Question

the anderson family went to destin, florida for a summer vacation. the table below shows the daily high temperatures for destin during their vacation. use the information to answer 7 - 10.

day	sun	mon	tues	wed	thu	fri
temperature (°f)	93	93	97	95	90	98

1. find the average high temperature during the andersons vacation.
2. which of the following is a true statement about the mean and the median for the temperatures above?

a. the mean and the median are equal.
b. the mean is greater than the median.
c. the mean is less than the median.
d. none of the above.
the andersons decide to stay an extra day, and the high temperature on saturday is 83°. mark each statement as true or false, and correct any false statements.

1. the mean of the data set decreases with the addition of saturdays temperature, but the median is unaffected.
2. the addition of saturdays temperature will cause the mean absolute deviation to decrease.

Explanation:

Step1: Calculate the sum for original 6 - day data

The original temperatures are 93, 93, 97, 95, 90, 96. The sum $S_1=93 + 93+97+95+90+96=564$.

Step2: Calculate the original mean

The number of data - points $n_1 = 6$. The mean $\bar{x}_1=\frac{S_1}{n_1}=\frac{564}{6}=94$.

Step3: Arrange original data in ascending order

The original data in ascending order is 90, 93, 93, 95, 96, 97. Since $n_1 = 6$ (even), the median $M_1=\frac{93 + 95}{2}=94$.

Step4: Add Saturday's temperature and calculate new sum

The new temperature is 83. The new sum $S_2=564+83 = 647$.

Step5: Calculate the new mean

The number of data - points $n_2=7$. The new mean $\bar{x}_2=\frac{S_2}{n_2}=\frac{647}{7}\approx92.43$.

Step6: Arrange new data in ascending order

The new data in ascending order is 83, 90, 93, 93, 95, 96, 97. Since $n_2 = 7$ (odd), the median $M_2 = 93$.

Step7: Analyze question 7

The average high temperature during the original vacation (6 - day) is 94°F.

Step8: Analyze question 8

The mean and median of the original data are equal. So the answer is a. The mean and the median are equal.

Step9: Analyze question 9

The mean decreases from 94 to approximately 92.43 and the median changes from 94 to 93. The statement is false. The correct statement is: The mean of the data set decreases with the addition of Saturday's temperature, and the median also decreases.

Step10: Analyze question 10

The mean absolute deviation measures the average distance between each data point and the mean. Since the new data point (83) is far from the original mean, it will increase the spread of the data, and thus the mean absolute deviation will increase. The statement is false.

Answer:

1. 94°F
2. a. The mean and the median are equal.
3. False. The correct statement is: The mean of the data set decreases with the addition of Saturday's temperature, and the median also decreases.
4. False.