To determine whether your friend's claims about the mean and median are correct, we will calculate both the mean and the median of the data set: 40, 38, 62, 70, 56, 41, 58, 48, 60, 45.
Step 1: Calculate the Mean
Mean is calculated by dividing the sum of all values by the number of values.
Sum of the data set: \[ 40 + 38 + 62 + 70 + 56 + 41 + 58 + 48 + 60 + 45 = 468 \]
Number of values: \[ 10 \]
Mean: \[ \text{Mean} = \frac{468}{10} = 46.8 \]
Step 2: Calculate the Median
To find the median, we first need to arrange the data in ascending order: \[ 38, 40, 41, 45, 48, 56, 58, 60, 62, 70 \]
Since there are 10 values (an even number), the median will be the average of the 5th and 6th values.
The 5th value is 48, and the 6th value is 56.
Median: \[ \text{Median} = \frac{48 + 56}{2} = \frac{104}{2} = 52 \]
Conclusion:
Based on these calculations, the correct mean is 46.8 and the correct median is 52.
Therefore, the answer is: My friend is not correct. The mean is 46.8. The median is 52.