Question

last weeks and this weeks low temperatures are shown in the table below.
low temperatures for 5 days this week and last week
low temperatures this week (°f) 4 10 6 9 6
low temperatures last week (°f) 13 9 5 8 5
which measures of center or variability are greater than 5 degrees? select three choices.
□ the mean of this weeks temperatures
□ the mean of last weeks temperatures
□ the range of this weeks temperatures
□ the mean absolute deviation of this weeks temperatures
□ the mean absolute deviation of last weeks temperatures

Explanation:

Step1: Calculate the mean of this week's temperatures

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For this - week's temperatures $x = \{4,10,6,9,6\}$, $n = 5$, and $\sum_{i=1}^{5}x_{i}=4 + 10+6 + 9+6=35$. So, $\bar{x}_{this - week}=\frac{35}{5}=7$.

Step2: Calculate the mean of last week's temperatures

For last - week's temperatures $y=\{13,9,5,8,5\}$, $n = 5$, and $\sum_{i = 1}^{5}y_{i}=13 + 9+5 + 8+5=40$. So, $\bar{y}_{last - week}=\frac{40}{5}=8$.

Step3: Calculate the range of this week's temperatures

The range is the difference between the maximum and minimum values. For this - week's temperatures, the maximum value is $10$ and the minimum value is $4$. So, the range $R_{this - week}=10 - 4 = 6$.

Step4: Calculate the mean absolute deviation (MAD) of this week's temperatures

First, find the deviation of each data point from the mean. The mean of this week's temperatures $\bar{x}=7$.
The deviations are $|4 - 7|=3$, $|10 - 7|=3$, $|6 - 7|=1$, $|9 - 7|=2$, $|6 - 7|=1$.
The sum of the absolute deviations is $3+3 + 1+2+1=10$. The MAD of this week's temperatures $MAD_{this - week}=\frac{10}{5}=2$.

Step5: Calculate the mean absolute deviation (MAD) of last week's temperatures

The mean of last - week's temperatures $\bar{y}=8$.
The deviations are $|13 - 8|=5$, $|9 - 8|=1$, $|5 - 8|=3$, $|8 - 8|=0$, $|5 - 8|=3$.
The sum of the absolute deviations is $5+1+3 + 0+3=12$. The MAD of last week's temperatures $MAD_{last - week}=\frac{12}{5}=2.4$.

Answer:

• the mean of this week's temperatures
• the mean of last week's temperatures
• the range of this week's temperatures