$Greater Half$ $\text(Greater Half)$

$Lower Quartile$ $\text(Lower Quartile)$	$=$ $=$	$\frac{8 + 9}{2}$ $(8+9)/2$

	$=$ $=$	$8.5$ $8.5$

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$\frac{14 + 16}{2}$ $(14+16)/2$

	$=$ $=$	$15$ $15$

$4$ $4$	$13$ $13$	$17$ $17$	$17$ $17$	$21$ $21$	$=$ $=$	$Lower Half$ $\text(Lower Half)$
$21$ $21$	$22$ $22$	$23$ $23$	$29$ $29$	$42$ $42$	$=$ $=$	$Greater Half$ $\text(Greater Half)$

$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$\frac{73 + 74}{2}$ $(73+74)/2$
$Upper Quartile$ $\text(Upper Quartile)$	$=$ $=$	$73.5$ $73.5$