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# The numbers of passengers on 9 airline ﬂights were 22, 33,

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The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  30 May 2019, 10:25
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The numbers of passengers on 9 airline ﬂights were 22, 33, 21, 28, 22, 31, 44, 50, and 19. The standard deviation of these 9 numbers is approximately equal to 10.2.

(a) Find the mean, median, mode, range, and interquartile range of the 9 numbers.
(b) If each ﬂight had had 3 times as many passengers, what would have been the mean, median, mode, range, interquartile range, and standard deviation of the 9 numbers?
(c) If each ﬂight had had 2 fewer passengers, what would have been the interquartile range and standard deviation of the 9 numbers?

[Reveal] Spoiler: OA
(a) mean=30,median=28,mode=22, range=31,interquartilerange=17 (b) mean=90,median=84,mode=66, range=93,interquartilerange=51, 940standarddeviation $$= 3 \sqrt{\frac{940}{9}} \approx 30.7$$ (c) interquartilerange=17,standarddeviation $$\approx 10.2$$

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Manager
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  04 Oct 2019, 01:19
May you pls explain how did you find the quartile and the interquartile here because we have an odd number set
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  04 Oct 2019, 01:31
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In this example that is mentioned in the Quant. Reasoning ETS P.308:
" Example 4.2.5: To find the quartiles for the ordered list of 16 numbers 2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, first divide the numbers in the list into two groups of 8 numbers each. The first group of 8 numbers is 2, 4, 4, 5, 7, 7, 7, 7 and the second group of 8 numbers is 7, 7, 8, 8, 9, 9, 9, 9, so that the second quartile, or median, is 7. To find the other quartiles, you can take each of the two smaller groups and find its median: the first quartile, Q sub 1, is 6 (the average of 5 and 7) and the third quartile, , Q sub 3, is 8.5 (the average of 8 and 9)."

When the set is divided into Q1 and Q3, each subset is 8 numbers. They took the 7s that were taken foe the median.

But at this example, the Median is excluded.

Pls Clarify.
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  04 Oct 2019, 02:29
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Inter quartile is dividing the list to 3 groups ( q1, q2 and q3) Lets say I have 11 numbers, then 3rd number will be q1, 6th will be q2, and 9th will be q3. So inter quartile is q3-q1.

If the list has even numbers i.e. 10, then q1 =(2nd +3rd)/2 q2=(5th + 6th)/2 and q3= (8th+9th)/2.
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  04 Oct 2019, 02:30
Can some one explain how the SD is calculated? As per my formula its not matching.
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  05 Oct 2019, 11:48
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List the 9 numbers, 19, 21, 22, 22, 28, 31, 33, 44, 50,

The middle one is 28. Q1=(21+22)/2=21.5; Q3=(33+44)/2=38.5; the IQR is their difference, so 17
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Re: The numbers of passengers on 9 airline ﬂights were 22, 33, [#permalink]  11 Oct 2019, 03:38
feibaobao wrote:
List the 9 numbers, 19, 21, 22, 22, 28, 31, 33, 44, 50,

The middle one is 28. Q1=(21+22)/2=21.5; Q3=(33+44)/2=38.5; the IQR is their difference, so 17

If we have 16 numbers as the 2nd example I mentioned. How do we solve it?

They took the median 7+7/2=7
why didn't they exclude the two 7s they use from the two groups ?
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