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.
