Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Stat 1150 > Unit 1 > Flashcards

Unit 1 Flashcards

1
Q

What is Statistics?

A

A branch of science which deals with collecting, organizing, analyzing, interpreting, summarizing and presenting data. (Understanding the world when we have limited information)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is a Unit/Individual?

A

An object on which we take a measurement or observation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is a population?

A

The collection of all individuals or units under consideration

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is a sample?

A

A subset of the population from which we obtain data

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Ho do statisticians commonly get lists of adults living in specific areas?

A

Voter registration

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is the point of statistics?

A

It is impractical to observe every value of our population, so we rely on sample data to make a representation of the population

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is a variable?

A

Any characteristic or property of an individual

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is Quantitative Data?

A

Takes numerical characteristics of an individual for which arithmetic operations make sense.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is Categorical Data?

A

Puts individuals into groups based on common characteristics for which numerical operations do not make sense

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is Categorical and Ordinal Data?

A

Categorical data for which there’s a logical, commonly accepted ordering with a sense of increasingness

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is Categorical and Nominal Data?

A

Categorical data for which there is no logical ordering of increasingness

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is a Distribution?

A

The distribution of a variable tells us what values a variable takes on and how often it takes these values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is a frequency distribution?

A

A count of how many of our data values fall into predetermined classes of intervals

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is Relative Frequency?

A

Aka. a proportion: the number of data values in a class divided by the total number of data values in the sample

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What are continuous random variables?

A

Quantitative variables that can take on any value within a given range.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What are discrete random variables?

A

Quantitative variables that can take on a countable number of values.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is a bar chart?

A

Used to represent the frequency distribution of categorical and nominal data.
- x axis displays the variable values
- y axis displays the frequencies
- bars are separated so as to not suggest continuity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is a histogram?

A

Used to represent the frequency distribution of quantitative data.
- x axis has equal length intervals showing the class boundaries
- y axis shows the frequencies or relative frequencies
- surface area of the bars are in ratio with relative proportions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is the location of the data?

A

Tells us where the centre of our data is located. (mean, median and mode)

20
Q

What is mean?

A

What people commonly call the average. It is the sum of the observations divided by the number of observations (x bar)

21
Q

What are properties of the mean?

A
  • the mean is highly affected by outliers
  • if we multiply each observation by a fixed quantity c then the mean is also multiplied by c
  • if we add a fixed quantity c to each observation, the mean is increased/decreased by c
22
Q

What is the median?

A

The middle value in an ordered data set. Half of the values are larger than the median and half of the values are smaller than the median

23
Q

What is the mode?

A

The most frequently observed value

24
Q

What is a symmetric distribution?

A

If the values to the left and right of centre are mirror images of each other

25
Q

What is a right-skewed distribution?

A

if the right tail extends out much longer than the left side

26
Q

What is a left-skewed distribution?

A

if the left tail extends out much longer than the right side

27
Q

What is the behaviour of the mean, median and mode in different distributions?

A
  • perfectly symmetric: mean = median = mode
  • right-skewed: the mean will be to the right of the median
  • left skewed: the mean will be to the left of the median
28
Q

What is the variability of data?

A

how “spread out” our observations are (range, quartiles, interquartile range, variance/standard deviation)

29
Q

What is the range?

A

the distance between the smallest and largest data value (heavily influenced by outliers)

30
Q

What are quartiles?

A

A measurement of spread that divide our data set into 4 equal parts (25% of observations <= Q1, 50% of observations <= 50%, 75% of observations <= Q3)

31
Q

What is the five number summary?

A

min, Q1, Q2, Q3, max

32
Q

What is the IQR?

A

Inter-Quartile Range: Q3-Q1: measures the spread of only the middle 50% of all observations (not affected by outliers)

33
Q

What is variance?

A

Loosely speaking, the “average” squared distance of the data from its mean.

34
Q

What is standard deviation?

A

The positive root of the variance: roughly the average absolute distance from the mean

35
Q

What are the properties of the variance?

A
  • reported in units squared
  • If we multiply each observation by a fixed quantity c, the variance is multiplied by c squared
  • if the add a fixed quantity to each observation, then the variance does not change
  • sensitive to outliers
36
Q

What are the properties of standard deviation?

A
  • reported in units
  • if we multiply each observation by a fixed quantity c, the standard deviation is multiplied by c
  • if we add a fixed quantity to each observation, then the standard deviation does not change
  • sensitive to outliers
37
Q

If our data is reasonably symmetric with no outliers, which method should we use to report a numerical summary of our data?

A

the sample mean and sample standard deviation

38
Q

If our data is skewed or has outliers, which method should we use to report a numerical summary of our data?

A

the five-number summary

39
Q

What is a box plot?

A

A technique to visually describe the behaviour of our observations in the middle and ends of our data set using the five-number summary

40
Q

What are the features to the box plot?

A
  • a centre line at the median
  • two lines around the median at Q1 and Q3 which form a box
  • a line which extends form the left side of the box to the minimum (whisker)
  • a line which extends from the right side of our box to the maximum
41
Q

What do the tails of a box plot tell us about the shape of the distribution?

A
  • if both tails are relatively equal, we have a symmetric distribution
  • if the right tail is longer than the left, we have a right-skewed distribution
  • if the left tail is longer than the right, we have a left-skewed distribution
42
Q

What is the modified (outlier) box plot?

A

a box plot where the whiskers extend to the most extreme values within the lower fence and the upper fence (outliers appear as points on the axis)

43
Q

What are the lower fence and upper fence?

A

The outlier cutoff points.
LF = Q1 - 1.5(IQR)
UF = Q3 + 1.5(IQR)

44
Q

What is an outlier?

A

Any point greater than the upper fence or less than the lower fene

45
Q

How does the sample size affect the sample distribution in comparison to the population distribution?

A

Larger sample sizes will make the distribution more similar to the original. Smaller sample sizes will appear more random

Stat 1150 (7 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions