8.2 Standard error of the mean

Students were given samples of five marbles each. Each sample generated a sample mean for the marble masses. The class as a whole acted as the population. 
I arrived early and passed out marbles as students entered. I opted to play Wintergatan to open the session.

As in prior terms I did not preload names, entering them on the fly. I handled all data entry from the tablet.
Ten students each had five marbles.

Treating the 50 marbles as the population allowed calculation of the population mean. Using Cathleen's sample as an example sample (a function captures the name of the second student) yields a sample mean that is different from the known population mean. Yet that is the best estimate of the population mean if the population mean is unknown. Which is usually the case. 

Cathleen's sample standard deviation is less that the population standard deviation (technically the spreadsheet is displaying STDEV not STDEVP, but the latter could confuse the students as to when to use that, and the difference at n=50 is vanishingly small). This is also as expected. The standard error of the mean thus functions as an estimate of the standard deviation of the means. For small sample sizes issues arise. 

This exercise still has the feel of the best explanation of the standard error of the mean. The SMARTboard allows me to sketch on top of the above chart. 

Comments

Post a Comment

Popular posts from this blog

Plotting polar coordinates in Desmos and a vector addition demonstrator

Image
In an earlier post I noted that Desmos did not directly plot polar coordinates. Not only was I incorrect, but Desmos responded to my blog to correct me! Although I had at some point seen that one could define a function f(x)=3x+5 and then have Desmos calculate f(6), I had not absorbed how this might be used to plot polar coordinates. The above works beautifully . Realizing that I could effectively program Desmos, I applied this thinking to demonstrating how to add two vectors when given the magnitudes m and the direction angles theta. The graph calculates the i and j components for the two vectors and then adds the vectors, graphically displaying the result while also providing information on the magnitude and direction of the vector sum. m1 and theta1 are the magnitude and direction angle for one of the two vectors, m2 and theta2 are the magnitude and direction for the other vector. All four are dynamically interactive and can be changed. The diagram purports to illustra
Read more

Setting up a boxplot chart in Google Sheets with multiple boxplots on a single chart

Image
The  Google Statistics  add-on for Google Sheets can display multiple boxplots in a single chart. The key is the layout of the data. One column should be the variable by which the data is to be grouped, the other column should be the data to be box plotted. Set up the Statistics add-on with the data to be plotted as the variable, and the grouping column as the "by" variable. In this image I had deselected all but the boxplot option, the result was the appearance of the Moment, Standard errors, and Confidence intervals options. The default is apparently a 95% confidence interval for the mean. The result is multiple boxplots on a single chart with a common scale. The new tab that is created also quotes 95% confidence intervals for the mean. Note that as of 2018 the Google Statistics add-on cannot be found by search in the add-ons. In addition, as of May 2018 the add-on no longer verifies, possibly due to the add-on not having been updated since August 2017. One may ha
Read more

Traditional food dishes of Micronesia

Image
Clara, Jennette, and Joanie presented ground hard taro cooked in an umw, effectively a hot rock oven. Pohnpeian: rotama. Pingelapese: sero. Mwoakillese: rodma. Mortlockese: Amahd. Kosrae: rodoma. After cooking in an umw the rotama is pounded with the petiole of a palm frond. Rotama is made from hard or swamp taro, known as mwahng on Pohnpei, mweian on Pingalap, pula in Mortlockese, and pahsruhk on Kosrae. In traditional times on the outer islands the women had primary responsibility for tending the taro while the men handled fishing and climbing tasks. Joesen and Noeleen presented fermented breadfruit from the outer islands of Yap such as Woleai and Eauripik. The raw ingredients were actually brought in from Yap, Noeleen prepared the maare.  The leaf wrap is ti leaf - Cordyline fruticosa. Pauleen, Barnson, Trisha, Verginia, Con-ray, and Maylanda from Kitti, Pohnpei brought in mahi umw, koahpnoair koakihr, and uht sukusuk. Above is breadfruit umw, mahi umw, one o
Read more