Chapter 2: Descriptive Stats

Pie chart

a circular graphic that is divided into sectors each showing relative proportions of a given piece of data. Used for visualization purposes.

Frequency table

Shows discrete data values, or scores, together with the frequency of each score. Often the percentage of the total frequency of each score is displayed in a separate column; show spread/dispersion of the data.

When to use n - 1 for standard deviation and variance...

When all the scores in a population is not known I.E. YOU ARE USING A SAMPLE

Standard deviation

the positive square root of the variance.

Relative frequency

the proportion of the total scores in the data set that are included in a particular class; can be expressed as a percentage of the total scores.

Sum of Squares

the sum of squared deviations = sum of (x - mu)^2 Short cut! [sum of (x^2)]-[(sum of x)^2)]/n

12, 72, 26, 77, 38, 34, 55, 67, 64, 51, 43, 48, 69, 77, 73, 44, 32, 8, 36, 78, 74, 33, 77, 72, 32 The cumulative frequency of the last class is ____.

25.0

Midpoint =

(lower class limit) + (upper class limit) / 2

mu =

(sum of scores or values in population)/N

X (bar) =

(sum of scores or values in sample)/n

If the standard deviation of some data is 0.6, what is the variance?

0.36

You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 Calculate the SUM OF SQUARES of the data set.

11239.7334

You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 Calculate the sample STANDARD DEVIATION of the data set. Use the formula for SAMPLES, not the POPULATION

28.3

Six students from a statistics class reported the number of hours of television they watch per week. Here are their data: 8, 10, 5, 14, 3, 6. What is the standard deviation of the number of hours of television watched per week for this SAMPLE of six students?

3.9

12, 72, 26, 77, 38, 34, 55, 67, 64, 51, 43, 48, 69, 77, 73, 44, 32, 8, 36, 78, 74, 33, 77, 72, 32 The relative frequency of the second class (10-19) is ______%.

4%

12, 72, 26, 77, 38, 34, 55, 67, 64, 51, 43, 48, 69, 77, 73, 44, 32, 8, 36, 78, 74, 33, 77, 72, 32 In the grouped frequency table of placement test scores shown above, the midpoint of the lowest class is ____________.

4.5

34, 68, 54, 48, 46, 55, 74, 42, 62, 66, 71, 39, 44, 54, 58, 47 Find mean

53.9

34, 68, 54, 48, 46, 55, 74, 42, 62, 66, 71, 39, 44, 54, 58, 47 Find median

54

34, 68, 54, 48, 46, 55, 74, 42, 62, 66, 71, 39, 44, 54, 58, 47 Find mode

54

Use the following data set to answer the question: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 Calculate the MEAN of the data set.

64.1

Use the following data set to answer the question: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 Calculate the MEDIAN of the data set.

73

Use the following data set to answer the question: 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 What is the MODE of the data set?

79

You previously found the mean of this data set. Use that in answering the question. 63, 89, 92, 73, 79, 72, 34, 36, 94, 21, 25, 93, 22, 90, 79 Calculate the Sample VARIANCE of the data set. Use the formula for SAMPLES, not the POPULATION

802.8381

The bars representing data touch each other in a ______. A Histogram B Bar chart C Polygon graph D Frequency table

A Histogram

How do histograms differ from bar graphs? A Histograms are used to depict frequencies of continuous data, but bar graphs are used to depict categorical data. B Histograms are used to depict categorical data, but bar graphs are used to depict frequencies of continuous data. C Histograms are used to depict means, but bar graphs are used to depict frequencies. D Histogram is just another word for bar graph—the two graphs do not differ.

A Histograms are used to depict frequencies of continuous data, but bar graphs are used to depict categorical data.

Mean

A MEASURE OF CENTRAL TENDENCY; symbol is mu or an x-bar!; it is the average. MOST SENSITIVE TO OUTLIERS

Median

A MEASURE OF CENTRAL TENDENCY; the midpoint score; if all scores are arranged in a numerical order you and you have an odd number of scores, you can simply cross out one score from each end until only one is left and that is the ___________, if you have even number of scores, then the average of the two central most scores is the __________.

Mode

A MEASURE OF CENTRAL TENDENCY; the score that occurs the most often

Statistic

A measure of a sample characteristic.

A positive skew means that a distribution has a tail with extreme scores \text{__________ } the center of the distribution. A Around B Below C Above D On either side of

C Above

A grouped frequency table is most useful when which of the following is true? A Scores in the data set vary over a small range of discrete values B Data are ordinal C Data vary over a large range of continuous values D Data are nominal

C. Data vary over a large range of continuous values

Frequency polygon

Can be used to display the same information as a table, but provides a different visual take on the data. A line graph that emphasizes the continuous change in frequencies, thus making it easy to see the "shape" of the distribution and to compare different distributions of data.

What do your answers to the previous three questions tell you about the distribution? A Nothing much B It is positively skewed C It is multimodal and negatively skewed D It is unimodal and negatively skewed

D It is unimodal and negatively skewed

B. Yes, it has a negative skew

Does this distribution show skew? A No, it is more or less evenly distributed. B Yes, it has negative skew. C No, it is unimodal. D Yes, it is positively skewed.

Parameter

Measure of a population characteristic; mu = mean; sigma = standard deviation sigma^2 = variance; rho = ?

Polymodal

NOT a GD word, sis!

Deviation

The distance of a score x from the mean of the distribution it is included in.

C. 77

The modal score is approximately _____. A 74 B 70 C 77 D 80

B. Histogram

This chart is an example of a _______. A Category chart B Histogram C Summary chart D Bar chart

Variance

average of the squared deviations from the mean; aka average "Sum of Squares"

Relative frequency =

class frequency/sample size = f/n

Numbers that describe populations are called \text{__________ }.

parameters

Cumulative frequency

equal to the sum of the frequency of that class and all classes before that in the distribution. The last class has a _______ equal to the total sample size.

Outliers

extreme scores

Skewed distribution

has many more scores on one side of a graph of the distribution than on the other side. Indication of the skewness of the data set. Frequently a result of having outliers in the data.

Multimodal

having multiple, approximately equal peaks; bimodal distributions can also be considered this.

unimodal

having one mode, having one score that appears at a higher frequency, a single peak, all other score have relatively lower frequency(?).

Bimodal

having two equal or approximately equally high score frequencies; NOTE: peaks should be very nearly equal

Variability

in a set of numbers, how widely dispersed the values are from each other and from the mean

The most frequently occurring score in a distribution is the \text{__________ }.

mode

Quantiles

numbers that can be used to divide an ordered data set into equal parts. For example, quartiles which divide the data into four equal parts, 25%, 50%, 75%, 100%.

Numbers that describe samples are called \text{__________ }.

statistics

Variance

sum of squared deviations /population; x = score; mu = mean; N = number of scores; sigma^2 = variance *hint*

sample variance

sum of squares / n - 1

A bimodal distribution has \text{__________ } modes.

two

Bar chart

used to show frequencies of categorical data; there are spaces between the bars.

Histogram

used to show frequencies of numerical data in contiguous categories; bars touch.

Grouped frequency table

useful when the number of scores is so large that displaying them incrementally would make the table too large to be useful as a summary; classes are placed into bins with specific increments/intervals.