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Janelle is training for a marathon. Her weekly mileage for the last eight weeks of training is shown below.

30, 40, 41, 33, 45, 50, 34, 50

This week, she runs a total of 9 miles before suffering a minor injury and taking the rest of the week off. Select the true statement about the effect of this week's mileage on Janelle's weekly mileage distribution.


(A) The median weekly mileage is the same with or without the inclusion of the 9-mile week.

(B) The interquartile range of the data increases when the 9-mile week is included in the data.

(C) The average weekly mileage is the same with or without the inclusion of the 9-mile week.

(D) The median weekly mileage is higher when the 9-mile week is included in the data.

Respuesta :

Answer:

The correct answer is B.The interquartile range of the data increases when the 9-mile week is included in the data.

Step-by-step explanation:

30,33,34,40,41,45,50,50

So the median will be

40+41=81

81/2=40.5

If we add the 9 then the median will be 40 so the median becomes less so the first and the last statement are wrong.

The interquartile range will be

33+34=77

77/2=38.5

45+50=95

95/2=47.5

47.5-38.5=9

If we add the 9 then the interquartile range will be

30+40=70

70/2=35.5

50+34=84

84/2=42

84-42=42

So the interquartile range changes and the statement is right.

To calculate the average we do

30+40+41+33+45+50+34+50=323

323/8=40.375

If we add the 9 we will get

9+30+40+41+33+45+50+34+50=332

332/9=36.8

So,the average changes and the statement is wrong.

The statement B is true. That is the interquartile range of the data increases when the 9-mile week is included in the data.

What is the interquartile range?

To find the interquartile range (IQR), ​first, find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Where the quartiles are the medians for the upper set of data and lower set of data.

The calculation for eight weeks of data:

Given the weekly mileage for the last eight weeks of training is

30, 40, 41, 33, 45, 50, 34, 50

Finding the median:

Arranging the data in ascending order,

30, 33, 34, 40, 41, 45, 50, 50

Since there are 8 data points, the median is between 40 and 41

So,

Median = [tex]\frac{40+41}{2}=40.5[/tex]

Finding the average:

To find the average add all the data points and divide by 2

30+33+34+40+41+45+50+50=323

323/2=161.5

Finding the IQR:

The quartile Q3 (upper quartile),

Q3=(50+34)/2=42

The quartile Q1 (lower quartile),

Q1=(40+41)/2=40.5

Thus, the IQR = Q3 - Q1

IQR = 42 - 40.5 = 1.5

Calculating when an extra week is added:

When 9 miles are added, the data is

30, 40, 41, 33, 45, 50, 34, 50, 9

Arranging the data in ascending order:

9, 30, 33, 34, 40, 41, 45, 50, 50

Median = 40

So, the median is decreased when 9 miles are added

Average = (323+9)/2 = 166

So, the average got increased

Finding IQR:

Q3 = 50 and Q1 = 40

IQR = Q3-Q1

      = 50 - 40

      = 10

So, the IQR is increased when 9 miles is added

Therefore, Option B is true.

Learn more about the interquartile range here:

https://brainly.com/question/4102829

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