Question
Ellie recorded the length of each piece of silver wire that she sold at her shop last week. She charged £ 5.25 per metre for the wire. Work out an estimate for the mean cost of these pieces of wire. Length, l (metres) & Frequency 4.5<l leq 5.5 & 1 5.5<l leq 6.5 & 13 6.5<l leq 7.5 & 20
Answer
4.7
(189 Votes)
Vernon
Expert · Tutor for 3 years
Answer
## Step 1: The midpoints of the length intervals are: ###
## Step 2: The total costs for each length interval are: ###
###
## Step 3: The overall total cost is: ###
## Step 4: The total number of pieces of wire sold is: ###
## Step 5: The mean cost is: ###
So, the estimated mean cost of the pieces of wire is £39.69.
Explanation
## Step 1: First, we need to find the midpoint of each length interval. The midpoint is the average of the lower and upper bounds of the interval. ## Step 2: Next, we multiply each midpoint by its corresponding frequency to find the total cost for each length interval. ## Step 3: Then, we add up all the total costs to find the overall total cost. ## Step 4: After that, we add up all the frequencies to find the total number of pieces of wire sold. ## Step 5: Finally, we divide the overall total cost by the total number of pieces of wire sold to find the mean cost.