MHB (IB18) A box contains 100 cards

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The discussion focuses on calculating statistical measures for a dataset of 100 cards. Participants confirm that the total frequency must equal 100 and calculate the median as 15.5 using the ordered list of data. For the interquartile range (IQR), they clarify that it should be calculated using the actual data values rather than frequencies, determining Q1 and Q3 from the appropriate elements. The final IQR is confirmed to be 4. The conversation emphasizes the importance of using the correct data for accurate statistical analysis.
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(a) I presume the frequency row has to equal 100
so
$$k=100 - (26 + 10 + 20 + 29 + 11)= 4$$(b)(i) again presume the median is based on frequency and on ordered list
so
median of $4\ 10\ 11 \ 20\ 26\ 29 = \frac{31}{2}$ or $15.5$

(ii) interquartile range? isn't this data list 100 numbers long?
or is $Q_1=10$ and $Q_3=26$ so interquartile range$=26-10=13$
 
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Re: (IB18) A box contains a 100 cards

For part b), you want to use the data, not the frequencies, in your calculations. To find the median (or $Q_2$) you observe that there is an even number of elements, so you take the arithmetic mean of the 50th and 51st elements.

Now, since there is an even number of elements in each half, you want to take the arithmetic mean of the 25th and 26th elements as $Q_1$ and the arithmetic mean of the 75th and 76th elements as $Q_3$. And then the inter-quartile range is given by:

$$IQR=Q_3-Q_1$$
 
Re: (IB18) A box contains a 100 cards

MarkFL said:
For part b), you want to use the data, not the frequencies, in your calculations. To find the median (or $Q_2$) you observe that there is an even number of elements, so you take the arithmetic mean of the 50th and 51st elements.

Now, since there is an even number of elements in each half, you want to take the arithmetic mean of the 25th and 26th elements as $Q_1$ and the arithmetic mean of the 75th and 76th elements as $Q_3$. And then the inter-quartile range is given by:

$$IQR=Q_3-Q_1$$

I got 5-1=4 IQR
 
Re: (IB18) A box contains a 100 cards

karush said:
I got 5-1=4 IQR

Yes, I got the same. :D
 
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