gracie loves to talk on the phone, but her parents try to limit the amount of time she talks. they decided…

Explanation:

Step1: Calculate the mean

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $x_{i}$ are the data - points $120,60,0,30,15,0,0,10,20$ and $n = 9$. $\sum_{i=1}^{9}x_{i}=120 + 60+0 + 30+15+0+0+10+20=255$. $\bar{x}=\frac{255}{9}=\frac{85}{3}\approx28.33$.

Step2: Calculate the median

First, order the data: $0,0,0,10,15,20,30,60,120$. Since $n = 9$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{9+1}{2}=5$-th value. So the median is $15$.

Step3: Analyze which measure is more accurate

The mean is affected by the out - lier value of $120$. The median is not affected by extreme values. In this case, the median gives a more typical value of the daily phone - use time as most of the values are in the lower range and the high value of $120$ skews the mean.

Answer:

a) Mean: $\frac{85}{3}\approx28.33$, Median: $15$ b) The median gives the most accurate information about her phone use because the mean is skewed by the outlier value of $120$.