SOLUTION: The marks of 10 pupils in JSH three are 88, 80, 75, 70, 38, 45, 70, 60, 60, 50. Find the (a) arithmetic mean mark (b) modal mark (c) third quartile

Question 1190711: The marks of 10 pupils in JSH three are 88, 80, 75, 70, 38, 45, 70, 60, 60, 50. Find the
(a) arithmetic mean mark
(b) modal mark
(c) third quartile
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Part (a)

Add up the scores and you should get 636
Divide that over n = 10 (the number of scores) to get the arithmetic mean

Answer: 63.6

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Part (b)

Start by sorting the data to go from this
{88, 80, 75, 70, 38, 45, 70, 60, 60, 50}
to this
{38, 45, 50, 60, 60, 70, 70, 75, 80, 88}

The mode is the most frequent value. In this case, there are two values that tie for the most frequent
60 shows up twice, and so does 70.
It's possible to get more than one mode.

Answer: Mode = {60, 70}

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Part (c)

The median of
{38, 45, 50, 60, 60, 70, 70, 75, 80, 88}
is the midpoint between slot 5 and slot 6

Averaging the numbers in those slots gets us (60+70)/2 = 130/2 = 65
The median is 65
Split the data set into two halves based on this middle marker

L = numbers lower than 65
L = {38, 45, 50, 60, 60}
U = numbers above 65
U = {70, 70, 75, 80, 88}

Now find the median of set L to get Q1 = 50
Q1 = first quartile

We also find that Q3 = 75 is the median of set U.

The five number summary of this data set is
min = 38
Q1 = 50
median (Q2) = 65
Q3 = 75
max = 88

Answer: 75 is the third quartile

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