Unit 3 Guided Notes

Box and Whiskers

5 Number Summary Provides a numerical Summary of a set of data The first quartile (Q 1 ) is the median of the data values to the left of the overall median The third quartile (Q 3 ) is the median of the data values to the right of the overall median. A box plot (sometimes called a box-and-whisker plot) is a graph of the five-number summary that consists of a central box from Q 1 to Q 3 that has a vertical line segment at the median. Horizontal line segments ("whiskers") extend from the box to the minimum and maximum data values.

A box-and-whiskers plot is a good way to show the spread (or variation) of a set of data visually.

A box-and-whiskers plot shows both the median and extremes of a data set. Median : the middle term, or the average of the two middle terms, when the terms are arranged from least to greatest. Extremes: the minimum and maximum values Lower Extreme Upper Extreme

The extreme values are used to find the range of the set of data by finding the difference between the lower extreme and the upper extreme. EXTREMES Lower Extreme Upper Extreme Upper Extreme – Lower Extreme = RANGE

Quartiles: the medians of the lower and upper halves of the data. Lower Quartile Upper Quartile Upper Quartile – Lower Quartile= INTERQUARTILE RANGE

Box-and-whiskers plots are uniform in the use of the box. Therefore, no matter the size of each section, the data is evenly divided in quarters (25%). 25%

Box-and-whiskers plots are uniformed in the use of the box. Therefore, no matter the size of each section, the data is evenly divided in quarters (25%). 25% 50%

Box-and-whiskers plots are uniformed in the use of the box. Therefore, no matter the size of each section, the data is evenly divided in quarters (25%). 25% 75%

Therefore the entire box-and-whiskers plot is equal to 100% of the data.

No matter how the diagram appears to be equally or unequally divided, each section is always 25% 25%

No matter how the diagram appears to be equally or unequally divided, each section is always 25% 25%

No matter how the diagram appears to be equally or unequally divided, each section is always 25% 25%

No matter how the diagram appears to be equally or unequally divided, each section is always 25% 25%

What is a dot plot? I am used to display numeric data I show each individual data point I Show univariate (one-variable) data when dealing with small data sets. Why do you think that I am used with small sets of data instead of large sets of data? Is it impossible to use a dot plot for a large set of data?

What does a dot plot look like? Number of pets per student.

How do I create a dot plot? Step 1 : Organize your data Step 2: Draw a horizontal line Step 3 : Title your display Step 4: Label your line with each value smallest to largest Step 5: Plot your dots

Step 1: Organizing data You can organize data in different ways. Put all of the data in order least to greatest becomes -> Create a frequency table 2I 3I 4I 5II 6I 7I

Step 2: Draw a horizontal line It is important to look at your values so that you draw your line with enough room to put a dot for every occurrence in a data set. If this is your paper the line near the middle represents a horizontal line.

Step 3: Title your Display Look at your data. The title should tell what data was collected. Examples Number of siblings Number of pets

Step 4: Label your line Label your line with each value smallest to largest (evenly space your values)

Step 4: Plot your dots Make a dot above the value for each time the value occurs in your data

Rules of Dot Plots Rule 1: Every data point must be shown Rule 2: Horizontal line must be labeled Rule 3: Labels must be evenly spaced Rule 4: Dots should be uniform (same size, shape and distance apart)

What is a Histogram? I am used to display numeric data. I use ranges to display data. I am used to display large sets of continuous data. How is a histogram different from a dot plot? Why do you think a histogram used ranges to display data instead of each individual data point? What do you think the phrase continuous data means?

What does a histogram look like? ≤ ≤≤ ≤ ≤ Number of sodas a student drinks in a month.

How do I create a Histogram? Step 1 : Organize your data Step 2: Draw your perpendicular lines Step 3 : Title your display Step 4: Label your lines Step 5: Draw your bars.

Step 1: Organizing data You can organize data in different ways. Put all of the data in order least to greatest becomes -> Create a frequency table 2I 3I 4I 5II 6I 7I

Step 2: Drawing your display

Step 3: Title your Display Look at your data. The title should tell what data was collected. Examples Height of all 7 th graders to the nearest quarter inch. Length of every G rated movie that came out after 2005.

Step 4: Labeling your Display Number of times Florida resident visit Disney each year. 0 –

Step 5: Completing the Display Number of times Florida resident visit Disney each year. 0 –

Rules of Histograms Rule 1 : Bars must touch Rule 2: Bars must be the same width. Rule 3: Both axis’ should be labeled. Rule 4: Axis’ labels must be evenly spaced. Rule 5: You must title your display.

Bellringer: Complete Number 4 and 5 on page 524 in Springboard

Today’s Goals and Agenda By the end of class today I will: I will be able to compare two sets of data distribution using center and spread. I plan to do this by: I Do: Data Distribution and Deviation Notes We Do: Standard Deviation Springboard Practice You Do: Calculate Standard Deviation

Data Distribution Spread indicates how far apart the data values are in the set. Range and Mean Absolute Deviation (MAD) are measures of spread The mean absolute deviation is the mean (average) of the absolute values of the deviations of the data. The deviation is a measure of how far a data value is from the mean

How to Find Mean Absolute Deviation-#8 pg Find the mean of the data 2.Subtract each individual data value from the mean 3.Find the sum of all the differences you found in step 2. 4.Divide the sum by the number of data values in the set

You Try: #10 pg. 526 Discuss your answer for part B with a partner

We Do: How to Find Standard Deviation-pg

You Do: On your white board Now use your chart to calculate standard deviation

Home Learning: Springboard pg. 535 #7-11

Bellringer Complete #1-4 on Page 596 of Springboard

Today’s Goals and Agenda By the end of class today I will: I will be able to analyze data and find outliers in data sets, as well as be able to represent categorical data using two-way frequency tables I plan to do this by: I Do: Data Analysis Notes We Do: Springboard Practice I Do: Two Way Frequency Table Notes You Do: Springboard Practice

Data Analysis-Springboard pg. 544 Outliers are values that differ so much from the rest of a one-variable data set that attention is drawn to them. It is important to consider the impact of outliers when summarizing and analyzing data. A data value is considered to be an outlier if it is less than or more than 1.5 × (IQR) from the nearest quartile. IQR stands for interquartile range and is the difference between the third quartile (Q 3) and the first quartile (Q1)

You Do: How to find Upper and Lower Boundary Values Use the following equation to solve #3-7 on page 545 in Springboard

Springboard Pg Data can be distributed in different ways…

Two- Way Frequency Tables: Summarizes the distribution of values for bivariate (2 variables) categorical data way-tables/v/interpreting-two-way-tables

You Do: Complete Number 5 on page 596 Page 597 Mark the Text: Row and column totals are usually included in two-way frequency tables. These are called marginal totals. We can convert frequencies into relative frequencies by dividing them by the grand total. Copy the Vocab under “Math Tip” into your Journal and then complete Number 6

Independently work on #7-11 on page 598

Home Learning Springboard Page 547, Lesson 37-2 Practice Springboard Page 599, Lesson 40-1 Practice