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Quiz 2: Measures of Spread

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
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?
a) Sample 2.   b) Sample 1.
c) Neither; they have the same spread.   d) There is not enough information to answer the question.

 

Your answer is correct.
The variance of sample 2 is larger.
Not correct. Choice (b) is false.
You should compare variances, not means.
Not correct. Choice (c) is false.
Try again.
Not correct. Choice (d) is false.
Try again.
 

Question 2

 
 
Consider the following ordered set of data

44 49 50 51 53 57 58 62

66 66 68 71 75 77 80 85


What is the IQR?

 

Your answer is correct
Q1 = 52 and Q3 = 73 so IQR= 21.
Not correct. You may try again.
Check your values for the first and third quartiles.
 

Question 3

 
 
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 σn- 1 when calculating the sample standard deviation.)
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 .

 

Your answer is correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 4

 
 
Consider the data set.
| --i-|-1---2---3-- xi 1.3 1.7 2.7
Write down 1.32 + 1.72 + 2.72 in summation notation.
a) ∑3 i2 i=1   b) ( ) ∑3 2 xi i=1
c) 3 ∑ x2 i=1 i   d) ( 3 )2 ∑ i i=1

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
∑3 2 2 2 2 2 2 2 xi = x1 + x2 + x3 = 1.3 +1.7 + 2.7 . i=1
Not correct. Choice (d) is false.
 

Question 5

 
 
The table below gives 5 pairs of numbers (xi,yi) .
| --i-|1--2-3--4---5- xi |1 2 3 4 5 yi 2 4 6 8 10
What is the value of ∑5 xiyi i=1 ?
a) 450   b) 45
c) 36   d) 110

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
∑3 xiyi = x1y1 + x2y2 + x3y3 + x4y4 + x5y5 = 2+ 8+ 18 +32 + 50 = 110 i=1 .
 

Question 6

 
 
Consider the following table:
| -i-|1--2--3-- xi |3 1 2 yi 4 2 1
Which of the following set of statements is true ?
a)
∑3 2 ∑3 2 ∑3 xi = 14, yi = 21, xiyi = 16, i∑=31 i∑=31 i∑=31 (xi - x)2 = 2, (yi - y)2 = 2, (xi - x)(yi - y) = 4 23. i=1 i=1 i=1
b)
∑3 ∑3 ∑3 x2i = 21, y2i = 14, xiyi = 16, i=31 i=31 i=31 ∑ (x - x)2 = 2, ∑ (y - y)2 = 14, ∑ (x - x)(y - y) = 2. i=1 i i=1 i 3 i=1 i i
c)
3 3 3 ∑ x2 = 14, ∑ y2 = 21, ∑ x y = 16, i=1 i i=1 i i=1 i i ∑3 -- ∑3 -- ∑3 -- -- (xi - x)2 = 2, (yi - y)2 = 134, (xi - x)(yi - y) = 2. i=1 i=1 i=1
d)
∑3 ∑3 ∑3 x2i = 14, y2i = 14, xiyi = 2, i=31 i=31 i=31 ∑ (x - x)2 = 2, ∑ (y - y)2 = 2, ∑ (x - x)(y - y) = 14. i=1 i i=1 i i=1 i i 3

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
 

Question 7

 
 
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?
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.

 

Not correct. Choice (a) is false.
Your answer is correct.
The mean increases by 2 but the standard deviation remains the same, as it is not affected by a shift of location.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 8

 
 
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.
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.

 

Not correct. Choice (a) is false.
Your answer is correct.
The mean has a added to it and the standard deviation remains the same. Question 7 gives a specific example of this.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 9

 
 
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.
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.

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Your answer is correct.
Both the mean and the standard deviation are affected by a change of scale and are multiplied by c.
 

Question 10

 
 
Consider the following table:
| -i--1--2--3-- xi |3 2 1 yi|1 2 3
Using the formula
∑n ( ∑n )( ∑n ) Sxy = xiyi - 1- xi yi , i=1 n i=1 i=1
find Sxy.
a) Sxy = -1   b) Sxy = 0
c) Sxy = -2   d) Sxy = 2

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
∑n xiyi = 10 i=1 , ∑n xi = 6 i=1 , ∑n yi = 6 i=1
so 1 Sxy = 10- 3 × 36 = - 2 .
Not correct. Choice (d) is false.