unit 1.2 – descriptive statistics standard deviationdegrees of freedomvariance68-95-99.7 rule data...
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Unit 1.2 – Descriptive Statistics
Standard Deviation Degrees of Freedom Variance 68-95-99.7 Rule
Data Types Individuals Categorical Quantitative
Graphing Categorical Variables Bar Graphs Pie Charts
Graphing Quantitative Variables Dot Plots Stem Plots Histograms
Unit 1.2 – Descriptive Statistics
Part 1
Standard Deviation
Degrees of Freedom
Variance
68-95-99.7 Rule
Unit 1 – Descriptive Statistics
Our data set on temperature readings has been modified using a transformation and is shown below:
The most commonly used measure of spread in AP Statistics is standard deviation. Find both the variance and standard deviation for the data set above. Make sure you understand the relationship between variance and standard deviation.
The degrees of freedom is simply n – 1 where n is the sample size. We will use n and n – 1 very often throughout the year.
70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Unit 1 – Descriptive Statistics
Understanding the 68-95-99.7 Rule
70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Often times we will talk about a data point or observation with respect to the mean and standard deviation.
Ex 1. Mean = 82.5Standard Deviation = 9.577
Unit 1 – Descriptive Statistics70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Ex 1. Mean = 82.5Standard Deviation = 9.577
There is a major assumption being made when using the 68-95 Rule and that is that the data is normally distributed.
We will talk more about this idea in Unit 1.3 but for now, know that this means the distribution is spread about the mean proportionally to it’s standard deviation. In otherwords N(x,s)
82.563.346
101.654
111.231
72.923
92.077
53.769
Unit 1 – Descriptive Statistics70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Ex 1. Mean = 82.5Standard Deviation = 9.577
Checking for Understanding…
82.563.346
101.654
111.231
72.923
92.077
53.769
1. What percent of days can we expect to have a temperature lower than 53.769˚ F?
2. What percent of days can we expect to have a temperature lower than 72.923˚ F?
3. What percent of days can we expect to have a temperature lower than 82.5˚ F?
4. What percent of days can we expect to have a temperature lower than 101.654˚ F?
Unit 1 – Descriptive Statistics70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Ex 1. Mean = 82.5Standard Deviation = 9.577
Checking for Understanding… continued…
82.563.346
101.654
111.231
72.923
92.077
53.769
1. What percent of days can we expect to have a temperature higher than 63.346˚ F?
2. What percent of days can we expect to have a temperature higher than 72.923˚ F?
3. What percent of days can we expect to have a temperature higher than 82.5˚ F?
4. What percent of days can we expect to have a temperature higher than 92.077˚ F?
Unit 1 – Descriptive Statistics70.2 77.4 74.7 90.9 104.4
81.9 85.5 86.4 86.4 75.6
74.7 68.4 94.5 84.6 81.9
Ex 1. Mean = 82.5Standard Deviation = 9.577
Checking for Understanding… continued…
82.563.346
101.654
111.231
72.923
92.077
53.769
1. What percent of days can we expect to have a temperature between 72.923˚ F and 92.077˚ F ?
2. What percent of days can we expect to have a temperature between 53.769˚ F and 111.231˚ F ?
3. What percent of days can we expect to have a temperature between 63.346˚ F and 92.077˚ F ?
4. What percent of days can we expect to have a temperature between 92.077˚ F and 111.231˚ F ?
Unit 1.2 – Descriptive Statistics
Part 2
Data Types
Individuals
Categorical
Quantitative
Unit 1.2 – Descriptive Statistics
Our next task was to gather more detailed data over a one week period. Our data is shown below:
Day Low High Humidity Precipitation
Air Quality
Monday 63 78 45% Light Good
Tuesday 66 88 13% No Fair
Wednesday 58 90 10% No Poor
Thursday 59 92 8% No Poor
Friday 60 97 18% No Fair
Saturday 63 96 15% No Fair
Sunday 64 98 8% No Poor
Unit 1.2 – Descriptive Statistics
1. Identify the individuals and categories
Day Low High Humidity Precipitation
Air Quality
Monday 63 78 45% Light Good
Tuesday 66 88 13% No Fair
Wednesday 58 90 10% No Poor
Thursday 59 92 8% No Poor
Friday 60 97 18% No Fair
Saturday 63 96 15% No Fair
Sunday 64 98 8% No Poor
Unit 1.2 – Descriptive Statistics
2. Classify each category as categorical or quantitative
Day Low High Humidity Precipitation
Air Quality
Monday 63 78 45% Light Good
Tuesday 66 88 13% No Fair
Wednesday 58 90 10% No Poor
Thursday 59 92 8% No Poor
Friday 60 97 18% No Fair
Saturday 63 96 15% No Fair
Sunday 64 98 8% No Poor
Unit 1.2 – Descriptive Statistics
4. For each column, identify the most appropriate graphing type
Day Low High Humidity Precipitation
Air Quality
Monday 63 78 45% Light Good
Tuesday 66 88 13% No Fair
Wednesday 58 90 10% No Poor
Thursday 59 92 8% No Poor
Friday 60 97 18% No Fair
Saturday 63 96 15% No Fair
Sunday 64 98 8% No Poor
Unit 1.2 – Descriptive Statistics
Ticket out the Door5. Come up with your own example of a data set that includes all 4 vocab words and check with Mr. Newton
Day Low High Humidity Precipitation
Air Quality
Monday 63 78 45% Light Good
Tuesday 66 88 13% No Fair
Wednesday 58 90 10% No Poor
Thursday 59 92 8% No Poor
Friday 60 97 18% No Fair
Saturday 63 96 15% No Fair
Sunday 64 98 8% No Poor
Unit 1.2 – Descriptive Statistics
Part 3
Graphing Categorical Variables
Bar Graphs Pie Charts
Graphing Quantitative Variables
Dot Plots Stem Plots Histograms
Unit 1.2 – Descriptive StatisticsCategorical Data - Bar Graph
Unit 1.2 – Descriptive StatisticsCategorical Data – Pie Chart
Unit 1.2 – Descriptive StatisticsQuantitative Data – Dot Plot
Unit 1.2 – Descriptive StatisticsQuantitative Data – Stem and Leaf Plot
Unit 1.2 – Descriptive StatisticsQuantitative Data – Histogram
Unit 1.2 – Descriptive StatisticsQuantitative Data – Histogram