e Pell e college nation o ic year pes in a percentage of women attending? 5.5 Th

Question

e Pell e college nation o ic year pes in a percentage of women attending? 5.5 The Pell Grant was created in 1972 to assist low-income college students. This table 5. 4 vides information on percentages of the academic year 2001-2002 at schools of PrivateState State-Related studen ts who were Pell Grant recipients for various types in a certain state. 21 38 19 35 36 36 30 41 40 a. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at private schools. b. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at state schools. c. Use a calculator or computer to find the mean and standard deviation of percentages of students with Pell Grants at state-related schools d. The highest mean is for state-related schools. Explain why it might be misleading to report that the percentage of students receiving Pell Grants is highest at state-related schools. e. For which type of school are the Pell Grants most evenly allocated, in the sense that percentages for all schools of that type are most similar to each other?

Explanation / Answer

We use here R software to compute mean & standard deviation .

(a) R-code to find mean & standard deviation of percentage of students with Pell Grants at Private School is ,

x=c(21,12,41,11,24,40,22,41,22,20)
mean(x)
sd(x)

Output:

mean(x)
25.4
sd(x)
11.35488  

(b) R-code to find mean & standard deviation of percentage of students with Pell Grants at State School is ,

y=c(38,33,36,36,30)
mean(y)
sd(y)

Output:

mean(y)
34.6
sd(y)
3.130495

(c) R-code to find mean & standard deviation of percentage of students with Pell Grants at State-Related School is,

,z=c(66,19,35,22)
mean(z)
sd(z)

Output:

mean(z)
[1] 35.5
sd(z)
21.48643

(d) Here, highest mean for State-Related Schools.Note that it might be misleading to report that percentage of Students receiving Pell-Grants is highest at State-Related School because standard deviation is too high as compare to other two standard deviations & high standard deviation indicates that there are some obervarions which are high (i.e. Outliers) which pull mean to 35.5 .  

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