Deck 4: Summarizing Scores With Measures of Variability

Question 1

What is wrong with the following formula?
$S_{X}^{2}=\sqrt{\frac{\sum X^{2}-\frac{(\Sigma X)^{2}}{N}}{N}}$

A)The symbol $S_{X}^{2}$ indicates the sample variance, but the formula indicates the sample standard deviation.
B)The symbol $S_{X}^{2}$ indicates the estimated population variance, but the formula indicates the estimated population standard deviation.
C)The symbol $S_{X}^{2}$ indicates the sample variance, but the formula indicates the estimated population variance.
D)There is nothing wrong with the formula.

Answer 1

The symbol $S_{X}^{2}$ indicates the sample variance, but the formula indicates the sample standard deviation.

Question 2

Measures of variability are used to

A)summarize and describe the extent to which scores in a distribution differ from one another.
B)summarize and 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)summarize and describe measures of central tendency.

Answer 2

A

Question 3

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

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.

Answer 3

C

Question 4

If you see the notation $\sum X^{2}$ , 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 5

A psychology professor wanted to describe the adolescents in her state in terms of the personality characteristic of introversion/ extroversion.She selects a sample and measures their scores on a test of introversion/extroversion.The measure of variability she should calculate is

A)the estimated population standard deviation, because she wants to make inferences about the population based on her sample.
B)the sample standard deviation, because she has measured a sample, not the entire population.
C)the population standard deviation, because the sample she selected is representative of the population.
D)the range, because the dependent variable is an ordinal measurement scale.

Question 6

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 7

A program evaluator for a large school district wants to know how much intelligence varies in the elementary schools.She 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 sum of the deviations
D)The mean

Question 8

The term variability is most opposite to

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

Question 9

What do $\left(S_{X}^{2}\right)$ , $\left(s_{X}^{2}\right)$ , and $\left(\sigma_{X}^{2}\right)$ 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 10

As with measures of centrality, the selection of a measure of variability should be based on

A)the mean and the variance.
B)measurement scale and the shape of the distribution.
C)population variance and standard deviation.
D)the range of the scores and their frequency.

Question 11

If you see the notation $(\Sigma X)^{2}$ , 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.

Question 12

The variance can never be

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

Question 13

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

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

Question 14

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 deviations about the mean always sum to zero

Question 15

The greater the variability, the more spread out the scores are around the

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

Question 16

The greater the variability in a set of scores,

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

Question 17

Suppose we compute $S_{X}$ and find 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 18

A program evaluator for a large school district wants to know how much intelligence varies in the elementary schools.She 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 sum of the deviations
D)The range

Question 19

Variance is defined as 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, squared.
D)sum of the squared deviations around the mean.

Question 20

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 21

In a normal distribution, approximately what percentage of scores is not between -1 $S_{X}$ and 1 $S_{X}$ ?

A)32%
B)68%
C)34%
D)50%

Question 22

Find and for the following distribution.
Score f 8 3
7 1
6 0
5 4
4 2
3 3
2 1
1 5

Question 23

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

Question 24

What is the range of the following data?

Question 25

To determine the range, we simply

A)subtract the highest score minus the lowest score.
B)subtract the lowest score minus the highest score.
C)need to know the lowest and highest scores.
D)average the lowest and highest scores.

Question 26

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

Question 27

Which of the following sets of data appears to show the greatest amount of variability?

A)99, 110, 153, 98, 64
B)92, 91, 89, 94, 95
C)10, 20, 5, 34, 29
D)188, 200, 201, 177, 169

Question 28

Which of the following is not viewed as a measure of variability?

A)The mean
B)The range
C)Variance
D)Standard deviation

Question 29

A cognitive psychologist found the mean recall of information increased consistently as the extent to which the participants elaborated on the material none, minimal, extensive) changed.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 30

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 ?

Question 31

June has obtained a sample of 150 people from their school records about their career aptitude.She has calculated = 867 and = 38,427.Calculate the sample standard deviation for these data.

Question 32

Find for the following data set.
8, 7, 2, 4, 4, 8, 2, 4, 6, 5, 7, 3, 9, 4, 5, 4, 7

Question 33

Find for the following data set.
8, 7, 2, 4, 4, 8, 2, 4, 6, 5, 7, 3, 9, 4, 5, 4, 7

Question 34

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 ?

Question 35

If we know the sample variance, can we use that information to find the sample standard deviation?

A)Yes, simply take the square root of the variance to find the standard deviation.
B)Yes, simply square the variance to find the standard deviation.
C)Yes, simply divide the variance by N to find the standard deviation.
D)No, it is not possible.

Question 36

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 37

Frankie has data from a sample of 45 people analyzing their knowledge about cholesterol.He has calculated = 600 and = 90.Calculate the sample standard deviation for these data.

Question 38

Suppose you have a set of normally distribution data where the mean is 120 and the standard deviation is 15.What score is located at -3 $S_{X}$ ?

A)75
B)105
C)165
D)90

Question 39

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

Question 40

When we are considering measures of variability, we are effectively considering

A)how spread out a distribution is.
B)the central location of a distribution.
C)the statistical significance of a set of data.
D)whether our data originates from a sample or a population.

Question 41

Identify the basic difference between the formulas for the computing estimated population standard deviation and sample standard deviation.

Question 42

Find for the scores in the following frequency distribution.

Question 43

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

Question 44

Suppose you have the following scores: 4, 3, 5, 5, and 2.What is the sum of squared Xs?

Question 45

Find and for the following data set.8, 7, 2, 4, 4, 8, 2, 4, 6, 5, 7, 3, 9, 4, 5, 4, 7

Question 46

Suppose you scored an 80 on a measure where the mean is 65 and the standard deviation is 5.How many standard deviations from the mean is your score?

Question 47

How would a mean of 28.75 and a standard deviation of 3.22 likely be reported in a journal following APA format?

Question 48

For the following data set, find the estimated population variance and the estimated population standard deviation.Score f
20 2
19 5
18 8
17 5
16 4
15 1

Question 49

Suppose you scored 95 on a measure where the mean was 110 and the standard deviation was 15.Assuming a normal distribution, what percentage of scores should fall between your score and the mean?

Question 50

Suppose you have the following scores: 4, 3, 5, 5, and 2.What is the squared sum of X?

Question 51

For the following data set, find and .Explain why is a larger value.Score f
37 2
36 4
35 8
34 3
33 1
32 8
31 3
30 1

Question 52

Ms.Gonzalez has recorded the test scores for each of her 25 students.She has calculated = 320 and = 5,000.Calculate the estimated population standard deviation for her data.

Question 53

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

Question 54

Find for the scores in the following frequency distribution.

Question 55

Suppose the sample variance and N both equal 10.What is the sample standard deviation?

Question 56

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.What would you estimate the population standard deviation to be?

Question 57

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

Question 58

Mr.Johnson has collected data from 100 people assessing their attitudes toward a recent referendum.He has calculated = 470 and = 150.Calculate the estimated population standard deviation for his data.