Answer :
The average weight was closer to 196 pounds as it was 0.3583 pounds away from 197 and 0.6417 pounds from 196.
To determine whether the average weight for this sample of orders was closer to 196 pounds or 197 pounds, we need to calculate the mean (average) weight of the orders.
Step 1 :**Calculate the mean weight**:
To find the mean weight, we sum up all the weights and divide by the total number of orders.
[tex]\[ \text{Mean} = \frac{196 + 196.1 + 196.2 + \ldots + 197}{\text{Number of orders}} \][/tex]
Step 2 :**Count the number of orders**:
From the given dot plot, we can count the number of orders. There are 12 data points.
Step 3 :**Calculate the mean**:
[tex]\[ \text{Mean} = \frac{196 + 196.1 + 196.2 + \ldots + 197}{12} \][/tex]
[tex]\[ \text{Mean} = \frac{2359.7}{12} \][/tex]
[tex]\[ \text{Mean} = 196.6417 \][/tex]
Step 4 :**Compare with 196 and 197**:
The mean weight, approximately 196.6417 pounds, lies between 196 and 197. However, since we're looking at which it's closer to, we compare the distance between the mean and each value.
The mean is 0.6417 pounds away from 197 (196.6417 - 197 = -0.3583), and it's 0.6417 pounds away from 196 (196.6417 - 196 = 0.6417).
The mean is closer to 196 pounds than to 197 pounds.
Therefore, the average weight for this sample of orders was closer to 196 pounds.
