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Numeracy Higher June 2022 Unit 1 Q5

WJECHigherCurrent spec10 marksBox PlotsCumulative FrequencyPercentages

5.

(a) An aquarium has 35 ray fish.
The cumulative frequency graph shows information about the lengths of these ray fish.
Cumulative frequency graph, cumulative frequency 0 to 35 against length of ray fish 0 to 100 cm, with points plotted at (0, 0), (20, 5), (40, 13), (60, 26), (80, 33) and (100, 35) joined by straight lines

Use the cumulative frequency diagram to give the best estimates for the answers to the following questions.

(i) What is the median length of these ray fish? [1]

…………………… cm

(ii) How many of these ray fish have lengths greater than 72 cm? [1]
(b) The aquarium also has guppies.
The table shows information about the length of the guppies in a sample of 60 guppies.
MinimumRangeMedianLower quartileInterquartile range
1·6 cm5·2 cm3·2 cm2·4 cm3·4 cm
(i) Draw a box-and-whisker plot of this data on the grid below. [4]
Blank grid with horizontal axis Length of guppies (cm) from 0 to 7
(ii) How many of the sample of 60 guppies have a length greater than or equal to 2·4 cm? [2]
(c) A carp was weighed in November 2021.
It was weighed again in April 2022.
The carp had a mass of 9·9 kg in April 2022.
Between these dates, the mass of the carp increased by 10%.

Calculate the mass of the carp in November 2021. [2]

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