A list consists of $n$ integers. Consider the following statements: P: $\quad n$ is odd. Q: The median of the list is one of the numbers in the list. Which one of the following is true? A P is necessary and sufficient for Q. B P is necessary but not sufficient for Q. C P is sufficient but not necessary for Q. D P is not necessary and not sufficient for Q.
In a foreign language course, the average age of students in classes $A , B$ and $C$ is 20, 26 and 29 respectively. The average age of students in classes A and B together is 23, and the average age of students in classes B and C together is 28. According to this, what is the average age of all students in these three classes? A) 25,5 B) 26 C) 26,5 D) 27 E) 27,5
In a data group, when the numbers are arranged from smallest to largest, if the number of data is odd, the number in the middle is called the median of the data group, if the number of data is even, the arithmetic mean of the two middle numbers is called the median, and the number that appears most frequently in the data group is called the mode (peak value). Consisting of integers and arranged from smallest to largest $$6, x, 10, y, 14, z, 23$$ in the data group, only two values are equal to each other. Given that the mode, median, and arithmetic mean values of this data group are equal to each other, what is the value of $\mathbf{z}$? A) 22 B) 21 C) 18 D) 16 E) 15
The number obtained by dividing the sum of the numbers in a data group by the number of terms in the group is called the arithmetic mean of that data group. In a group consisting of people of different ages, the youngest person is 1 year old and the oldest person is 92 years old. When the youngest person in the group is excluded, the arithmetic mean of the ages of the others is 45, and when the oldest person in the group is excluded, the arithmetic mean of the ages of the others is 38. Accordingly, how many people are in the group? A) 12 B) 14 C) 16 D) 18 E) 20
In a data group, when the numbers are arranged from smallest to largest, if the number of terms in the group is odd, the median (middle value) is the middle number; if it is even, the median is the arithmetic mean of the two middle numbers. The ages and heights of the 9 players on a volleyball team, with the first component representing their ages and the second component representing their heights, are given as the sorted data group by height: $(18; 1.76), (17; 1.79), (18; 1.82), (19; 1.84), (20; 1.84)$, $(21; 1.88), (17; 1.90), (20; 1.92), (19; 1.96)$. One player left this 9-person team, but the median of both the ages and heights of the remaining players did not change. Accordingly, which of the following correctly gives the age and height of the player who left the team? A) $(17; 1.79)$ B) $(17; 1.90)$ C) $(19; 1.84)$ D) $(19; 1.96)$ E) $(21; 1.88)$
Temperature conversions between Fahrenheit (${}^{\circ}\mathrm{F}$) and Celsius (${}^{\circ}\mathrm{C}$) are calculated using the formula $\mathrm{F} = \frac{9}{5} \cdot \mathrm{C} + 32$. Cem has been assigned to measure the classroom temperature in Celsius at the same time each day for five days they go to school and find the average temperature of these five days in Celsius. On one of these five days, Cem did not go to school, and his classmate Deniz took the measurement for that day. However, Deniz mistakenly recorded the F value instead of the C value for that day's temperature in the list. Based on the values in the list, Cem calculated the average temperature for these five days as $33.8^{\circ}\mathrm{C}$.
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Monday
Tuesday
Wednesday
Thursday
Friday
Temperature (${}^{\circ}\mathrm{C}$)
23
27
25
20
26
After Deniz's measured temperature value is converted to Celsius and the five-day measurement has the values in the list as shown above, on which day did Cem not go to school? A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday
When the numbers in a data set are arranged from smallest to largest, if the number of data is odd, the median (middle value) is the middle number; if the number of data is even, the median is the arithmetic mean of the two middle numbers. Consisting of distinct integers and arranged from smallest to largest $$9, 10, a, 13, 16, b$$ the arithmetic mean and median of the data set are consecutive integers. Accordingly, what is the sum $a + b$? A) 30 B) 36 C) 42 D) 48 E) 54