Value # 1 2 3 4 5 6 7 8 9 10 Dataset 1 168 177 180 176 179 185 187 182 174 191 D

Question

Value #

1

2

3

4

5

6

7

8

9

10

Dataset 1

168

177

180

176

179

185

187

182

174

191

Dataset 2

silver

red

blue

silver

blue

silver

black

red

black

silver

In the first dataset, the mean is 179.9 and the standard deviation is 6.71. As it is height, the variable is ratio level of measurement. The second dataset is represented by the values in the nominal measurement level. The mode is silver. Here is the question: How would the 10 heights differ if the mean was still 179.9 but the standard deviation was 16.71 instead of 6.71?

Value #

1

2

3

4

5

6

7

8

9

10

Dataset 1

168

177

180

176

179

185

187

182

174

191

Dataset 2

silver

red

blue

silver

blue

silver

black

red

black

silver

Explanation / Answer

Now, the question is about the precision of the mean estimate value because precision is inversely related to variance. Hence, precision of the mean of 10 heights will reduce when the standard deviation was 16.71 instead of 6.71.

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