1: What is Stats, Frequency Data, Numerical Measures

Question 1

What are three reasons to study statistics?

1. ___
2. ___
3. ___

Answer 1

(1) data requires statistical knowledge to make the information useful
(2) statistical techniques are used to make professional and personal decisions
(3) you will need a knowledge of statistics in any career

Question 2

___ is the set of knowledge and skills used to organize, summarize, and analyze data; the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.

Answer 2

Statistics

Question 3

What are the two types of statistics?

Answer 3

(1) descriptive statistics

(2) inferential statistics

Question 4

___ are methods of organizing, summarizing, and presenting data in an informative way.

Answer 4

Descriptive statistics

Question 5

___ are methods used to estimate a property of a population on the basis of a sample.

Answer 5

Inferential statistics

Question 6

A ___ is an entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.

Answer 6

Population

Question 7

A ___ is a portion, or part, of the population of interest.

Answer 7

Sample

Question 8

What are the two types of variables in statistics?

I.e., In car sales?

Answer 8

(1) qualitative (location of sale and type of vehicle sold)

2) quantitative (age of buyer, profit earned on the sale of vehicle, and number of previous purchases

Question 9

Observations of a___ variable can assume any value within a specific range.
I.e., How much milk in a glass, temperature in New Orleans.

Answer 9

Continuous

Question 10

___ variables can assume only certain values, and there are “gaps” between the values.
I.e., Weight of a box of apples, number of customers who use the ATM in a day

Answer 10

Discrete

Question 11

What are the four levels of measurements in statistics?

Answer 11

(1) nominal
(2) ordinal
(3) interval
(4) ratio

Question 12

___ level of measurement are data recorded and measured and represented as labels or names. They have no order. They can only be classified and counted.
I.e., Types of fruit in a grocery

Answer 12

Nominal level of measurement

Question 13

___ level of measurement are data based on a relative ranking or rating of items based on a defined attribute or qualitative variable. They can only ranked or counted.
I.e., Movie ratings

Answer 13

Ordinal level of measurement

Question 14

___ level of measurement are the distance between values based on a scale with a known unit of measurement.
I.e., Shoe size

Answer 14

Interval level of measurement

Question 15

___ level of measurement are data based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale.
I.e., Stock prices

Answer 15

Ratio level of measurement

Question 16

___ is a grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class; a relative frequency captures the relationship between a class frequency and the total number of observations.

Answer 16

Frequency tables

Question 17

A ___ is a graph that shows qualitative classes on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.

Answer 17

Bar graph

Question 18

A ___ is a chart that shows the proportion or percentage that each class represents of the total number of frequencies.

Answer 18

Pie chart

Question 19

A ___ is a grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

Answer 19

Frequency distribution

Question 20

___ is simply a listing of the individual and observed profits.

Answer 20

Raw or ungrouped data

Question 21

The number of observations in each class is called the ___.

Answer 21

Class frequency

Question 22

___ is halfway between the lower or upper limits of two consecutive classes; computed by adding the lower or upper limits of consecutive classes and dividing by 2.

Answer 22

Class midpoint

Question 23

A ___ is a graph in which the classes are marked on the y-axis (represented by the heights of the bars) and the class frequencies on the x-axis. Can observe shape of distribution, concentration and spread of data, and approx. number of observations. Used for quantitative variables such as the interval and ratio levels.

Answer 23

Histogram

Question 24

What are the four steps of constructing a frequency distribution?

Answer 24

(1) Decide on number of classes
(2) Determine class width
(3) Set individual class limits
(4) Tally number of observations in each class

Question 25

A useful recipe to determine the number of classes (k) is the ___ rule. (K) is the largest/smallest number.

Answer 25

“2 to the k rule” | 2 raised to the power of k where K is the smallest number

Question 26

``` ___ allows us to compare, directly, two or more frequency distributions, shows the shape of a distribution, and consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies. X-axis = midpoint of each class Y-axis = class frequencies. ```

Answer 26

Frequency polygon

Question 27

___ is a type of frequency polygon that shows cumulative frequencies. In other words, the cumulative percents are added on the graph from left to right less the upper limits of the class.

Answer 27

Cumulative frequency polygon

Question 28

___ is the sum of the class and all classes below it in a frequency distribution. In other words, adding up a value and all of the values that came before it.

Answer 28

Cumulative frequency distribution

Question 29

___ ?? a relative frequency captures the relationship between a class frequency and the total number of observations.

Answer 29

Cumulative relative frequency polygon

Question 30

___ ?? a relative frequency captures the relationship between a class frequency and the total number of observations.

Answer 30

Cumulative relative frequency distribution

Question 31

___ occurs when classes do not overlap.

Answer 31

Mutually exclusive classes

Question 32

___ occurs when there is a class for each observation.

Answer 32

Collectively exhaustive classes

Question 33

___ are a single value that is typical of the data which pinpoints the center of a distribution of data; also called averages; arithmetic mean, weighted mean, median, mode, and geometric mean.

Answer 33

Measures of location

Question 34

___ are values which show the spread of data set; range, variance, and standard deviation.

Answer 34

Measures of dispersion

Question 35

Dispersion is also called ___ or ___.

Answer 35

Variation | Spread

Question 36

A ___ is a characteristic of a population.

Answer 36

Parameter

Question 37

A ___ is a characteristic of a sample.

Answer 37

Statistic

Question 38

What are the major properties of a mean? 1. ___ 2. ___ 3. ___ 4. ___

Answer 38

1. The data must be measured at the interval or ratio level 2. All the values are included in computing the mean 3. The mean is unique 4. The sum of the deviations of each value from the mean is zero

Question 39

The ___ is the midpoint of the values after they have been ordered from low to high values; must be at least an ordinal level of measurement

Answer 39

Median

Question 40

What are the major properties of a median? 1. ___ 2. ___

Answer 40

1. It is not affected by extremely large or small values | 2. It can be computed for ordinal-level data or higher

Question 41

The ___ is the value of the observation that appears most frequently; not affected by extreme high or low values.

Answer 41

Mode No MODE if no value appears more than once

Question 42

A mode can be ___ when there are two modes. | I.e., 27 and 31 appear more than once.

Answer 42

Bimodal

Question 43

A ___ occurs when a distribution is non-symmetrical; the relationship among the measures changes.

Answer 43

Skewed distribution

Question 44

The ___ is a convenient way to compute the arithmetic mean when there are several observations of the same value; add all observations and divide by the total number. I.e., 1+2+3+4+5/5

Answer 44

Weighted mean

Question 45

The ___ is useful in finding the average change of percentages, ratios, indexes, or growth rates over time; often find the percentage changes in sales, salaries, or economic figures.

Answer 45

Geometric mean

Question 46

What are the two reasons to study dispersion? 1. ___ 2. ___

Answer 46

1. | 2. To compare the spread in two or more distribution

Question 47

A ___ is the simplest measure of dispersion; the difference between the high and low values in a data set; it does not take into consideration all of the values and is therefore its limitation.

Answer 47

Range

Question 48

___ measures the mean amount by which the values in a population, or sample, vary from their mean.

Answer 48

Variance

Question 49

___ is the mean of the squared difference between each value and the mean; for populations whose values are near the mean, the variance will be small; for populations whose values are dispersed away from the mean, the population variance will be large. Overcome the weakness of the range by using all the values in the population, not just high and low.

Answer 49

Population variance

Question 50

The square root of the population variance is the ___.

Answer 50

Population standard deviation

Question 51

A ___ is used to calculate how varied a sample is by the average of the squared differences from the mean.

Answer 51

Sample variance

Question 52

The ___ is used as an estimator of the population standard deviation and is the square root of the sample variance.

Answer 52

Sample standard deviation

Question 53

___ states that regardless of the shape of the distribution, at least 1 − 1/k2 of the observations will be within k standard deviations of the mean, where k is greater than 1.

Answer 53

Chebyshev’s theorem

Question 54

The ___ states that for a bell-shaped distribution about 68% of the values will be within one standard deviation of the mean, 95% within two, and virtually all within three.

Answer 54

Empirical Rule

Question 55

___ is an estimate of the corresponding actual values; statistical software packages make it easy to calculate these values, even for large data sets.

Answer 55

Standard deviation of grouped data