Mathematics · May / June 2023 · Paper 61 · Question 1

eg 1 person = 0.025 large squares/0.6 medium squares/2.5 small squares or

eg [1 small square =] 0.4 people/[1 medium square =] 10 people/[1 large square =] 40 people

eg a correct f.d. eg 60/(20 – 10) [= 6]

eg a correct frequency, 100, 70, 20, 24 associated with the appropriate bar

eg 8

or 15

or 40

or 30

10 ×

20

30 ×

24

or 8 2

×

or 0.8 15

×

2.5 or 8 5 0.4

××

2.5

2 15 0.4

×

×

or 16 or 12 or 70 0.4

×

28 people

5

5

Median

=

[5]

+

×

37

[10]

−

×

33

or

70

70

= 7.642... awrt 7.64

[

]

midpoint

×

freq

=

2.5 100

×

+

7.5 70

×

+

15 60

×

+

25

×

20

+

45

×

24

=

3255

"3255"

Mean

=

274

= 11.879… awrt 11.9

Notes

(a)

B1: for finding a ratio between people and area. Allow just the numbers for 1 person or for 1 square ie

0.025, 0.6, 2.5, 0.4, 1.66 or 40 or

calculating f.d. for any bar correctly, fd = 20, 14, 6, 2 or 0.8

Information may be seen on diagram. Must be clear it is a fd either by correct use, seen on axes

associated with correct bar or stated as an fd. May be implied by M1

M1: for a correct method to find the number of people between 22 and 30 km or 30 and 45 km or

between 22 and 45 km

A1: 28

NB An answer of 28 gains 3/3 unless from obvious incorrect working

(b)

5

−

137 100

−

33

−

170 137

−

Q

n

n

Q

n +

×

37

M1: Allow equivalent for

or

2

=

or

n −

×or

5

2

=

70

5

170 100

70

5

170 100

−

−

−

5

137

−

170

Q

Allow alternative methods eg

2

=

10

170 137

−

Q

−

2

Allow 37.5 for 37, 137.5 for 137, 32.5 for 33

A1: awrt 7.64 or 107

or allow awrt 7.68 or 215

28 if using n + 1 Allow awrt 7640 m or 7680 m but must

14

have units.

(c)

M1: Attempt at correct expression for

midpoint

×

freq

at least 3 products with correct midpoints

added with at least 1 of these products fully correct . Allow for 3255

M1: dep on M1 being awarded for dividing “their sum” by 274

A1: awrt 11.9 or 3255

274

Allow awrt 11900 m but must have units