The histogram gives information about the distribution of the weights of some onions grown by a farmer. Onions less than 60 grams in weight are used for pickling. Onions greater than 120 grams in weight are sold at the market. The rest of the onions are sent to a food processing factory. A pie chart is drawn using the information opposite to show what the farmer does with the onions he grows. The angle of the sector for the onions sent to the food processing factory is $x^\circ$. Work out the value of $x$.

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The histogram gives information about the distribution of the weights of some onions grown by a farmer - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

Question 22

The histogram gives information about the distribution of the weights of some onions grown by a farmer. Onions less than 60 grams in weight are used for pickling. O... show full transcript

Worked Solution & Example Answer:The histogram gives information about the distribution of the weights of some onions grown by a farmer - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

Step 1

Find total frequency

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Answer

To find the total area under the histogram, we add the areas of each bar. For the given histogram:

The bar from 0 to 60 grams has a height of 5.
The bar from 60 to 90 grams has a height of 9.
The bar from 90 to 120 grams has a height of 15.
The bar from 120 to 180 grams has a height of 3.
The bar from 180 to 210 grams has a height of 0.

Calculating the total frequency:

$ext{Total Frequency} = (60 - 0) \times 5 + (90 - 60) \times 9 + (120 - 90) \times 15 + (180 - 120) \times 3 + (210 - 180) \times 0$

This simplifies to:

$= 60 \times 5 + 30 \times 9 + 30 \times 15 + 60 \times 3$ $= 300 + 270 + 450 + 180 = 1200$

Step 2

Calculate onions sent to the factory

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Answer

From the information provided:

Onions less than 60 grams: Used for pickling = 300.
Onions greater than 120 grams: Sold at the market = 180.

Thus, the number of onions sent to the food processing factory:

$ext{Onions} = \text{Total} - (\text{Pickling} + \text{Market})$ $= 1200 - (300 + 180)$ $= 1200 - 480 = 720$

Step 3

Calculate the angle for the pie chart

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Answer

To find the angle $x$ for the onions sent to the food processing factory, we use the formula:

$x = \left(\frac{\text{Number of onions sent to factory}}{\text{Total number of onions}}\right) \times 360$

Substituting the values:

$x = \left(\frac{720}{1200}\right) \times 360\approx 216$

Thus, the value of $x$ is approximately 216 degrees.

The histogram gives information about the distribution of the weights of some onions grown by a farmer - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

Worked Solution & Example Answer:The histogram gives information about the distribution of the weights of some onions grown by a farmer - Edexcel - GCSE Maths - Question 22 - 2019 - Paper 3

Find total frequency

Calculate onions sent to the factory

Calculate the angle for the pie chart

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