Question

Rankings of research universities.Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.43 (p. 95). Recall that data on academic reputation score, financial aid awarded, and net cost to attend for the top 50 research universities are saved in the TOPUNIV file. The 50 academic reputation scores are listed in the accompanying table.

99 92 94 95 97 91 91 92 92 89 84 85 100 87 83 83 89 79 94 79 79 87 76 67 76 76 76 70 74 64 74 69 66 72 65 76 64 65 61 69 62 69 52 64 64 47 60 57 63 62

a.Find the median, lower quartile, and upper quartile for the data.

b.Find IQR for the data.

c.Graph the data with a box plot.

d.Do you detect any outliers? Suspect outliers?

Short answer

(a) Median = 76, lower quartile = 64.75, upper quartile = 89.25

(b) IQR = 24.5

(c)

(d) No

Step-by-step solution

Finding the median, lower quartile, and upper quartile

Arranging the data in ascending order,

(47,52,57,60,61,62,62,63,64,64,64,64,65,65,66,67,69,69,69,70,72,74,74,76,76,76,76,76,79,79,79,83,83,84,85,87,87,89,89,91,91,92,92,92,94,94,95,97,99,100)$$\begin{gathered} Q1=\frac{N+1}{4}=\frac{50+1}{4}=\frac{51}{4}=12.{75}^{th}term=64.75 \\ Q2=\frac{N+1}{2}=\frac{50+1}{2}=\frac{51}{2}=25.5^{th}term=76 \\ Q3=\frac{3\left(N+1\right)}{4}=\frac{3\left(50+1\right)}{4}=\frac{153}{4}=38.{25}^{th}term=89.25 \end{gathered}$$

Therefore, Median = 76, lower quartile = 64.75, upper quartile = 89.25

Computing the IQR

IQR = Q_U – Q_L

= 89.25 – 64.75

= 24.5

Constructing the box plot

Lower Inner Fence = Q_L - 1.5(IQR)

= 64.75 – 1.5(24.5)

= 64.75 – 36.75

= 28

Upper Inner Fence = Q_U + 1.5(IQR)

= 89.25 + 1.5(24.5)

= 89.25 + 24.5

= 113.75

Detecting outliers and Suspect outliers

No, I do not detect any outliers or suspect outliers.