Descriptive Statistics- Graphs

Question 1

What do descriptive statistics present?

Answer 1

An overview of collected information (data)

Question 2

What do descriptive statistics make coherent & easily digestible?

Answer 2

Large sets of information

Question 3

What do descriptive statistics avoid?

Answer 3

Distorting the data

Question 4

What do descriptive statistics suggest?

Answer 4

The appropriate inferential test to use.

Question 5

How many parts are involved in the presentation of descriptive statistics?

Answer 5

3

Question 6

What are the 3 parts involved in the presentation of descriptive statistics?

Answer 6

Graphical presentation (figures), numbers (often in table format), & verbal description (written in a report).

Question 7

What do descriptive statistics provide?

Answer 7

An integrated, coherent & concise summary of data that can be related back to any question being asked.

Question 8

What do we aim to do with collected data?

Answer 8

Get a visual summary of it (by transferring numbers into a graphical presentation).

Question 9

How many levels of measurement are there?

Answer 9

4

Question 10

What levels of measurement are there?

Answer 10

Nominal (measuring name-based data), ordinal (measuring order-based data), interval (measuring numerical data with no real zero point), & ratio (measuring numerical data with a true zero point) levels.

Question 11

What are examples of nominal data?

Answer 11

Eye colours, car models, & favourite colours.

Question 12

What are examples of ordinal data?

Answer 12

Rankings & rating scales

Question 13

What are examples of interval data?

Answer 13

Times of the day & temperatures.

Question 14

What are examples of ratio data?

Answer 14

Heights, weights, reaction times, & exam scores.

Question 15

Which mathematical notation can be applied to nominal data?

Answer 15

”=” & “≠”

Question 16

Which mathematical notation can be applied to ordinal data?

Answer 16

”=”, “≠”, “>”, & “<”

Question 17

Which mathematical notation can be applied to interval data?

Answer 17

”=”, “≠”, “>”, “<”, “+”, & “-“

Question 18

Which mathematical notation can be applied to ratio data?

Answer 18

”=”, “≠”, “>”, “<”, “+”, “-“, “x”, & “÷”

Question 19

In which order does each level of measurement increase in complexity & informativity?

Answer 19

Nominal data, then ordinal data, then interval data, then ratio data.

Question 20

What limits the choice of statistical test that can be applied to data?

Answer 20

The mathematical notation that can be applied to each data’s level of measurement.

Question 21

Which levels of measurement are discrete?

Answer 21

Nominal & ordinal levels.

Question 22

Which levels of measurement are continuous?

Answer 22

Interval & ratio levels.

Question 23

What is the aim of displaying the frequencies from categorical data?

Answer 23

To display it in the simplest way that conveys all the relevant bits of information.

Question 24

What do we present if we want to create a visual summary (or plot) of nominal data?

Answer 24

A bar chart of frequencies.

Question 25

When visually summarising nominal data, how do we indicate that we do not have a continuous scale on the x-axis?

Answer 25

By placing spaces in between each bar.

Question 26

If you show 10 people a face & ask them to judge the age of the face shown, how many responses will you get?

Answer 26

10 (N = 10)

Question 27

If you show 10 people a face & ask them to judge the age of the face shown, what responses might you get?

Answer 27

52, 49, 52, 61, 57, 57, 56, 54, 55, & 59

Question 28

What does N = 50 mean?

Answer 28

You have 50 scores.

Question 29

What must we do to make sense of continuous (interval & ratio) data?

Answer 29

Organise it

Question 30

Once our data has been divided into (meaningful) intervals, what do we graph to assess frequency distribution?

Answer 30

The number of items in each interval.

Question 31

How can we divide data into intervals?

Answer 31

By determining the smallest & largest score in our data set, & counting how many times these scores and every score in between are present.

Question 32

What does a frequency table look like?

Answer 32

It has the dependent variable (e.g. "Score") and the independent variable (e.g. "Frequency") in separate cells at the top of the table, then 2 rows of numbers underneath each of these headings.

Question 33

What does a frequency histogram look like?

Answer 33

It has the independent variable (e.g. "Age Scores") on the x-axis, and the dependent variable (e.g. "Frequency") on the y-axis, with bars representing each independent variable in the middle.

Question 34

How do you group data in order to create a frequency histogram?

Answer 34

By locating your minimum & maximum values (e.g. a minimum score of 57 & a maximum score of 96), & identifying how many intermediate values you have (e.g. 40).

Question 35

How do you create a frequency histogram?

Answer 35

By using a frequency table.

Question 36

What is an example of data that could be grouped & transformed into a frequency histogram?

Answer 36

The frequency of scores (in percentages) on a statistics test.

Question 37

If you have scattered & sparse data that have not been grouped, what will its frequency histogram look like?

Answer 37

It will have the independent variable (e.g. "Score) along the x-axis, and the dependent variable (e.g. "Frequency Count") along the y-axis, with clusters of bars of varying lengths in the middle.

Question 38

What is an example of a range of scores & their frequencies that could be grouped together in a frequency histogram?

Answer 38

Scores of 57, 58, 59, & 60, with frequencies of 1, 2, 1, & 0.

Question 39

How would you represent scores of 61, 62, 63, and 64 with frequencies of 1, 1, 0, & 0, in a frequency table for use in a frequency histogram?

Answer 39

Under the heading "Scores", you would put "61-64", and under the heading "Frequency", you would put "2".

Question 40

What does a histogram of grouped data look like?

Answer 40

It has the independent variable (e.g. "Score") on the x-axis, & the dependent variable (e.g. "Frequency Count") on the y-axis, with several bars all joined together in the centre.

Question 41

What is the advantage of presenting grouped data in a histogram?

Answer 41

It means that the data has not been changed, but that the shape of the histogram is clear.

Question 42

What tells you the number of times an individual score appears (along the y-axis) in a histogram?

Answer 42

The height of each bar

Question 43

What tells you what each score is (along the x-axis) in a histogram?

Answer 43

The position of each bar.

Question 44

What are we interested in when creating a histogram?

Answer 44

The range of our values.

Question 45

What do the tails of a histogram look like?

Answer 45

They are short assorted purple bars, either side of a bump in the middle.

Question 46

What does the centre of a histogram look like?

Answer 46

An array of thin bars of different heights.

Question 47

What are some possible differences that could be present between 2 histograms?

Answer 47

Their shapes (they could have 1 or 2 centres), their location on the graphs, & the colour of their bars.

Question 48

What does a histogram with a negative skew look like?

Answer 48

It has 1 centre (towards the right) & 1 tail (towards the left), each located in the middle of the graph.

Question 49

What does a histogram with a positive skew look like?

Answer 49

It has 1 centre (towards the left) & 1 tail (towards the right), each located in the middle of the graph.