Question

Teachers are being trained to standardize the scores they give to students' essays. The same essay wasscored by 10 different teachers at the beginning and at the end of their training. The results are shown inthe tables.Scores for Essay at Beginning of Teachers' Training75 78 86 75 89 87 88 77 90 78Scores for Essay at End of Teachers' Training79 81 83 80 78 85 81 81 79 83Calculate the MADs for the teachers' scores. Did the teachers make progress in standardizing their scores?(select), the MAD before the training was IIand the MAD at the end of the training isso (select) was made toward standardizing test scores.

Answer 1

For this case we have the following two datasets:

Scores for Essay at Beginning of Teachers' Training

75 78 86 75 89 87 88 77 90 78

Scores for Essay at End of Teachers' Training

79 81 83 80 78 85 81 81 79 83

And we need to calculate the mean Absolute deviation for each case. We need to remember the definition of MAD given by:

And the mean is defined as:

`mean=(\sum ^n_(i\mathop=1)x_i)/(n)`

We can calculate the mean for each case and we got:

`\text{mean}_{\text{beginning}}=(75+78+86+75+89+87+88+77+90+78)/(10)=82.3`
`\text{mean}_{\text{end}}=(79+81+83+80+78+85+81+81+79+83)/(10)=81`

Then finally we can calculate the MAD for each case:

`\text{MADbegin}=5.7,\text{ MAD\_end=}1.6`