Question

A, B, C are three sets of values of x:
A: 2, 3, 7, 1, 3, 2, 3
B: 7, 5, 9, 12, 5, 3, 8
C: 4, 4, 11, 7, 2, 3, 4
Which one of the following statements is correct?
A. Mean of A =Mode of C
B. Mean of C = Median of B
C. Median of B = Mode of A
D. Mean, Median and Mode of A are equal.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:

A: 2, 3, 7, 1, 3, 2, 3

B: 7, 5, 9, 12, 5, 3, 8

C: 4, 4, 11, 7, 2, 3, 4

To find:

The correct statement

Solution:

The correct statement is that the Mean, Median and Mode of A are equal. (Option D)

We can find the solution by following the given steps-

We know that the mean is the average value of the data, the median is the middle value and the mode is the data with the highest frequency.

We will calculate the mean of sets A and C, the mode of sets A and C, and the median of sets A and B.

The mean of the given sets can be obtained by adding the elements of the sets and dividing by the number of elements in the set.

Mean of set A=Sum of elements in A/Number of elements in A

Mean of set A=(2+3+7+1+3+2+3)/7

Mean of set A=21/7

Mean of set A=3

Similarly, the mean of set C=(4+4+11+7+2+3+4)/7

Mean of set C=35/7

Mean of set C=5

Now, the mode of sets A and C is the element occurring the maximum number of times.

Mode of A=3

Mode of C=4

The median is the middle value of the given data.

We will calculate the median of sets A and B by arranging them in ascending order and picking the middle term.

A: 1, 2, 2, 3, 3, 3, 7

B: 3, 5, 5, 7, 8, 9, 12

The number of terms in each of the sets A and B, N=7, which is odd.

Median term=(N+1)/2=(7+1)/2=8/2=4th term

Median of A=3

Similarly, the median of B is also the 4th term.

Median of B=7

We see that the mean, median, and mode of A are equal i.e., 3.

Therefore, the correct statement is that the Mean, Median and Mode of A are equal.