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Foundations in statistics STA10003 > Week 2 > Flashcards

Week 2 Flashcards

1
Q

What is a frequency distribution?

A

A table or graph that shows the frequency of different variable values or class intervals within a sample/population.

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2
Q

What does f denote in frequency tables?

A

It denotes the frequency of each variable value or class interval in a sample or population.

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3
Q

What are proportions in statistics?

A

A number that indicates the portion of the sample or population that possesses a certain attribute, characteristic, variable value or class interval.

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4
Q

How do you calculate proportion and what symbol is used to denote proportion?

A

A lower case p is used to denote proportion and it is calculated with the equation p = f/N

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5
Q

What equation do you use to express a proportion as a percentage?

A

Percentage = f/N*100

Frequency divided by total amount (population or sample) times 100.

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6
Q

What are ungrouped frequency tables?

A

Frequency tables in which all variable values are distinct.

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7
Q

What are grouped frequency tables?

A

Grouped frequency tables group variable values into classes with consistent intervals such as 1-9, 10-19, 20-29 etc.
The bottom score should be a multiple of the interval width chosen.

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8
Q

What graphs or tables can you use for frequency distribution?

A

Histogram graphs, polygon graphs, bar graphs, pie chart, stem and leaf plots, boxplots and smooth curves.

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9
Q

What are histogram graphs?

A

A graph where bars are centred above variable values or class intervals, the height of the bar corresponds to the frequency while the width of the bar extends to the real limits. (Good for metric data)

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10
Q

What are polygon graphs?

A

A graph where a dot is centred above each score with the height corresponding to the frequency of the score.
Continuous lines are drawn from dot to dot, the graph in completed by drawing a line down to the X-axis at each end of the range of scores.

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11
Q

What are bar graphs?

A

Similar to a histogram with the exception of using categorical data as apposed to metric data, spacing is left between adjacent bars indicating that each category is distinct OR the categories are not the same size.

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12
Q

What are pie charts?

A

Graphs that are used to represent categorical data, where each section of the circle (pie) represents the percentage value of each category.
(Often become difficult to read with multiple categories)

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13
Q

What are population distribution graphs?

A

Graphs that are capable of representing the proportion of variable values or class intervals across an entire population.

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14
Q

What are smooth curves?

A

Smooth curves are a used to show population distributions in cases where the data is metric.
(Histogram and polygon graphs are used for this too however)

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15
Q

What are features or characteristics of distributions?

A

Central tendency (averages), variability, shape, extreme scores (known as outliers).

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16
Q

What are the basic shapes of distributions?

A

Symmetrical, in which the left and right side of the graph are (roughly) mirrored.
Skewed, in which scores are highest on one end of the distribution.
The tapered ends of the distributions are called the “tail of the distribution”.

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17
Q

Explain negative skew and positive skew.

A

Negative skew is where the tail of the distribution tapers at the left (lower scores), positive skew is where the tail of distribution tapers at the right (higher scores).

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18
Q

What is a percentile rank?

A

A score that indicates the percentage of a sample or population with scores at or below a particular value.
(An IQ score of 100 has a percentile rank of 50%)

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19
Q

What is a percentile?

A

When a score is defined by it’s percentile rank, it is referred to as a percentile.
(An IQ score of 100 is in the 50th percentile)

20
Q

What are some useful or common percentiles?

A 
Median, which indicates the 50th percentile. 
First quartile (Q1), which indicates the 25th percentile. 
Third quartile (Q3), which in indicates the 75th percentile.
21
Q

What are boxplots?

A

Boxplots are graphs used to show data the minimum, Q1, median, Q3 and maximum ranges.

22
Q

What are cumulative frequency distributions?

A

The cumulative frequency of individuals at or below a variable value or class interval.
This can be expressed as a cumulative number.
OR
This can be expressed as a cumulative percentage.

23
Q

The cumulative percentage or frequency, is the upper real limit of the score: true or false?

A

True.

24
Q

What is a stem and leaf plot?

A

A table that organises large amounts numerical data into stems, the tens place of the number and the leaf, the ones place of the number.

25
Q

What equation can find the range or number of rows that would be needed to complete a ungrouped frequency distribution table? This equation can also be used to determine the width of interval classes.

A

Equal to the highest value minus the lowest value plus one.

Highest value - Lowest value + 1

26
Q

For a complete frequency distribution table, what is ∑f/N?

A

1, because the accumulative proportions would equal 1.

27
Q

What is central tendency?

A

A statistical measure that defines the centre of a distribution.

28
Q

What are the three different measures of central tendency?

A
  1. Mean
  2. Median
  3. Mode
29
Q

What does the symbol M represent?

A

The sample mean.

30
Q

What does the symbol μ represent?

A

The population mean.

31
Q

What is the mean?

A

The mean for a distribution is the sum of the scores divided by the number of scores.
You can think of the mean as the sum of the scores equally distributed among all individuals in the distribution OR as a balance point for all scores.

32
Q

What equation would you use to calculate the population mean?

A

μ = ∑X/N

33
Q

What equation would you use to calculate the sample mean?

A

M = ∑X/n

34
Q

What is the median?

A

If all scores are ordered from smallest to largest the median will be the score at the midpoint, with 50% of the scores either side of the median.

35
Q

How do you find the median?

A

For odd numbers, list all scores in order by value, the median will be the middle score in the list.
For even numbers, list all scores in order by value, the median will be the number between the two middle scores.

36
Q

What is the mode?

A

The score in the distribution with the highest frequency, unlike the mean and median it is possible to have more than one mode (bimodal or multimodal).

37
Q

When is it appropriate to use the mean?

A

With continuous data, numerical data and symmetrical/normally distributed data.

38
Q

When is it appropriate to use the mode?

A

It is the only measure of central tendency that is appropriate for nominal data and can sometimes be useful for ordinal data.
Can also be used to describe shape.

39
Q

When is it appropriate to use the median?

A

With skewed distributions or ordinal data.

40
Q

What order, from smallest to largest are you likely to see each measure of central tendency on a positively skewed distribution?

A

Mode, median and mean.

41
Q

What order, from smallest to largest are you likely to see each measure of central tendency on a negatively skewed distribution?

A

Mean, median and mode.

42
Q

What is the weighted mean?

A

Used to find the mean of two combined sets of scores, with one set contributing more “weight” to the combined mean.

43
Q

What is the equation used to find the weighted mean?

A

W = ∑X₁ + ∑X₂ / n₁ + n₂

44
Q

What is the major mode?

A

The higher peak in a bimodal or multimodal distribution.

45
Q

What is the minor mode?

A

The lower peak in a bimodal or multimodal distribution?

Foundations in statistics STA10003 (12 decks)

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