Working out quartiles Q1, Q2, Q3???

Hello, for edexcel statistics S1 what is the best way to work out the quartiles, Q1,median,Q2? I know there are a few ways and in past paper questions sometime one method will give the right answer but other times it wont.

So does it matter which method you use, or do the examiners expect varied answers?

Is the best method e.g. for median: n/4 and if whole number it is the midpoint of the corresponding term and the term above but if it is not a whole number round up and find the corresponding term?

Reply 1

Crash_Brinicombe

Use this formula for a frequency table (see attached file)

for Q1 use n/4
for Q2 use 3n/4

Median.jpg24.0KB

Reply 2

beelz

For continuous data, use n/4, n/2, and 3n/4 for Q1, Q2 and Q3 respectively.

For discrete variables: For Q1, find the midpoint of the (n/4)th value and the value above the (n/4)th value
For Q2, find the midpoint of the (n/2)th value and the value above the (n/2)th value
For Q3, find the midpoint of the (3n/4)th value and the value above the (3n/4)th value

This is the method that you should use for Edexcel exams.

Reply 3

Groat

13

Original post by beelz

For continuous data, use n/4, n/2, and 3n/4 for Q1, Q2 and Q3 respectively.

For discrete variables: For Q1, find the midpoint of the (n/4)th value and the value above the (n/4)th value
For Q2, find the midpoint of the (n/2)th value and the value above the (n/2)th value
For Q3, find the midpoint of the (3n/4)th value and the value above the (3n/4)th value

This is the method that you should use for Edexcel exams.

Just to clarify with a set of discrete variables (Z):

If

\frac{n}{4} = x, x \in \mathbb{Z}

then:

Q_{1} = \frac{Z_{x} + Z_{x+1}}{2}

If

\frac{n}{4} = x, x \notin \mathbb{Z}

then:

Round x up to y, and use

Q_{1} = Z_{y}

Sorry for all the LaTeX, I've never really used it before so I doubt my notation is any good!

Reply 4

al_habib

1

Question on probability

A six-sided die is biased such that there is an equal chance of scoring each of the numbers from 1 to 5 but a score of 6 is three times more likely than each of the other numbers.
(a) Write down the probability distribution for the random variable, X, the score on a single throw of the die.

Reply 5

gdunne42

21

Original post by al_habib

Question on probability

A six-sided die is biased such that there is an equal chance of scoring each of the numbers from 1 to 5 but a score of 6 is three times more likely than each of the other numbers.
(a) Write down the probability distribution for the random variable, X, the score on a single throw of the die.

P(X=1) = k, P(X=2) = k, P (X=3) = k, P(X=4) = k, P(X=5) = k, P(X=6)= 3k

can you work it out from there?

Reply 6

al_habib

1

Original post by gdunne42

P(X=1) = k, P(X=2) = k, P (X=3) = k, P(X=4) = k, P(X=5) = k, P(X=6)= 3k

can you work it out from there?

the ans reads as

x 1 2 3 4 5 6

P(X=x) 1/8 1/8 1/8 1/8 1/8 3/8

i wonder y they are using /8 instead of /6

Reply 7

al_habib

1

i did part a & b struggling with c & d

The individual letters of the word STATISTICAL are written on 11 cards which are then shuffled.
One card is selected at random. Find the probability that it is

(a) a vowel, (1 mark)

(b) a T, given that it is a consonant. (2 marks)
The 11 cards are then shuffled again and the top three are turned over. Find the probability that

(c) all three of the cards have a T on them, (3 marks)

(d) at least two of the cards show a vowel. (6 mark

Working out quartiles Q1, Q2, Q3???

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