Your friend finds the mean and median of the data set: 40, 38, 62, 70, 56, 41, 58, 48, 60, 45. Your friend says that the mean and median are both 52. Is your friend correct? If not, find the correct answer.(1 point)
Responses
To determine if your friend is correct, we need to calculate the mean and median of the given data set:
Mean:
To find the mean, add up all the values in the data set and divide by the total number of values:
40 + 38 + 62 + 70 + 56 + 41 + 58 + 48 + 60 + 45 = 518
Total number of values = 10
Mean = 518/10 = 51.8
Median:
To find the median, first, arrange the values in ascending order:
38, 40, 41, 45, 48, 56, 58, 60, 62, 70
Since there are 10 values in the data set, the median will be the average of the two middlemost values. In this case, the two middlemost values are 48 and 56. So, the median = (48 + 56)/2 = 52.
Now, comparing your friend's claim to the calculated mean and median:
Your friend claims: Mean = 52 and Median = 52
Calculated: Mean = 51.8 and Median = 52
Your friend is almost correct. The mean is very close to 52, with a slight difference due to rounding the mean to one decimal place. However, your friend is correct about the median; it is indeed 52.
To determine if your friend is correct, let's calculate the mean and median of the given data set.
Mean:
To find the mean, we sum up all the numbers in the data set and divide by the total number of values.
Sum of the numbers in the data set:
40 + 38 + 62 + 70 + 56 + 41 + 58 + 48 + 60 + 45 = 518
Total number of values:
There are 10 values in the data set.
Mean = Sum of the numbers / Total number of values
Mean = 518 / 10
Mean = 51.8
So, the mean of the given data set is 51.8.
Median:
To find the median, we first arrange the numbers in ascending order.
38, 40, 41, 45, 48, 56, 58, 60, 62, 70
Since there are 10 values, the median will be the average of the 5th and 6th value.
Median = (48 + 56)/2
Median = 52
Therefore, your friend is correct. Both the mean and median of the data set are 52.