the mean x and standard deviation s measure center and variability but are not a complete description of a distribution. Data sets with diffrent shapes can have the same mean and standard deviation. to demonstrate this fact use your calculator to find x and s for these two small data sets. then make a stem plot of each and comment on the shape of each distributiondata a : 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74data b : 6.58 5.76 7.71 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50

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Asked Feb 14, 2019
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the mean x and standard deviation s measure center and variability but are not a complete description of a distribution. Data sets with diffrent shapes can have the same mean and standard deviation. to demonstrate this fact use your calculator to find x and s for these two small data sets. then make a stem plot of each and comment on the shape of each distribution
data a : 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74
data b : 6.58 5.76 7.71 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50

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Expert Answer

Step 1

Obtain mean of the dataset a.

The data points of the dataset a are:

a: 9.14, 8.14, 8.74, 8.77, 9.26, 8.1, 6.13, 3.1, 9.13, 7.26 and 4.74.

Mean:

Mean is an important measure of center when the data is quantitative. Mean of a data set is the sum of the data set divided by the size.

The mean of the dataset a is obtained as 7.501 from the calculation given below:

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Step 2

Obtain standard deviation of the dataset a.

The mean of the dataset a is 7.501.

Standard deviation:

The standard deviation indicates by how much each observation differs from a central point represented by the mean. In general, the variance and standard deviation increases with the increase in the distances between the individual observations and the mean of the data set.

The general formula for standard deviation is,

Standard deviation s = SQRT(sum of (xix-bar)2)/n-1.

The standard deviation of the dataset a is obtained as 2.032 from the calculation given below:

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Step 3

Construct the stem and leaf plot for the dataset a.

Here, MINITAB software is used to construct the stem and leaf plot.

Software Procedure:

Step-by-step procedure to draw the stem and leaf plot using the MINITAB software:

  • Choose Graph > Stem and leaf.
  • In Graph variables, enter the colu...
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