Deck 5: Variability: the Law of Life

Question 1

In a dataset with 10 observations, the range is a measure of variability that takes all 10 into account

Answer 1

False

Question 2

The range only takes two data points into account

Answer 2

True

Question 3

large variability will lead to a small standard deviation

Answer 3

False

Question 4

The interquartile range is the difference between the score in the 75^th percentile and the 25^th percentile.

Question 5

Measurement error can be due to issues with the instrument that is being used.

Question 6

The range rule suggests that the standard deviation is roughly the range divided by 4

Question 7

If you calculate the sum of deviation scores from each data point in a dataset from the mean of the dataset, you will always end up with a sum of 0.

Question 8

Standard deviation and variance are both measures of variability, but standard deviation is a better measure because it takes into account all data points where as the variance only takes into account half of the data points

Question 9

In the data set: 15, 14, 10, 18, 9, 22, 28, 39, 11, the range is 48.

Question 10

"Measurement error" in science refers to a discrepancy between the observed value and the true value

Question 11

Fisher states that a good statistic should be simple, novel, and controlled

Question 12

The variance is the average absolute deviation score from the mean

Question 13

If the range of a dataset is 100, the range rule would estimate that the standard deviation is 20

Question 14

Variance can be negative

Question 15

The standard deviation must be greater than 0

Question 16

Measurement error can always be controlled for after the data have been collected

Question 17

When the variance is of a sample is 64, the standard deviation of that same sample is 32

Question 18

a perfectly made measurement instrument without error is generally the current standard. Most tools can achieve this with modern technology

Question 19

two datasets can have the same range, but different variance.

Question 20

Which of the following measures is most sensitive to every data point in a dataset?

A) The range
B) The interquartile range
C) The Variance
D) All of the above

Question 21

Consider the following dataset: 110, 320, 293, 284, 281, 279, 380, 227, 293, 183. What is the range of the dataset?

A) 380
B) 270
C) 183
D) 293

Question 22

How are the interquartile range and the range similar and different?

A) Both are measures of variability that take a difference between two numbers, but the range compare two extreme values whereas the interquartile range compares the 3^rd and 1^st quartiles.
B) The interquartile range and range are both measures of variability, but the interquartile range is highly sensitive to every data point in the dataset whereas the range does not.
C) The interquartile range uses extreme values, and the range uses all values. Both are useful measures of mean difference
D) None of the above are correct.

Question 23

When variability in a dataset is _____________, we expect the data to be ___________.

A) unknown, consistent
B) small, consistent
C) high, consistent
D) large, sufficient

Question 24

Which of the following describe the standard deviation?

A) Square root of the sum of deviation scores from the mean.
B) Square root of the average squared deviation from the mean.
C) Square root of the sum of square deviation from the mean
D) The average deviation from the mean.

Question 25

Imagine a data set with 10 observations. If each observation increases by 10 (i.e., add 10 to each data point), which of the following will happen to the standard deviation?

A) The amount of variability stays the same. So the standard deviation will be the same value.
B) The variability stays the same. But because the value of each data point is larger, the standard deviation will also increase by 10.
C) The standard deviation will increase, but it not in a systematic way that can be described.
D) The standard deviation will be 10 times the original value.

Question 26

How is measurement error best described?

A) Measure error only exists for psychological research because we are measuring constructs that are hard to observe.
B) State of the art equipment and measurement tools will not have any measurement error.
C) Measurement error is often unavoidable.
D) All of the above.

Question 27

Measurement errors can be…

A) Easily accounted for after data have been collected.
B) beyond a researcher's control.
C) Minimized if the sample is sufficiently small
D) all of the above

Question 28

The range is a form of…?

A) central tendency
B) inferential statistic
C) measure of variability
D) nominal scale data

Question 29

The range is best described as…:

A) The average variability
B) the distance from each point to the mean
C) The distance from a dataset's maximum value to its minimum value
D) a highly sensitive measure of variability in a dataset

Question 30

In a town, there are two candy factories. Over the course of the year, they log the number of pounds of candy they produce a day. Factory A has a range of 5000 and a standard deviation of 500. Factory B has a range of 7000 and a standard deviation of 600. Which of the following is true?

A) The maximum number of candy produced on any given day is larger in factory B than factory A
B) Factory B has greater variability in their candy production than factory A
C) Factory B has less variability in their candy production than factory A
D) Factory A produced less candy than factory B in the year.

Question 31

If two datasets have the same range, then… ?

A) They have the same maximum and minimum value.
B) The have the same variance
C) They have the same interquartile range
D) none of the above.

Question 32

Which of the following is true regarding variability and range?

A) Range and interquartile range are equally sensitive measures of variability when compared to the variance and standard deviation
B) The range is not a sensitive measure of variability, but the interquartile range is sensitive to every data point in a dataset, in the same way that the variance and standard deviation are.
C) The variance of a dataset is sensitive to every data point in the dataset, but the range is not.
D) None of the above is true.

Question 33

Why do we use the sum of squared deviation scores from the mean and not sum of deviation scores when calculating the variance?

A) The sum of deviation scores will always be zero.
B) The sum of deviation scores is not a valid.
C) The sum of deviation scores is used when calculating from the mode
D) All of the above

Question 34

Why is it generally the case that one does not use the range to describe a dataset, but instead the standard deviation?

A) The range is not a measure of variability.
B) The range only takes into account two extreme values in a dataset
C) The range is too sensitive to the middle of the data
D) Both a and C

Question 35

To obtain the standard deviation, what is the correct procedure?.

A) Square the variance
B) Square root of the variance
C) Subtract each score from the mean, and divide it by the sample size
D) Half the variance

Question 36

If the variance of a dataset is 16, what is the standard deviation?

A) 4
B) 16
C) 2
D) 8

Question 37

If the standard deviation of a sample is 15, the variance would be?

A) 225
B) 30
C) 150
D) 3.87

Question 38

Imagine a dataset with 50 observations. Now imagine multiplying each score by 5. Which of the following will occur?

A) the standard deviation will by 5 times larger.
B) The standard deviation will increase, but unpredictably
C) The standard deviation will not change
D) The standard deviation will increase by 25 times.

Question 39

How does the population variance and sample variance differ?

A) The population variance is always larger.
B) If you have a dataset and do both calculations, the population variance will always be smaller
C) With the same dataset, calculating the population variance will always be a better estimate of the sample standard deviation than if you had calculated the sample variance.
D) The sample variance is the square root of the population variance.

Question 40

Which of the following is not possible, given the formula of the variance?

A) obtaining a variance that is larger than the range
B) obtaining a negative variance
C) obtaining a variance that is smaller than the mean
D) All of the above

Question 41

Which of the following are the necessary components to obtain the standard deviation of a dataset?

A) The range and sample size
B) The mean and the sample size
C) Half of a dataset
D) The variance

Question 42

The Interquartile Range (IQR) is generally better than the range as a measure of variability because...

A) It takes more of how the data is into account
B) It is less focused on extreme values
C) The IQR uses data closer to the center of the dataset
D) All of the above

Question 43

The mean of a dataset is 8, what is the deviation score for an individual who scored 3?

A) -5
B) 5
C) 11
D) 25

Question 44

Below is a dataset showing the number of steps from a population of toddlers when completing a maze:
114, 180, 194, 280, 297, 240, 266, 217, 288, 293, 283, 255, 219, 140, 130, 160
What is the range of the data?

Question 45

Below is a dataset showing the number of steps from a population of toddlers when completing a maze:
114, 180, 194, 280, 297, 240, 266, 217, 288, 293, 283, 255, 219, 140, 130, 160
What is the interquartile range?

Question 46

Below is a dataset showing the number of steps from a population of toddlers when completing a maze:
114, 180, 194, 280, 297, 240, 266, 217, 288, 293, 283, 255, 219, 140, 130, 160
What is the population variance?

Question 47

Below is a dataset showing the number of steps from a population of toddlers when completing a maze:
114, 180, 194, 280, 297, 240, 266, 217, 288, 293, 283, 255, 219, 140, 130, 160
What is the population standard deviation?

Question 48

Explain why the variance uses the sum of squared deviation scores from the mean, as opposed to merely the sum of deviation scores from the mean.

Question 49

What is the range rule?

Question 50

Fisher stated that the standard deviation is a good statistic based on three qualities. What are they, and what do they each mean, in the context of the standard deviation?

Question 51

Consider the following data of IQ scores:
99, 111, 95, 94, 104, 101, 96, 110, 87, 100, 115
what is the range?

Question 52

Consider the following data of IQ scores:
99, 111, 95, 94, 104, 101, 96, 110, 87, 100, 115
Based on the range, what is the estimated standard deviation?

Question 53

Consider the following data of IQ scores:
99, 111, 95, 94, 104, 101, 96, 110, 87, 100, 115
What is the actual standard deviation (assuming that this is the population)?