vestirme4
2021-09-01
Answered

Create a problem for additional rules and do the two-way tables, please.

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Macsen Nixon

Answered 2021-09-02
Author has **117** answers

A class of 20 students, 8 of which are boys were asked whether they take additional classes or not.
5 girls have additional classes and 5 boys do not have them. Create a two-way table to illustrate the results. A student is chosen at random.
1) Arrange the data from above in a two-way table.
2) A boy and has additional classes.
3) A girl and does not have additional classes.
4) A boy is chosen, and he has additional classes.
5) A girl is chosen, and she does not take additional classes.

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asked 2022-06-14

Suppose we have data set: $19,21,22,22,28,31,33,44,50$. Find the interquartile range of this set.

First solution: Firstly, we should find the $75$th percentile of this set. $0,75\cdot 9=6,75$ and rounding up this number to nearest whole we get $7$. So the $75$th percentile of this set is $33$. Secondly, should find the $25$th percentile of this set. $0,25\cdot 9=2,25$ and rounding up this number to nearest whole we get $3$. So the $25$th percentile of this set is $22$. Hence,

$\text{interquartile range}={Q}_{3}-{Q}_{1}=33-22=11.$

Second solution: The median of this set is $28$. First quartile is the median of lower set. Hence ${Q}_{1}={\displaystyle \frac{21+22}{2}}=21.5$, third quartile is the median of upper set. Hence ${Q}_{3}={\displaystyle \frac{33+44}{2}}=38.5$

$\text{interquartile range}={Q}_{3}-{Q}_{1}=38.5-21.5=17.$

Which one is correct? Please explain why one of the solutions is false.

First solution: Firstly, we should find the $75$th percentile of this set. $0,75\cdot 9=6,75$ and rounding up this number to nearest whole we get $7$. So the $75$th percentile of this set is $33$. Secondly, should find the $25$th percentile of this set. $0,25\cdot 9=2,25$ and rounding up this number to nearest whole we get $3$. So the $25$th percentile of this set is $22$. Hence,

$\text{interquartile range}={Q}_{3}-{Q}_{1}=33-22=11.$

Second solution: The median of this set is $28$. First quartile is the median of lower set. Hence ${Q}_{1}={\displaystyle \frac{21+22}{2}}=21.5$, third quartile is the median of upper set. Hence ${Q}_{3}={\displaystyle \frac{33+44}{2}}=38.5$

$\text{interquartile range}={Q}_{3}-{Q}_{1}=38.5-21.5=17.$

Which one is correct? Please explain why one of the solutions is false.

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