Deck 5: Measures of Variability: Range, variance, and Standard Deviation

Question 1

What is the range of the following data? 15,9,17,12,15,19,18,15,16,10,13

A)5
B)10
C)14.45
D)15

Answer 1

10

Question 2

If you see the notation you should

A)sum all the Xs,then square the sum.
B)square all the Xs,then sum the squares.
C)sum the Xs,then divide by 2.
D)divide all the Xs by 2.

Answer 2

sum all the Xs,then square the sum.

Question 3

A program evaluator for a large school district wants to study intelligence in the elementary schools.She randomly selects one classroom at each grade level in each elementary school and administers an intelligence test to the children in those classrooms.In order to find out which school has the most consistent intelligence level,which of the following should she calculate for each school?

A)The mean
B)The standard deviation
C)The median
D)The range

Answer 3

The standard deviation

Question 4

When computing the variance,why do we square the deviations from the mean?

A)To return the units of measure to their original form
B)To compensate for the fact that the number of degrees of freedom is different from N
C)To transform the raw scores into squared scores
D)To compensate for the fact that deviations about the mean always sum to zero

Question 5

A program evaluator for a large school district wants to study intelligence in the elementary schools.She randomly selects one classroom at each grade level in each elementary school and administers an intelligence test to the children in those classrooms.If the program evaluator wants to find out which school has the highest intelligence level,which of the following should she calculate for each school?

A)The variance
B)The standard deviation
C)The percentile
D)The mean

Question 6

A group of 10 students participated in a study of nutritional awareness.What is the sample variance of their scores?
20,19,22,20,15,18,15,21,19,20

A)2.21
B)2.33
C)4.89
D)5.43

Question 7

What is the range of the following data?

A)3
B)5
C)6
D)9

Question 8

If you see the notation you should

A)sum all the Xs,then square the sum.
B)sum the Xs,then divide by 2.
C)square all the Xs,then sum the squares.
D)divide all the Xs by 2.

Question 9

Which of the following is not communicated by a measure of variability?

A)The location of the distribution
B)How consistently close to the mean the scores are
C)How spread out the distribution is
D)The differences among the scores

Question 10

Sample variance is defined as the

A)average of the deviations around the sample mean.
B)average of the squared deviations of scores around the sample mean.
C)sum of the deviations around the sample mean,squared.
D)sum of the squared deviations around the sample mean.

Question 11

Measures of central tendency indicate the _____ of a distribution;measures of variability indicate the _____ between the scores in a distribution.

A)similarities;differences
B)mean;variance
C)location;distance
D)distance;location

Question 12

The greater the variability in a set of scores,

A)the less accurately the scores are represented by the mean.
B)the more accurately the scores are represented by the mean.
C)the more similar and consistently close they are to the mean.
D)the less similar and more consistently close they are to the mean.

Question 13

The term variability is most opposite to

A)central tendency
B)consistency
C)association
D)homoscedasticity

Question 14

Measures of variability are used to

A)describe the extent to which scores in a distribution differ from one another.
B)describe the extent to which scores in a distribution differ from the extreme scores.
C)make appropriate decisions regarding graph size,shape,and style.
D)describe measures of central tendency.

Question 15

When all the scores in a set of data are the same,what is ?

A)0
B)Greater than 0
C)Less than 0
D)Unknown;cannot compute without the scores

Question 16

The variance and standard deviation indicate how much the scores are spread out around

A)the range.
B)the mean.
C)the median.
D)the deviation.

Question 17

Which of the following mathematically indicates the amount a score deviates from the mean?

A)
B)
C)
D)

Question 18

The average of the deviations, ,can never actually be computed.Why?

A)You cannot subtract the mean from every number in the sample.
B)When you subtract the mean from some numbers,you get negative numbers.
C)The sum of all deviations from the mean always equals zero.
D)The actual N is never truly known.

Question 19

The range is the descriptive statistic that indicates the

A)distance from the median.
B)distance between the two most extreme scores.
C)variability among means.
D)distance between the mean and the extreme scores.

Question 20

is the symbol for

A)population variance.
B)sample variance.
C)population standard deviation.
D)sample standard deviation.

Question 21

If the variance for a sample is computed and it is found to be rather large,the numbers

A)are tightly packed around the mode.
B)are tightly packed around the mean.
C)are spread out around the mean.
D)in the sample are close to one another.

Question 22

The variance can never be

A)greater than the standard deviation.
B)zero.
C)a negative number.
D)greater than the mean.

Question 23

A group of 10 students participated in a study of nutritional awareness.What is the sample standard deviation of their scores? Their scores follow: 20,19,22,20,15,18,15,21,19,20

A)2.21
B)2.33
C)4.89
D)5.43

Question 24

In a positively skewed distribution,the estimated population variance will be _____ than the estimated population standard deviation .In a negatively skewed distribution the estimated population variance will be _____ than the estimated population standard deviation .

A)smaller;smaller
B)smaller;larger
C)larger;smaller
D)larger;larger

Question 25

and are considered biased estimates for the population standard deviation and variance because,over many calculations,they tend to be

A)overestimates.
B)underestimates.
C)inaccurate in an unpredictable way.
D)accurate estimates.

Question 26

In general,the larger the value of the standard deviation,

A)the less spread out the distribution.
B)the more tightly packed the distribution around the mean.
C)the wider the distribution.
D)the more asymmetrical the distribution.

Question 27

The standard deviation, ,is a measure of how far scores deviate from

A)the median.
B)each other.
C)the mean.
D)the most frequently occurring score.

Question 28

If we add to and subtract from ,the interval we have created

A)encompasses approximately 34% of the scores in the sample.
B)encompasses approximately 68% of the scores in the sample.
C)is approximately 68% of the range.
D)is approximately 68% of the semi-interquartile range.

Question 29

Suppose we compute and find that it is equal to 5.5.How do we interpret this number?

A)The numbers in the sample deviate,on the average,5.5 units from one another.
B)The numbers in the sample deviate,on the average,5.5 units from the two extreme scores.
C)The numbers in the sample deviate,on the average,5.5 units from the mean.
D)The numbers in the sample deviate no more than 2.25 units from the mean.

Question 30

In roughly normal distributions,the standard deviation is approximately

A)equivalent to the variance.
B)one-sixth of the range.
C)equivalent to the deviation of the median from the mean.
D)one-fifth of the absolute value of the mean.

Question 31

If the sample standard deviation for a set of data with N = 6 is found to be 3.17,then what is the sample variance ?

A)3.47
B)1.78
C)12.06
D)10.05

Question 32

The standard deviation is always

A)twice as large as the variance.
B)half as large as the variance.
C)the square of the variance.
D)the square root of the variance.

Question 33

Sample standard deviation is defined as the square root of the

A)average of the deviations around the mean.
B)average of the squared deviations around the mean.
C)sum of the deviations around the mean.
D)sum of the squared deviations around the mean.

Question 34

Unbiased estimators and of the population parameters will produce values that are _____ those produced by the biased estimators and .

A)smaller than
B)larger than
C)the same as
D)sometimes larger than and sometimes smaller than

Question 35

If the sample standard deviation for a set of data with N = 6 is found to be 3.17,then what would be the estimated population standard deviation ?

A)3.47
B)1.78
C)12.06
D)10.05

Question 36

If a sample has a small standard deviation,we can say that the scores in the sample are

A)variable.
B)small.
C)extreme.
D)consistent.

Question 37

and are considered biased estimates for the population standard deviation and variance because

A)they come from sample data.
B)N for the sample is less than N for the population.
C)they are not randomly selected.
D)they reflect the random variability of only N - 1 scores.

Question 38

Multiplying each of the scores in a distribution by a constant

A)multiplies the standard deviation by the same constant.
B)multiplies the standard deviation by half the amount of the constant.
C)multiplies the standard deviation by 34% of the constant.
D)does not change the value of the standard deviation.

Question 39

A psychology professor wanted to describe his/her class in terms of the personality characteristic of introversion/extroversion.The population variance was estimated to be 2.56.What does this mean?

A)When the professor uses the population mean to predict individuals' scores,he/she should expect to be in error by about 2.56.
B)When the professor uses the population mean to predict individuals' scores,he/she should expect to be more accurate by about 2.56.
C)It is impossible to tell because the mean is not known.
D)The sample mean differs from the population mean by about 2.56.

Question 40

Adding a constant to or subtracting a constant from each of the scores in a distribution

A)changes the value of the standard deviation by the amount of the constant.
B)changes the value of the standard deviation by half the amount of the constant.
C)changes the value of the standard deviation by 34% of the amount of the constant.
D)does not change the value of the standard deviation.

Question 41

A group of 10 students participated in a study of nutritional awareness.What is the estimated population standard deviation ? 20,19,22,20,15,18,15,21,19,20

A)5.43
B)2.21
C)4.89
D)2.33

Question 42

The quantity N -1 has a special name.It is known as the

A)unbiased estimate.
B)biased estimate.
C)degrees of freedom.
D)freedom of variation.

Question 43

A program evaluator for a large school district randomly selects one classroom at each grade level in each elementary school and administers an intelligence test to the children in those classrooms.She knows from previous research that performance is strongly related to a student's intelligence.If the program evaluator wants to predict how well a new student will fare in this school district,she should

A)calculate the mean and standard deviation of the new student's school performance.
B)calculate the mean and standard deviation for the district's intelligence scores.
C)calculate the range and the median for both intelligence and school performance.
D)conduct further research into the relationship between intelligence level and elementary school performance within her own district.

Question 44

The proper way to describe errors of prediction is to compute

A)the variance.
B)the range.
C)a z-score.
D)a T-score.

Question 45

What is the estimated population standard deviation of the following data?

A)1.83
B)3.36
C)3.16
D)1.78

Question 46

is used to describe _____; describes _____; describes _____.

A)the estimate of the population variance;the population variance;the sample variance
B)the sample variance;the population variance;the population variance
C)the sample variance;the sample variance;the population variance
D)the sample variance;the estimate of the population variance;the population variance

Question 47

A doctor wants to know how well elderly patients remember to take their medicine.The doctor measures the percentage of times during the week that patients remembered to take their medicine.For a sample of 10 patients,the mean percentage was 75,with a variance of 15.If the doctor could test his/her entire patient population,what would he/she expect the population variance to be?

A)3.87
B)15
C)16.67
D)150

Question 48

Of the three kinds of variances,which use(s)N -1 in the final division?

A)The estimated population variance
B)The sample variance
C)The population variance
D)All three

Question 49

What do , ,and have in common?

A)All are forms of standardized variance.
B)All are forms of standard deviation.
C)All are forms of variance.
D)All represent the location of a set of scores.

Question 50

The Red Cross wanted to know whether an ad campaign designed to persuade people to donate blood actually increased blood donations.For a sample of N = 4 blood donation centers,the mean increase in blood donations was 10 pints,with a standard deviation of 2 pints.If the Red Cross could collect data from the entire population of blood donation centers,what would one expect the population standard deviation to be?

A)2
B)2.31
C)2.67
D)20

Question 51

For the following data set,calculate the estimated population standard deviation. 1.72,4.01,2.55,0.67,1.93,2.05,2.69,3.13,1.22,3.84

A)1.0243
B)1.0492
C)1.0797
D)1.1659

Question 52

For the following data set,calculate the estimated population variance. 1.72,4.01,2.55,0.67,1.93,2.05,2.69,3.13,1.22,3.84

A)1.0243
B)1.0492
C)1.0797
D)1.1659

Question 53

For the following data set,calculate the sample variance. 1.72,4.01,2.55,0.67,1.93,2.05,2.69,3.13,1.22,3.84

A)1.0243
B)1.0492
C)1.0797
D)1.1659

Question 54

If we are going to predict future performance on the basis of a sample mean and sample standard deviation,it is desirable to have a

A)small mean.
B)small standard deviation.
C)large mean.
D)large standard deviation.

Question 55

Which of the following studies shows the strongest relationship between the independent and dependent variables?

A)Study A
B)Study B
C)Study C
D)Study D

Question 56

A cognitive psychologist found that the mean recall of information increased as a function of the extent to which the participants elaborated on the material (none,minimal,extensive).Also,the standard deviation for each condition was small.What does this suggest about the relationship between the amount of elaboration and recall?

A)A strong relationship exists.
B)A weak relationship exists.
C)No relationship exists.
D)A moderate relationship exists.

Question 57

In the language of statistics,how well a relationship helps predict different Y scores is the extent it

A)reduce the variance.
B)increase the variance.
C)accounts for the variance in X scores.
D)accounts for the variance in Y scores.

Question 58

A program evaluator for a large school district wants to study intelligence in the elementary schools.She randomly selects one classroom at each grade level in each elementary school and administers an intelligence test to the children in those classrooms.If the program evaluator wants to predict how well the students will fare in a citywide Academic Bowl tournament,she should

A)calculate the mean and standard deviation for tournament performance.
B)calculate the variance and standard deviation for intelligence.
C)calculate the range and the median for both tournament performance and intelligence.
D)first conduct a study to determine if there is a relationship between intelligence level and tournament performance.

Question 59

For the following data set,calculate the sample standard deviation. 1.72,4.01,2.55,0.67,1.93,2.05,2.69,3.13,1.22,3.84

A)1.0243
B)1.0492
C)1.0797
D)1.1659