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

Fatma and U\u011fur collected 10, 15, and 30 gram chocolates. Together they collected a total of 255 grams of chocolate.
When they returned home, after both of them gave some of their collected chocolates to their sister Nilay, each of the three siblings had an equal weight of chocolate.
Given that Nilay had no chocolate initially, how many chocolates does she have in the final situation?
A) 7
B) 6
C) 5
D) 4
E) 3

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) $(21; 1.88)$

When the numbers in a data group are arranged from smallest to largest, if the number of terms in the group is odd, the median is the middle number; if it is even, the median is the arithmetic mean of the two middle numbers.
The mode is the value that appears most frequently among the data.
The average temperature values measured in a region over one week are given below.
Monday : $16^{\circ}\mathrm{C}$ Tuesday : $18^{\circ}\mathrm{C}$ Wednesday : $16^{\circ}\mathrm{C}$ Thursday : $20^{\circ}\mathrm{C}$ Friday : $20^{\circ}\mathrm{C}$ Saturday : $19^{\circ}\mathrm{C}$ Sunday : $20^{\circ}\mathrm{C}$
The mode of the data group formed by these average temperature values is found, and the days whose temperature values equal the mode of the data group are removed from the data group.
Accordingly, what is the median of the new data group formed by the temperature values of the remaining days?
A) 16 B) 17 C) 18 D) 19 E) 20

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