2: Displaying and Exploring Data; Sampling Methods and Central Limit Theorem

Question 1

A ___ summarizes the distribution of one variable by stacking dots at points on a number line that shows all values of the variable; identical observations are stacked.; most useful in smaller data sets.

Answer 1

Dot plot

Question 2

A ___ is a method used to display a variable distribution using every value; classified by data’s leading digit.

Answer 2

Stem-and-leaf display

Stem: the leading digit or digits
Leaf: the trailing digits

Question 3

___ are values of an ordered data set (small to large) that divide the data into four intervals.

Answer 3

Quartiles

Question 4

___ are values of an ordered data set (small to large) that divide the data into 10 equal parts.

Answer 4

Deciles

Question 5

___ are values of an ordered data set (small to large) that divide the data into 100 intervals.

Answer 5

Percentiles

Question 6

___ is the most widely used measure of dispersion.

Answer 6

Standard deviation

Question 7

___ is a graphical display that shows the general shape of a variable’s distribution; based upon five statistics: the minimum value, the first and third quartile, and the maximum value.

Answer 7

Box plots

Question 8

An ___ is a value on a box plot that is inconsistent with the rest of the data. It is defined as a value that is more than 1.5 times the interquartile range smaller than Q1 or larger than Q3.

Answer 8

Outlier

Question 9

There are four shapes commonly observed:

1. ___
2. ___
3. ___
4. ___

Answer 9

1. Symmetric
2. Positively skewed
3. Negatively skewed
4. Bimodal

Question 10

In a ___ distribution the mean and median are equal and the data values are evenly spread around these values. The shape of the distribution below the mean and median is a mirror image of distribution above the mean and median.

Answer 10

Symmetric

Question 11

A distribution of values is ___ if there is a single peak, but the values extend much farther to the right of the peak than to the left of the peak; the mean is larger than the median.

Answer 11

Positively skewed or skewed to the right

Question 12

In a ___ distribution there is a single peak, but the observations extend farther to the left, in the negative direction, than to the right; the mean is smaller than the median.

Answer 12

Negatively skewed

Question 13

A ___ distribution will have two or more peaks; when the values are from two or more populations.

Answer 13

Bimodal

Question 14

A ___ is a graph in which the values of two variables (X and Y) are plotted along two axes, the pattern of the resulting points revealing any correlation present; required to be at least interval scale.

Answer 14

Scatter diagram

Question 15

A ___ is a table used to classify observations according to two identifiable characteristics.

Answer 15

Contingency table

Question 16

What are the 5 reasons to sample?

1. ___
2. ___
3. ___
4. ___
5. ___

Answer 16

1. To contact the whole population would be time-consuming
2. The cost of studying all the items in a population may be prohibitive
3. The physical impossibility of checking all items in the population
4. The destructive nature of some tests
5. The sample results are adequate

Question 17

A ___ is a sample selected so that each item or person in the population has the same chance of being included.
I.e., name in a hat OR a table of random numbers (not always effective)

Answer 17

Simple random sample

Question 18

___ is when a random starting point is selected, and then every k’th member of the population is selected (can be biased)

Answer 18

Systematic random sampling

Question 19

A ___ occurs when a population is divided into subgroups, called strata, and a sample is randomly selected from each stratum.
I.e., college students can be grouped as full time or part time; male or female; freshman, sophomore, junior, or senior.

Answer 19

Stratified random sample

Question 20

When a population can be divided into groups based on some characteristic; the group is called ___.

Answer 20

Strata

Question 21

___ occurs when a population is divided into groups using naturally occurring geographic or other boundaries. Then, are randomly selected and a sample is collected from each group; often employed to reduce the cost of sampling a population scattered over a large geographic area.

Answer 21

Cluster sampling

Question 22

___ is the difference between a sample statistic and its corresponding population parameter.

Answer 22

Sampling error

Question 23

The ___ is a probability distribution of all possible sample means of a given sample size.

Answer 23

Sampling distribution of the sample mean

Question 24

The ___ theorem states that, for large random samples, the shape of the sampling distribution of the sample mean is close to the normal probability distribution; this theorem is true for all population distributions.

Answer 24

Central limit theorem

Question 25

The sampling distribution will be normally distributed under two conditions:

1. ___
2. ___

Answer 25

1. When the samples are taken from populations known to follow the normal distribution.
2. When the shape of the population distribution is not known, sample size is important.

Question 26

The ___ will be exactly equal to the population mean if we are able to select all possible samples of the same size from a given population

Answer 26

Mean of the distribution of sample means

μ=μx

Question 27

There will be less dispersion in the sampling distribution of the sample mean than in the___.

Answer 27

Population

Question 28

___ destroys a sample in the course of measuring it.

I.e., breaking a table to determine weight capacity

Answer 28

Destructive Testing