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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

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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

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

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VernonExpert · Tutor for 3 years

Answer

## Step 1: <br />The midpoints of the length intervals are: <br />### \(5.0, 6.0, 7.0, 8.0, 9.0\)<br /><br />## Step 2: <br />The total costs for each length interval are: <br />### \(5.0*£5.25*1, 6.0*£5.25*13, 7.0*£5.25*20, 8.0*£5.25*11, 9.0*£5.25*5\)<br />### \(£26.25, £409.50, £735.00, £577.50, £236.25\)<br /><br />## Step 3: <br />The overall total cost is: <br />### \(£26.25 + £409.50 + £735.00 + £577.50 + £236.25 = £1984.50\)<br /><br />## Step 4: <br />The total number of pieces of wire sold is: <br />### \(1 + 13 + 20 + 11 + 5 = 50\)<br /><br />## Step 5: <br />The mean cost is: <br />### \(£1984.50 ÷ 50 = £39.69\)<br /><br />So, the estimated mean cost of the pieces of wire is £39.69.

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## Step 1: <br />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. <br /><br />## Step 2: <br />Next, we multiply each midpoint by its corresponding frequency to find the total cost for each length interval. <br /><br />## Step 3: <br />Then, we add up all the total costs to find the overall total cost. <br /><br />## Step 4: <br />After that, we add up all the frequencies to find the total number of pieces of wire sold. <br /><br />## Step 5: <br />Finally, we divide the overall total cost by the total number of pieces of wire sold to find the mean cost.
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