Math 515 Official - Descriptive Statistics & Dot Plot & Box Plot

Autor:Mark Endres, Dr. Jack L. Jackson II

Learning Objectives for the Geogebra Activity

Students will be able to utilize data to create descriptive statistics about a data set.
Students will be able to interpret dot plots and box plots of a data set.
Students will be able to answer questions regarding specific attributes of descriptive statistics.

Descriptive Statistics

We want to analyze the historic daily temperatures in Milwaukee, WI from May 2024. Click on the following link to see a spreadsheet table of every high temperature in Milwaukee, WI from the month of May 2024. https://docs.google.com/spreadsheets/d/141kJQIhVOetMu8DKgozlF7hvUmNIgzX1bhrPcvT8jhs/edit?usp=sharing Then copy the temperature data into Column A1 on this screen, under the heading of D.T. (daily Temperatures). Enter your data into cells A2 to A33. Note that the current data displayed in this activity is there just for example, in order to see the box plot. The dot plot for the data is displayed with blue dots. The scale is automatically adjusted. Click on the various check boxes to see the following numerical and graphical statistics displayed: Box Plot (unmodified without indicating outliers) Quartiles (Measures of Relative Standing: 5 values divide the data into four parts with the same amount of data in each part) (Note that there are multiple methods for computing quartiles Q1 and Q3. GeoGebra uses the same method used by TI-84 calculators. Rank the data and find the median of the lower half for Q1 and the median of the upper half for Q3. The median is not counted as part of either half when there is an odd number of data values.) Fences for Outliers (Dots outside the fences are outliers. Fences are 1.5 IQR below Q1 and above Q3). Measures of Central Tendency Mean: Add up the data values and divide by the number of data values (average) Median: 1/2 of ranked data is below and 1/2 of ranked data is above the median Mode: The most often occurring data value(s) Midrange: (minimum + maximum)/2 Midquartile: (Q1 + Q3)/2 Measures of Variability Range = Maximum - Minimum IQR = Q3 - Q1 MAD = sum(absolute value of mean - data)/number of data points Standard Deviation = sum(mean - data)^2/(n-1) Variance = sqrt(sum(mean - data)^2/(n-1))

Question #1

How does the 1.5*IQR rule work for identifying outliers within a data set?

Question #2

For the daily high temperatures in Milwaukee, WI in May 2024, are there any outliers?

Marca todas las que correspondan

A
Yes
B
No

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Question #3

If there are any outliers, please list those data points? If not, please type N/A.

If You Need Help with Understanding Outliers - Please Watch if You Need a Reminder on How to Calculate an Outlier!

Question #4

What type of data is daily temperatures? (Think: nominal, ordinal, interval, ratio)

Marca todas las que correspondan

A
Nominal
B
Ordinal
C
Interval
D
Ratio

Revisa tu respuesta (3)

Question #5

How do you determine the appropriate measure of central tendency (mean, median, mode) for this data set?

Question #6

How do you calculate the range of a data set, and what does it tell you about the data?

Question #7

Why is standard deviation a useful measure of dispersion, and how do you interpret it in the context of a data set?

Question #8 - Extension Challenge Problem!

What would the shape of the box plot look like and how would it change, if we added one very low temperature outlier to the data or if we added one very high temperature to the data set?

Question #9 - Super Extension Challenge Problem!

Mr. Endres loves to have a day in May with a high temperature between 70 - 72 degrees. Assuming that the temperatures follow a normal distribution, find the probability that a randomly selected day in May will have a high temperature between 70 - 73 degrees? Remember to calculate the standard deviation as well!