Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 41: Exercise 6J

The mean, median and mode of  $1,3,5,5,8$ is $4.4,5,5$ and the mean, median and mode when $4$ is added to each value of the data is $8.4,9,9$.

Describe the effect that adding $4$ to each value has on the mean, median and mode.

Find the standard deviation and variance of the set $7,9,3,0,1,8,6,4,10,5,5$.

Given data set is $7,9,3,0,1,8,6,4,10,5,5$. Multiply each member of the data set by $3$ and find the new standard deviation and variance.

The variance and standard deviation of the data values $7,9,3,0,1,8,6,4,10,5,5$ is $9.11, 3.02$ and the variance and standard deviation of the data values when $3$ is added to each value of the data is $82,9.06$.

Describe the effect that multiplying $3$ to each value has on the variance and standard deviation.

The mean age of a group of friends at school is $17.2$ years, their median age is $17$, and the standard deviation of their ages is $0.5$ years. They meet again $4$ years later at a school reunion. What are the new mean, median and standard deviation of their ages?

All of the items in a data set are doubled. State which of the following are also doubled: mean, median, standard deviation, variance.

If the variance of a data set is $x$ and all of the numbers in a data set are multiplied by $9$, state the new variance.

Find the mode of the data.

$2,8,1,5,0,4,4,1,1,6$.