1. Find the mean of the first five prime numbers. 2. If the median of 17, 13, 10, 15, a is 14, find a if a is an integer. 3. Find 'a' if the mean of 6, 16, a, 12 is 14.
Answer (1)
Let's solve each part of the question step-by-step:
Find the mean of the first five prime numbers.
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. The first five prime numbers are: 2, 3, 5, 7, and 11.
To find the mean, you add all the numbers together and then divide by the number of numbers.
Mean = 5 2 + 3 + 5 + 7 + 11 = 5 28 = 5.6
If the median of 17, 13, 10, 15, a is 14, find a if a is an integer.
First, arrange the numbers in ascending order, which means from smallest to largest. We have the numbers: 10, 13, 15, 17, and a .
The median is the middle number in a list when the numbers are written in order. For a list with five numbers, the median is the third number. Therefore, if the median is 14, a must be the third number when placed in order.
To make 14 the median, arrange the numbers as 10, 13, 14, 15, 17. Therefore, a = 14 .
Find 'a' if the mean of 6, 16, a, 12 is 14.
The mean is calculated by adding all the numbers together and dividing by the total count of the numbers.
Set up the equation:
4 6 + 16 + a + 12 = 14
Multiply both sides by 4 to eliminate the fraction:
34 + a = 56
Subtract 34 from both sides to solve for a :
a = 56 − 34 = 22
Thus, a = 22 .
These steps help you solve each part of the problem methodically, ensuring that you understand how each result is reached.
