Question

The following data refers to the OAC average grades of students being accepted into first year of several Ontario universities. University Brock Guelph McMaster Queen's Ryerson Toronto Grade Distribution of New 1st Year Students 60 - 70 70 - 75 75 - 80 80 - 85 85 - 90 5.8 22.1 26.7 26.0 13.1 0 0.2 27.6 37.9 21.4 0.1 10.5 24.2 32.4 19.7 0 0.2 3.2 21.9 36.8 0.5 23.0 31.0 29.3 12.4 0 1.2 8.9 26.0 36.6 > 90 6.3 12.9 13.1 37.9 3.8 27.3 REMARKS: This was ACTUAL DATA OF THE ONTARIO University Population in 2010! The line with number ranges are classes, e.g., 60-70 so midpoints MUST be used. Use 95 for 902! The numbers in the tables are percentages that add up to 100 in each row. a) Based on the above data, is the average entering grade higher for Brock or Ryerson, or is the average about the same? Which of the following is the best answer? O A. There is not sufficient information to make a decision. B. The entering grades at Ryerson are at least 1% higher than the entering grades at Brock. C. The entering grades at Brock are at least 1% higher than the entering grades at Ryerson. D. The entering grades at Brock and Ryerson are within 1/2 of 1% of each other

Answer 1

a)

Class Frequency () Mid value (x) (1) (2) (3) X-A d = = x - 82.5 h A = 82.5, h = 1 f.d (5) = (2) (4) 60 - 70 5.8 65 -17.5 -101.5 5.8 70 - 75 22.1 72.5 -10 -221 27.9 75 - 80 26.7 77.5 -5 -133.5 54.6 80 - 85 26 82.5=A 0 0 80.6 85-90 13.1 87.5 5 65.5 93.7 90 - 100 6.3 95 12.5 78.75 100 --- n = 100 ----- ----- f.d= - 311.75 --- Σfd Mean i = A + n h = 82.5+ 311.75 99 1 = = 82.5+ - 3.149.1 = 82.5 + - 3.149 = 79.351

d Class Frequency (0) Mid value (x) (1) (2) (3) X-A = x - 82.5 h A = 82.5, h = 1 fod (5) = (2) (4) cf (7) 60 - 70 0.5 65 -17.5 -8.75 0.5 70 - 75 23 72.5 -10 -230 23.5 75 - 80 31 77.5 -5 -155 54.5 80 - 85 29.3 82.5=A 0 0 83.8 85 - 90 12.4 87.5 5 62 96.2 90 - 100 3.8 95 12.5 47.5 100 --- n = 100 ----- ---- Ef.de - 284.25 ----- Σfd Mean x = A + .h n 284.25 = = 82.5+ 1 100 = 82.5 + - 2.8425 · 1 = 82.5 + - 2.8425 = 79.6575

OB. The entering grades at Ryerson are at least 1% higher than the entering grades at Brock.

2)

Toronto:

Class (1) Frequency (0) Mid value (x) (2) (3) x - A d = = x - 82.5 h A = 82.5, h = 1 f.d (5) = (2) (4) (7) 60 - 70 0 65 -17.5 0 0 1.2 70 - 75 1.2 72.5 -10 -12 8.9 77.5 -5 -44.5 10.1 75 - 80 80 - 85 26 82.5=A 0 0 36.1 85 - 90 36.6 87.5 5 183 72.7 90 - 100 27.3 95 12.5 341.25 100 --- --- n = 100 ----- Ef. d = 467.75 ---- Σfd Mean x = A + .h n 467.75 = 82.5+ 100 - 1 = 82.5 + 4.6775 · 1 = 82.5 + 4.6775 = 87.1775

Queen:

x - A =X - Class Frequency ) Mid value (x) (1) (2) d = :- 82.5 h A = 82.5, h = 1 fod (5) = (2) (4) of (7) 60 - 70 0 65 -17.5 o 0 70 - 75 0.2 72.5 -10 -2 0.2 75-80 3.2 77.5 -5 -16 3.4 80 - 85 21.9 82.5=A 0 0 25.3 85-90 36.8 87.5 5 184 62.1 90 - 100 37.9 95 12.5 473.75 100 --- O- n = 100 ----- Ef.d = 639.75 ----- Σfd Mean x = A + .h n 639.75 = 82.5+ 100 1 = 82.5 + 6.3975 · 1 = 82.5 + 6.3975 = 88.8975

OA. The entering grades at Queens are at least 1% higher than the entering grades at Univ. of Toronto.

3)

Brock:

(58.d)? Ef.d. 72 Sample Standard deviation S = .h n-1 5965.625 - (-311.75)2 99 = 1 98 5965.625 - 981.6976 98 1 4983.9274 98 = 1 = 50.8564 · 1 = 7.1314.1 = 7.1314

Ryenrson:

f.d. (98. d)2 72 Sample Standard deviation S = .h n-1 (-284.25) 4131.875 - 100 99 II 1 4131.875 - 807.9806 99 1 3323.8944 99 1 = 33.5747 · 1 = 5.7944 · 1 = 5.7944

4)

Brock:

S Co-efficient of Variation (Sample) 100% X 7.1314 · 100% 79.351 = 8.99 %

Ryenrson:

S Co-efficient of Variation (Sample) 100% X 5.7944 · 100% 79.6575 = 7.27%

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