Question

The data 11, 6, 22, 7, 10, 6, 15 is the time in minutes it takes seven students to go to school from their homes. Which statement about the data is false?
A) The median is 11
B) The mean is 11
C) The range is 16
D) The mode is 6

Answer 1

Hint:
Here we will first find the mean. For that, we will first find the sum of value of time taken by the total number of students. Then we will find the median, for that we will first arrange the numbers in the ascending order and then we will find the middle value. Then we will find the range of the given data which will be equal to the difference of the largest value and smallest value. For finding mode, we will find repeating value in the data. After solving all these values, we will get the false statement given.

Complete step by step solution:
The given data: 11, 6, 22, 7, 10, 6, 15, these are the times taken by the seven students to go to their homes.
We will first find the mean. Where, mean will be equal to the ratio of the sum of the time taken by the seven students to the number of students.
$mean=\dfrac{11+6+22+7+10+6+15}{7}=\dfrac{77}{7}=11$ . Value of mean is the same as given in the question.
We will find the median which will be the middle value. We will arrange the given values of time in ascending order.
6, 6, 7, 10, 11, 15, 22
Here middle value is ${{\left( \dfrac{7+1}{2} \right)}^{th}}term={{4}^{th}}term$
Therefore, the median is 10. Thus, the value of the median given in the question is wrong.
Now, we will calculate the range.
Maximum value is 22 minutes and minimum value is 6.
$\therefore range=22-6=16$
Value of range in the given question is correct.
The mode will be the most repeating number in the data.
So the mode here is 6.
Value of mode given in the question is correct.

Hence, the false statement is in option A.

Note:
There is a relation between mean, median and mode which is known as empirical relationship. It states that the difference between the values of mean and mode is equal to three times the difference between the values of mean and median.
$mean-\bmod e=3\left( mean-median \right)$