Data Sets: Mean and Standard Deviation In the interactive spreadsheet, create a data set consisting of any five numbers in column B (cells B2 through B6, which currently contain the numbers 1, 2, 3, 4, and 5. You can just click on the cell and type over them). The mean and sample standard deviation of these five numbers will be computed in cells B7 and B8 respectively. Columns C through F, create new data sets by transform your data as indicated in the first cell. In column C, you would add 10 to each of the numbers you entered in column B. The means and sample standard deviations of the cells will be computed below each data set. What conclusion can you make about changes in the mean and the standard deviation when the same number is added to or subtracted from each score in a data set? Use the conclusion you just reached to simplify the calculation of the mean and standard deviation for the distribution 598, 597, 599, 596, 600. Check yourself by entering this data in cells G2 through G6. 9999 G 99 Your data Add 10 Add 20 Subtract 5 Subtract 10 Check 3 6. Mean= 3. Cample SD= 1.58 Steve Phelps Jlmedia.pearsoncmg.com/aw/aw_pimot_mathallaround_6/geogebra/C14-Data-Sets-Mean-and-Standard-Deviation/mpATdddVH-Data-Sets-Mean...
Data Sets: Mean and Standard Deviation In the interactive spreadsheet, create a data set consisting of any five numbers in column B (cells B2 through B6, which currently contain the numbers 1, 2, 3, 4, and 5. You can just click on the cell and type over them). The mean and sample standard deviation of these five numbers will be computed in cells B7 and B8 respectively. Columns C through F, create new data sets by transform your data as indicated in the first cell. In column C, you would add 10 to each of the numbers you entered in column B. The means and sample standard deviations of the cells will be computed below each data set. What conclusion can you make about changes in the mean and the standard deviation when the same number is added to or subtracted from each score in a data set? Use the conclusion you just reached to simplify the calculation of the mean and standard deviation for the distribution 598, 597, 599, 596, 600. Check yourself by entering this data in cells G2 through G6. 9999 G 99 Your data Add 10 Add 20 Subtract 5 Subtract 10 Check 3 6. Mean= 3. Cample SD= 1.58 Steve Phelps Jlmedia.pearsoncmg.com/aw/aw_pimot_mathallaround_6/geogebra/C14-Data-Sets-Mean-and-Standard-Deviation/mpATdddVH-Data-Sets-Mean...
Data Sets: Mean and Standard Deviation In the interactive spreadsheet, create a data set consisting of any five numbers in column B (cells B2 through B6, which currently contain the numbers 1, 2, 3, 4, and 5. You can just click on the cell and type over them). The mean and sample standard deviation of these five numbers will be computed in cells B7 and B8 respectively. Columns C through F, create new data sets by transform your data as indicated in the first cell. In column C, you would add 10 to each of the numbers you entered in column B. The means and sample standard deviations of the cells will be computed below each data set. What conclusion can you make about changes in the mean and the standard deviation when the same number is added to or subtracted from each score in a data set? Use the conclusion you just reached to simplify the calculation of the mean and standard deviation for the distribution 598, 597, 599, 596, 600. Check yourself by entering this data in cells G2 through G6. 9999 G 99 Your data Add 10 Add 20 Subtract 5 Subtract 10 Check 3 6. Mean= 3. Cample SD= 1.58 Steve Phelps Jlmedia.pearsoncmg.com/aw/aw_pimot_mathallaround_6/geogebra/C14-Data-Sets-Mean-and-Standard-Deviation/mpATdddVH-Data-Sets-Mean...
Use the data sets: Mean and standard deviation applet to answer the question below. Understand the mean and standard deviation of a data set.
You are asked to fill out a spreadsheet to create some data and then change the data according to the direction ( that is, add 10, and 20, etc.). The spreadsheet found the mean and the SD of your data sets. What pattern did you find for the SD of the data sets?
Transcribed Image Text:Data Sets: Mean and Standard Deviation
In the interactive spreadsheet, create a data set consisting of any five numbers in column B (cells B2
through B6, which currently contain the numbers 1, 2, 3, 4, and 5. You can just click on the cell and
type over them). The mean and sample standard deviation of these five numbers will be computed in
cells B7 and B8 respectively.
Columns C through F, create new data sets by transform your data as indicated in the first cell. In
column C, you would add 10 to each of the numbers you entered in column B. The means and sample
standard deviations of the cells will be computed below each data set.
What conclusion can you make about changes in the mean and the standard deviation when
the same number is added to or subtracted from each score in a data set?
Use the conclusion you just reached to simplify the calculation of the mean and standard deviation
for the distribution 598, 597, 599, 596, 600. Check yourself by entering this data in cells G2 through
G6.
9999
G
99
Your data
Add 10
Add 20
Subtract 5
Subtract 10
Check
3
6.
Mean=
3.
Cample SD=
1.58
Steve Phelps
Jlmedia.pearsoncmg.com/aw/aw_pimot_mathallaround_6/geogebra/C14-Data-Sets-Mean-and-Standard-Deviation/mpATdddVH-Data-Sets-Mean...
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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