Question

Please see the attachment below.
Need explanation

Answer 1

16.(a) 24

16.(b) See attachment.

Explanation:

Cumulative frequency means ‘running total’. A cumulative frequency diagram plots this running total so you can estimate the median and the quartiles easily.

Part (a)

According to the given cumulative frequency graph, the number of necklaces that have a mass 21 g or less is 16.

Therefore, an estimate of the number of necklaces with a mass of 21 g or greater is:

`\implies 40-16=24`

Part (b)

To draw a box plot to represent the data, estimate the median and quartiles from the graph.

Calculate the position of the median and quartiles, then go to the position on the vertical scale of the graph and read off the value from the horizontal axis. (See attached annotated graph).

`\sf Median \; position=(40)/(2)=20`

So the median = 22

`\sf Q_1 \; position = (1)/(4) * 40=10`

So Q₁ = 18

`\sf Q_3 \; position = (3)/(4) * 40=30`

So Q₃ = 24

Draw the box plot with the calculated median and quartiles, and the given lowest and highest values. (See second attachment).

• Draw a box from Q₁ to Q₃ (18 to 24).
• Add the median as a the vertical line through the box at 22.
• Draw whiskers from each quartile to the minimum value 3 and maximum value 28.