Question

carson has the following data:
50 32 45 c 40 45
if the mean is 42, which number could c be?
22
40

Explanation:

Step1: Recall the mean formula

The mean of a set of numbers is the sum of the numbers divided by the count of the numbers. For the data set \(50, 32, 45, c, 40, 45\), the count \(n = 6\) and the mean \(\bar{x}=42\). The formula for the mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), so we can write \(42=\frac{50 + 32+45 + c+40 + 45}{6}\).

Step2: Simplify the numerator

First, calculate the sum of the known numbers: \(50+32 + 45+40 + 45=50+32=82\), \(82 + 45 = 127\), \(127+40 = 167\), \(167+45 = 212\). So the equation becomes \(42=\frac{212 + c}{6}\).

Step3: Solve for \(c\)

Multiply both sides of the equation by 6: \(42\times6=212 + c\). Calculate \(42\times6 = 252\), so \(252=212 + c\). Then subtract 212 from both sides: \(c=252 - 212=40\)? Wait, no, wait. Wait, let's check again. Wait, 50+32 is 82, 82 + 45 is 127, 127+40 is 167, 167+45 is 212. Then \(42\times6=252\), so \(c = 252-212 = 40\)? But wait, the options are 22 and 40? Wait, no, maybe I made a mistake. Wait, let's recalculate the sum of known numbers: 50 + 32 = 82, 82 + 45 = 127, 127 + 40 = 167, 167 + 45 = 212. Then total sum should be 426=252. So c=252 - 212=40. But wait, the other option is 22. Wait, maybe I miscalculated. Wait, 50+32=82, 82+45=127, 127 + c+40 +45=127 + c + 85=212 + c. So 212 + c=426=252. So c=252 - 212=40. But let's check with c=22: sum would be 212 + 22=234, mean is 234/6=39, which is not 42. With c=40: sum is 212 + 40=252, mean is 252/6=42. So c is 40. Wait, but the first option is 22, second is 40. So the correct one is 40.

Answer:

40