Question

Fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play. Which statements are correct?

Answer 1

Fredrick’s data set contains an outlier.

The mean value is about 12.6 home runs.

The median describes Fredrick’s data more accurately than the mean.

Answer 2

Answer:

The correct options are:

• Fredrick’s data set contains an outlier.
• The mean value is about 12.6 home runs.
• T he median describes Fredrick’s data more accurately than the mean.

Step-by-step explanation:

It is given that the runs hit by Fredrick in 10 seasons of play are:

14, 18, 13, 12, 12, 16, 13, 12, 1, and 15

• We know that outlier of  data points are the points that stand out of the rest of data i.e. it is either too high or too low value as compared to the other data points.

Hence, here the outlier is: 1

Now, we arrange the data points in the increasing order or ascending order to obtain:

1   12    12    12   13   13   14   15   16   18

• We know that median of a data is the central tendency of the data and always exits in the middle of the data set.

Hence, here we see that the median lies between 13 and 13.

Hence,

Median= 13 home runs.

• Now, we know that the mean is the average of the data points and is solved as:

$Mean=\dfrac{1+12+12+12+13+13+14+15+16+18}{10}\\\\Mean=12.6$

Hence, Mean=12.6 home runs.

• Since, the median remains unchanged even after the removal of an outlier.

Hence, the median describes Fredrick’s data more accurately than the mean.

• Now, when the outlier is removed than the mean value is calculated as:

$Mean=\dfrac{12+12+12+13+14+15+16+18}{9}\\\\Mean=\dfrac{125}{9}\\\\Mean=13.88888$

Hence, the mean is changed with the removal of an outlier.