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MATH1005 Quizzes

Quiz 2: Measures of Spread
Question 1 Questions
Summary statistics for two samples of data are
Sample 1: mean = 19 variance = 10
Sample 2: mean = 10 variance = 19

Which sample has the larger spread of observations? Exactly one option must be correct)
a)
Sample 2.
b)
Sample 1.
c)
Neither; they have the same spread.
d)
There is not enough information to answer the question.

Choice (a) is correct!
The variance of sample 2 is larger.
Choice (b) is incorrect
You should compare variances, not means.
Choice (c) is incorrect
Try again.
Choice (d) is incorrect
Try again.
Consider the following ordered set of data

4449505153575862
6666687175778085

What is the IQR?

Correct!
Q1 = 52 and Q3 = 73 so IQR = 21.
Incorrect. Please try again.
Check your values for the first and third quartiles.
Put your calculator into statistics mode and input the following data,
 
15,21,24,16,13,18,
 
treating the data as a sample.
 
What are the sample mean and the sample standard deviation (to 2 decimal places)? (Note that we use σn1 when calculating the sample standard deviation.) Exactly one option must be correct)
a)
The mean is 17.83 and the standard deviation is 4.07 .
b)
The mean is 17.83 and the standard deviation is 3.72 .
c)
The mean is 17.67 and the standard deviation is 4.07 .
d)
The mean is 17.67 and the standard deviation is 3.72 .

Choice (a) is correct!
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Consider the data set. i 1 2 3 ̲ ̲ ̲ ̲ x i1.31.72.7 Write down 1.32 + 1.72 + 2.72 in summation notation. Exactly one option must be correct)
a)
i=13i2
b)
i=13x i 2
c)
i=13x i2
d)
i=13i2

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
i=13x i2 = x 12 + x 22 + x 32 = 1.32 + 1.72 + 2.72.
Choice (d) is incorrect
The table below gives 5 pairs of numbers (xi,yi). i1234 5 ̲ ̲ ̲ ̲ ̲ ̲ x i1234 5 y i246810 What is the value of i=15x iyi ? Exactly one option must be correct)
a)
450
b)
45
c)
36
d)
110

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
i=13x iyi = x1y1 + x2y2 + x3y3 + x4y4 + x5y5 = 2 + 8 + 18 + 32 + 50 = 110.
Consider the following table: i123 ̲ ̲ ̲ ̲ x i312y i421 Which of the following set of statements is true ? Exactly one option must be correct)
a)
i=13x i2 = 14, i=13y i2 = 21, i=13x iyi = 16, i=13(x i x¯)2 = 2, i=13(y i y¯)2 = 2, i=13(x i x¯)(yi y¯) = 42 3.
b)
i=13x i2 = 21, i=13y i2 = 14, i=13x iyi = 16, i=13(x i x¯)2 = 2, i=13(y i y¯)2 = 14 3 , i=13(x i x¯)(yi y¯) = 2.
c)
i=13x i2 = 14, i=13y i2 = 21, i=13x iyi = 16, i=13(x i x¯)2 = 2, i=13(y i y¯)2 = 14 3 , i=13(x i x¯)(yi y¯) = 2.
d)
i=13x i2 = 14, i=13y i2 = 14, i=13x iyi = 2, i=13(x i x¯)2 = 2, i=13(y i y¯)2 = 2, i=13(x i x¯)(yi y¯) = 14 3 .

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Consider the 3 observations
3,7,11
for which the mean is 7 and the standard deviation is 4.
 
If we add 2 to each value, what are the new mean and standard deviation? Exactly one option must be correct)
a)
The mean is 9 and the standard deviation is 2.
b)
The mean is 9 and the standard deviation is 4.
c)
The mean is 7 and the standard deviation is 4.
d)
The mean is 7 and the standard deviation is 6.

Choice (a) is incorrect
Choice (b) is correct!
The mean increases by 2 but the standard deviation remains the same, as it is not affected by a shift of location.
Choice (c) is incorrect
Choice (d) is incorrect
The mean of a sample of n values is x¯ and the standard deviation is s. Suppose we add a constant value a, to each observation so that the new data values are
x1 + a,x2 + a,,xn + a.
Find the new mean and the new standard deviation. Exactly one option must be correct)
a)
The new mean is x¯ + a and the new standard deviation is s + a.
b)
The new mean is x¯ + a and the new standard deviation is s.
c)
The new mean is x¯ and the new standard deviation is s + a.
d)
The new mean is x¯ and the new standard deviation is s.

Choice (a) is incorrect
Choice (b) is correct!
The mean has a added to it and the standard deviation remains the same. Question 7 gives a specific example of this.
Choice (c) is incorrect
Choice (d) is incorrect
The mean of a sample of n values is x¯ and the standard deviation is s. Suppose that the observations are multiplied by a constant value c, so that the new data values are
cx1,cx2,,cxn.
Find the new mean and the new standard deviation. Exactly one option must be correct)
a)
The new mean is x¯ and the new standard deviation is cs.
b)
The new mean is cx¯ and the new standard deviation is s.
c)
The new mean is x¯ and the new standard deviation is s.
d)
The new mean is cx¯ and the new standard deviation is cs.

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
Both the mean and the standard deviation are affected by a change of scale and are multiplied by c.
Consider the following table: i123 ̲ ̲ ̲ ̲ x i321y i123 Using the formula
Sxy = i=1nx iyi 1 n i=1nx i i=1ny i ,
find Sxy. Exactly one option must be correct)
a)
Sxy = 1
b)
Sxy = 0
c)
Sxy = 2
d)
Sxy = 2

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
i=1nx iyi = 10, i=1nx i = 6, i=1ny i = 6
so Sxy = 10 1 3 × 36 = 2.
Choice (d) is incorrect