Question

Find the mean, median, and mode of 3, 5, 1, 5, 1, 1, 2, 3, 15 after each data value increases by 4.

Answer 1

Solving for the Mean, Median and Mode of a Data Set

Answer:

Mean: $8$

Median: $7$

Mode: $5$

Step-by-step explanation:

If we increase each element in the data set by $4$, our new data set will be...

$\{ 7, 9, 5, 9, 5, 5, 6, 7, 19 \}$

The mean of a data set is the sum of all of its elements divided by the number of elements.

Solving for the mean:

$\frac{7 +9 +5 +9 +5 +5 +6 +7 +19}{9} \\ \frac{72}{9} \\ 8$

The median of a data set is just the middle number if and only if the elements of the data set is arranged according to how less to how great each element is.

If we arrange our data set it will be...

$\{ 5, 5, 5, 6, 7, 7, 9, 9, 19 \}$

We can do see that our middle number is $7$ so this our median.

The mode of a data set is the number that repeated the most. We can see in our data set that the number $5$ repeated $3$ times. $6$ and $19$ is $1$. $7$ and $9$ is $2$. Since $5$ is the number that repeated the most, this is our median.