Question

Consider data below 20,40,50,50,60,80,80,80

Answer 1

Answer:

20,40,50,50,60,80,80,80

For this case we see that the mean is given by:

$\bar x = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X= 57.5$

The original median is:

$Median = \frac{50+60}{2}= 55.5$

And the mode:

$Mode= 80$

And for this case if our new dataset is this one:

20,40,50,50,60,80,80,160

The new mean would be:

$\bar X= 67.5$

And the median would be:

$Median = \frac{50+60}{2}=55.5$

And we have two values for the mode 50 and 80.

So then the statement is FALSE since we see that if we increase the mean by 10 and the median is the same and not changes and the same for the mode.

Step-by-step explanation:

For this case we have the following dataset :

20,40,50,50,60,80,80,80

For this case we see that the mean is given by:

$\bar x = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X= 57.5$

The original median is:

$Median = \frac{50+60}{2}= 55.5$

And the mode:

$Mode= 80$

And for this case if our new dataset is this one:

20,40,50,50,60,80,80,160

The new mean would be:

$\bar X= 67.5$

And the median would be:

$Median = \frac{50+60}{2}=55.5$

And we have two values for the mode 50 and 80.

So then the statement is FALSE since we see that if we increase the mean by 10 and the median is the same and not changes and the same for the mode.