436 Final Exam Stats Questions

Here are some statistics questions from former finals -- taken from all parts of the exams.
The letter in brackets (A, B or C) indicates from which part of the exam the question came.
Note: a box-and-whisker plot tells us nothing about the mean! Don't let them fool you.

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1) This box-and-whisker plot represents the math marks of a grade 10 class.(A)

2) The table data displays the number of chocolate bars sold to raise funds for their soccer team by 17 students at Wise Guy Academy.

a) Construct a box and whisker plot for the data.(B)
b) In which quartile is the data most condensed and most dispersed?
c) What is the InterQuartile Range (IQR)?

 36 37 37 38 38 39 39 42 43 47 48 51 51 53 55 59 60 (solution)

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3) The table data displays the final math marks for two classes of 20 students
at TeachemGood High School. Trevor and Shaun both got 89%.
Trevor is in Class A, Shaun is in Class B.

 Marks for students in Class A (Trevor's class) 75 76 77 79 81 83 84 85 86 87 87 87 89 90 91 91 96 97 97 98

 Marks for students in Class B (Shaun's class) 75 75 75 76 77 77 78 78 79 84 85 85 87 88 88 89 94 95 96 98

The parents committee needs to find out who gets the awards for
achievement in math so they do some stats on the data.
Which student's position in his group will give him a better chance of winning an award?(C)

(hint: find percentiles first) (click for solution)

4) The data shows the distribution of 13,000 voters in Blunderville by gender.

 Age Women Men Total [18, 30[ 1,200 1,100 2,300 [30, 45[ 2,600 2,300 4,900 [45, 60[ 1,800 2,100 3,900 [60, + º [ 1,000 900 1,900 Total 6,600 6,400 13,000

How many women aged 30 to 45 should there be in a representative sample of 390 voters? (B)
(click for solution).

5) The data shows the marks (%) for 26 math students on their final exam.

 49 54 57 58 58 60 61 61 63 66 69 70 71 75 79 79 82 85 86 87 88 91 91 93 94 99

• Sarah's mark is one of the quartiles.
• No one else in the class got the same mark as Sarah.
• Both marks have the same quintile rank.
• Carl's mark is an odd number.

What did both Sarah and Carl get on their exam? (C) (click for solution)

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6) Annie, Claude, Kim and Sam were given this information about their math marks:

• Annie's mark was given a quintile rank of 5.
• Claude's mark lies in the 60th percentile.
• Kim's mark is between the 1st and 2nd quartile, and
• Sam's mark is equal to the 3rd quartile.

Who had the highest mark on the exam?(A) (click for solution)

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Solutions

1) obviously the 2nd quartile.

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.2)

 min = 36 Q1 = 38 Q2 = 43 Q3 = 52 max = 60

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R100 = (# < or = 89) ÷ total (20) × 100

Shaun: R100 = (16) ÷ (20) × 100 = 80; Trevor: R100 = (13) ÷ (20) × 100 = 65

Shaun has the best chance of an award. His percentile rank is 80 whereas Trevor's is 65.
They're both in the same quintile.

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4) If x is the number of women aged 30 to 45 in the sample, we know

There should be 78 women aged 30 to 45 in the sample.
(same proportion as the population).

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5) Since there are an even number of students in the class, Q2 , the median, is the average of the 2 middle marks which is 73 -- so that can't be Sarah's mark since no one got 73. Therefore, her mark must be Q 1 or Q 3 .
Since Q 1 = 7th data value or 61 and someone else got 61, that can't be Sarah's mark.
Q 3 = 87% and since they both have the same quintile rank and Carl's mark is an odd number,

Sarah got 87%, Carl got 85%.

6) Forget about Annie; in quintile 5 -- the bottom 20% of the class; (quintiles ranked backwards)
Claude is better than 60% of the class; Kim between Q 1 and Q 2 is lower than Claude.

Sam with mark = Q 3 is better than 75% of the class, so Sam got the highest mark.

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