Math

QuestionCreate a box and whisker plot for the heights: 62, 63, 64, 64, 66, 67, 68, 72, 72, 74, 75, 76. Find the interquartile range.

Studdy Solution

STEP 1

Assumptions1. The data provided are the heights of a random sample of8th graders. . The heights are in inches.
3. The data are62,63,64,64,66,67,68,72,72,74,75,76.

STEP 2

First, we need to arrange the data in ascending order.
62,63,64,64,66,67,68,72,72,74,75,7662,63,64,64,66,67,68,72,72,74,75,76

STEP 3

Next, we need to find the median of the data set. Since there are12 data points, the median will be the average of the6th and7th data points.
Median=(67+68)/2Median = (67 +68) /2

STEP 4

Calculate the median.
Median=(67+68)/2=67.Median = (67 +68) /2 =67.

STEP 5

Now, we need to find the first quartile (Q1), which is the median of the first half of the data set. Since there are data points in the first half, the first quartile will be the average of the3rd and4th data points.
Q1=(64+64)/2Q1 = (64 +64) /2

STEP 6

Calculate the first quartile.
Q1=(64+64)/2=64Q1 = (64 +64) /2 =64

STEP 7

Next, we need to find the third quartile (Q3), which is the median of the second half of the data set. Since there are6 data points in the second half, the third quartile will be the average of the3rd and4th data points in the second half.
Q3=(72+74)/2Q3 = (72 +74) /2

STEP 8

Calculate the third quartile.
Q3=(72+74)/2=73Q3 = (72 +74) /2 =73

STEP 9

Now, we can find the interquartile range (QR), which is the difference between the third quartile and the first quartile.
QR=Q3QQR = Q3 - Q

STEP 10

Plug in the values for Q3 and Q to calculate the IQR.
QR=7364QR =73 -64

STEP 11

Calculate the IQR.
QR=7364=9QR =73 -64 =9The middle50% of the heights are between64 inches and73 inches, making the interquartile range9 inches.

STEP 12

To create the box and whisker plot, draw a number line from the smallest value (62) to the largest value (76). Draw a box from the first quartile (64) to the third quartile (73), with a line inside the box at the median (67.5). Draw whiskers from the box to the smallest and largest values.

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