Question

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Answer 1

Answer:

I. p = 7

II. 17 litres

Step-by-step explanation:

I. Determination of the value of p

Mean = 17.7

p =.?

Let the number of litre be L

Let the number of motorist be M

Mean = summation LM / summation M

Summation of LM = (16×11) + (17×10) + (18×p) + (19×4) + (20×8)

= 176 + 170 + 18p + 76 + 160

= 582 + 18p

summation M = 11 + 10 + P + 4 + 8

= 33 + p

Mean = summation LM / summation M

17.7 = 582 + 18p / 33 + p

Cross multiply

17.7(33 + p) = 582 + 18p

584.1 + 17.7p = 582 + 18p

Collect like terms

584.1 – 582 = 18p – 17.7p

2.1 = 0.3p

Divide both side by 0.3

p = 2.1 / 0.3

p = 7

II. Determination of the median number of litre.

Let the number of motorist be M (i.e the frequency)

summation M = 11 + 10 + P + 4 + 8

p = 7

summation M = 11 + 10 + 7 + 4 + 8

summation M = 40

The median is the middle term i.e

Median = (summation M / 2)ᵀʰ motorist

Median = (40 / 2)ᵀʰ motorist

Median = 20ᵀʰ motorist

Considering the table in the question above, the 20ᵀʰ motorist has 17 litres.

Therefore, the median number of litres is 17 litres.