Data Unit 1 Test

Question 1

Statistics is the process of:

Answer 1

1. Collecting data
2. Organizing data
   3: Interpreting data

Question 2

Data:

Answer 2

Facts or pieces of information. A single fact is called datum.

Question 3

Raw Data:

Answer 3

Unprocessed information (i.e. Not yet compiled in a frequency table, chart or graph).

Question 4

Aggregate Data:

Answer 4

Data that is organized or grouped such as finding the sum over a given period or time, for example, monthly or quarterly. Data can be organized into any grouping such as geographic area. The data is not individual records.

Question 5

Micro Data:

Answer 5

Non-aggregated data about the population sampled. For surveys of individuals, microdata contains records for each individual interviewed; for surveys of organizations, the microdata contains records for each organization.

Question 6

Experimental Data:

Answer 6

Data gathered through experimentation.

Question 7

Observational Data:

Answer 7

Data gathered by observation of the “subject.” For example, the subject is recorded then the behaviours are noted over a period of time.

Question 8

Primary Data:

Answer 8

Data gathered directly by the researcher in the act of conducting research or an experiment. Data can be gathered by surveys or through experimentation.

Question 9

Secondary Data:

Answer 9

Data gathered by someone other than the researcher.

Question 10

Numerical Value:

Answer 10

• A quantitative variable that describes a numerically measured value
• These variables can be either continuous or discrete.

Question 11

Continuous Variable:

Answer 11

• A numeric variable which can assume an infinite number of real values
• i.e. the unit of measure can be broken down into smaller units or decimals.
• Example: age, distance, temperature, and school marks
• A histogram graph displays continuous data

Question 12

Discrete Variable:

Answer 12

• A numeric variable that takes only a finite number of real values
• i.e. can only have separate values, of integers (no decimals)
• Example: number of people, animals, x can equal only 0, 1, 2, 3, etc.
• A Bar graph displays discrete data

Question 13

Categorical Data:

Answer 13

• Consists of data that can be grouped by specific categories (also known as qualitative variables).
• Categorical variables may have categories that are naturally ordered (ordinal variables) or have no natural order (nominal variables).

Question 14

Nominal Variable:

Answer 14

• Type of categorical variable that describes a name, label, or category with no natural order.
• Example: subjects in school, hair colour,
• Alphabetical order is nominal because you can put the names in alphabetical order, but the names have no rank. A is not “better” than B

Question 15

Ordinal Variable:

Answer 15

• Type of categorical variable that has a natural ordering of its possible values, but the distances between the values are undefined.
• Example: Excellent, Good, Fair and Poor to rate something, the answer is only a category but there is a natural ordering in those categories.

Question 16

Frequency Table:

Answer 16

a table which shows the distribution of values of the variable

Question 17

Key Features of a Frequency Table:

Answer 17

3 columns: Range, Tally, Frequency

Question 18

Range column

Answer 18

Make sure the magnitude ofthe all the intervals are the same
Square brackets: includes the value.
Round brackets: up to but not including the value.

Question 19

Cumulative Frequency Table -

Answer 19

the running total of the frequencies from the top down to the corresponding row.
- (add the total frequencies as you go down the columns.)

Question 20

Relative Frequency Table (%)

Answer 20

shows the frequency of a range (data group) as a percentage of the whole data set. (used for pie graph)
- Take each frequency and divide it by the total frequency then multiply by 100

Question 21

Bar Graph:

Answer 21

Bars don’t touch
Each bar is a different colour
Categorical/discrete

Question 22

Frequency =

Answer 22

Histogram

Question 23

Relative frequency =

Answer 23

Pie chart

Question 24

Cumulative Relative Frequency =

Answer 24

Ogive

Question 25

Histogram:

Answer 25

- Coloured in with one colour - This type of graph is best suited to show a continuous range of values; hence, the bars touch - The area of the bars is proportional to the frequencies of the variable. - To determine the interval ranges, take the range of the entire set and divide it by the number of bars that you want. (Range = Highest-Lowest)

Question 26

Frequency Polygon (or Line Graph)

Answer 26

- Can illustrate the same information as a histogram or bar graph. - Points are plotted with the midpoints of the intervals versus the frequency. Then a line is drawn connecting the points. - This type of graph is best suited to illustrate (changing) trends.

Question 27

Cumulative Frequency Polygon (or Ogive)

Answer 27

- Illustrates the running total of the frequency from the lowest value up. - Plot the x-values on the upper end of the range.

Question 28

Circle (Pie) Graph

Answer 28

- Best suited to illustrate categorical data relative to the whole or to each other (using relative frequencies). - Need a protractor to draw the sections accurately (each segment size = relative frequency x 360) --To get the angle multiply the relative frequency by 360

Question 29

Population:

Answer 29

All individuals that belong to a group being studied. e.g. For a survey to find out what sport was the favourite of students of SDSS, all students are asked.

Question 30

Sample:

Answer 30

A group of items or people selected from a population (to represent the whole population). e.g. For a survey to find out what sport was the favourite of students of SDSS, 20 random students from each grade were asked.

Question 31

Simple Random Sample:

Answer 31

Every member of the population has an equal chance of being selected for the survey. Non-biased. - The risk is you could pick too many of the same category. - Roland writes the apartment number of each occupied apartment on a piece of paper. He puts them in a hat and randomly selects 15 of them.

Question 32

Systematic Sample:

Answer 32

- Sort the population sequentially. - The intervals are determined by the following formula: Interval = population size/sample size - A starting point is selected at random. - Go through the population sequentially, selecting members at regular intervals. - Roland will sort the apartment numbers from lowest to highest. Interval = 54/15 = 4. He picks a random number between 1 & 4. He starts at the apartment in this position and jumps every 4 for the next apartments.

Question 33

Stratified Sample:

Answer 33

- A strata is a group of people that share a common characteristic such as gender, age, education level. (natural grouping) - A stratified sample contains the same proportion of members from each stratum as the population does. - The proportion of each stratum taken is the proportion of the sample size to the population size. - Roland uses the floors on which her tenants live on as strata. - If the sample is 15, proportion = 15/54 = 0.278. So, Roland would multiply 0.278 by how many people live on each floor.

Question 34

Cluster Sample:

Answer 34

- Use a random sample of one representative group (all from one strata) - Clusters are not necessarily representative of the population. - Roland would select 15 of the 18 apartments on the 5th floor (since the 5th floor is the only group that’s large enough for a cluster).

Question 35

Multi-Stage Sample:

Answer 35

- Several levels of random sampling. - Roland randomly selects 3 floors and then randomly selects 5 tenants from each floor.

Question 36

Convenience Sample:

Answer 36

- Easily accessible members are selected. - May not be random, so results are not always reliable. - Roland talks to the next 15 tenants who come through the door.

Question 37

Voluntary Response Sample:

Answer 37

- Invite members of the entire population to participate in the survey. - Respondents are not necessarily representative of the population. - Roland sends out a letter to all the tenants seeking a response.

Question 38

Bias:

Answer 38

An inclination or prejudice for or against one person or group, especially in a way considered to be unfair. In terms of sample selection, bias would be present where there are factors that favour certain outcomes or responses. Bias can be intentional or unintentional.

Question 39

Sampling Bias:

Answer 39

When the chosen sample does not reflect the population. The bias is in direct reference to the sample itself. Example: Ask “What is Canada’s favourite sport?” outside the ACC after a Leafs’ game. To avoid this, the sample must include a variety of respondents

Question 40

Non-Response Bias (a form of sampling bias):

Answer 40

When surveys are not returned, thereby influencing the result. Particular groups are then under-represented. - It may also be that insufficient time was given to respond and/or not enough information was given to the respondents to respond to. - It is a significant bias if the number of non-respondents is greater than the difference between two other responses. Example: Conduct a survey about snowmobiling at a school in Florida. - To avoid this, researchers must choose a sampling process that is random and provide enough time and information so that respondents are able to make an informed decision.

Question 41

Measurement Bias:

Answer 41

When there is a bias with the survey question and/or the method of data collection. - The person collecting the data has biased the results of the survey. Example: A police officer records how fast cars are travelling down a stretch of highway. - Use of leading questions -> Surveys give suggested answers to a question Example: What is your favourite candy: a) smarties b) Aero c) Kit Kat d) Coffee Crisp - Use of loaded questions -> Surveys which use words or information intended to influence a respondent's decision. Example: Are you in favour of the government controlling a woman’s freedom to choose whether or not to have an abortion?

Question 42

Response Bias:

Answer 42

When respondents give false or misleading answers because they want to influence the results or are afraid/embarrassed to answer truthfully. - Always in response to a question posed. Example: Have you ever accidentally taken something home from work that you didn’t pay for?

Question 43

‘E” means

Answer 43

‘sum’ “Sigma”

Question 44

Mean:

Answer 44

most commonly referred to as “the average”

Question 45

Mean Usage:

Answer 45

with numeric data having no outlines and/or a large sample size.

Question 46

Mean of a population:

Answer 46

µ “mu” - add up all the numbers and divide by the total of numbers

Question 47

Mean of a sample:

Answer 47

x̄ “x bar” - add up all the numbers and divide by the total of numbers

Question 48

Median:

Answer 48

the middle value

Question 49

Median Usage:

Answer 49

with numeric data where outliers exist or the sample size is small.

Question 50

How to find Median:

Answer 50

- After arranging the data in ascending order, then -- If there are odd number of datum, then use the middle value -- If there are even number of datum, then find the middle 2 values and find the midpoint

Question 51

Mode:

Answer 51

the value that occurs the most frequently

Question 52

Mode Usage:

Answer 52

With categorical data

Question 53

Wi is the

Answer 53

weighting factor

Question 54

Class sizes could be a ?, they would appear at the ? of the formula being multiplied by the ?, and at the ?.

Answer 54

weighting factor top marks bottom

Question 55

Mi is the ? of an interval

Answer 55

midpoint

Question 56

Fi is the ? for that interval

Answer 56

frequency

Question 57

Steps for frequency mean: 1. Find the ? of the intervals 2. ? the ? of the intervals by the ? in that interval 3. Get the total ? 4. Get the total frequency ? 5. ? the total frequency mean by the total frequency

Answer 57

1. midpoint 2. Multiple, midpoint, frequency 3. Frequency 4. Midpoint 5. Divide

Question 58

To determine the frequency median, you have to go to the interval where the ? occurs. If we have 18 data values, the median is the ? of the 9th and 10th values. So ? up the frequencies until they are 9 or 10. Since they point occurs in the 2-3 hours interval, the median is the ? of that interval - ? hours a day.

Answer 58

middle value mean add midpoint 2.5

Question 59

Range:

Answer 59

The difference between the highest value and the lowest value.

Question 60

Interquartile Range:

Answer 60

Found by putting the data in ascending order and then breaking it into four groups. The IQR is the distance between the extreme groups (1st and 3rd quartiles).

Question 61

Steps for IQR:

Answer 61

1. Put data in ascending order 2. Find the median and call it Q2 3. Find the median of the first group and call it Q1 4. Find the median of the second group and call it Q3 5. The interquartile range is Q3 - Q1 6. The IQR is where 50% of the data is clustered relative to the median.

Question 62

Box & Whisker Plot:

Answer 62

Illustrates how clustered the data is around the median.

Question 63

Steps for Box & Whisker Plot:

Answer 63

1. Draw a horizontal line and write down the lowest and highest values, labelling equal intervals (like a ruler) between them to represent the range. 2. Draw another horizontal line and mark off the start and end of the data with small vertical lines 3. Represent Q1 Q2 & Q3 with big vertical lines at the appropriate locations in the range 4. Draw a box from Q1 to Q3 5. Note: If a data value is 1.5 times the box length (ie. IQR) from the box, it is considered an outlier.

Question 64

Deviation:

Answer 64

The difference between an individual value in a set of data and the mean for the data.

Question 65

Deviation Formulas:

Answer 65

Population x - µ Sample x - x̄

Question 66

Standard Deviation:

Answer 66

The square root of the mean of the squares of the deviation

Question 67

Standard Deviation Formulas:

Answer 67

Population: σ (lower case sigma) = √Σ(x - µ)^2/N Sample: s = √Σ(x - x̄)^2/n - 1

Question 68

In a population formula, ? a is used, the ? symbol is used, and it is divided by the ?

Answer 68

lower case sigma mu number of terms

Question 69

In a sample formula, ? is used, the ? symbol is used, and it is divided by the ?.

Answer 69

s x bar number of terms minus one.

Question 70

*The sample formula denominator is

Answer 70

n — 1 in order to compensate for the fact that a sample taken from a population tends to underestimate the deviations in the population.

Question 71

Variance:

Answer 71

The standard deviation squared σ^2 or s^2

Question 72

To find the Standard Deviation:

Answer 72

1. Add all the data up 2. Count the number of data points 3. Divide the data by the amount of data points to get the mean 4. Take every data point and minus the mean (x - mean) 5. Take every new number from the subtraction and square it 6. Add all of the squared numbers 7. Divide the total by the number of data points or if sample the number of data points minus 1 8. SQUARE ROOT THAT NUMBER

Question 73

Z-Scores:

Answer 73

- The z-score is the number of standard deviations from the mean - Variable values below the mean (left) have negative z-scores, values above(right) the mean have positive z-scores, and values equal to the mean have a zero z-score.

Question 74

Z-Score Formulas:

Answer 74

Population: z = x - µ/σ Sample: z = x - x̄/s

Question 75

Percentiles:

Answer 75

- Divides the data into 100 intervals with the same number of values in each interval. - As with quartiles, when dividing the data up, the actual value of each data is unimportant but rather the physical count of all of the individual datum is required. - First, order the data.

Question 76

To find the percentile with a mark, the formula is:

Answer 76

Percentile = # of marks below value given + (0.5 x # of marks equal to value given)/ Total # of marks all times 100

Question 77

To find the mark from percentile:

Answer 77

- Count each line in between the data (from 10 to 90) the mark will be the mean of the two marks in between the line - OR do N (mark) = K (number of marks) x percentile (e.g 0.9 for 90)