Calculate reasonable value for $PR_{70}$ and $PR_{80}$ for example no. 43 (given in Percentile rank of grouped data).

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Accepted Answer

> [!TLDR] The method for $PR_{70}$ and $PR_{80}$ (the 70th and 80th percentiles of grouped data) follows directly from the percentile formula applied twice with $k=70$ and $k=80$ — but this question explicitly reuses Example 43's frequency table from the textbook, which is not part of the extracted content available to us, so we present the exact method rather than invent class-interval figures.

> [!FORMULA] For a grouped (continuous) frequency distribution with total frequency $N=\sum f$:
> $$P_k = l + \frac{\dfrac{kN}{100}-cf}{f}	imes h$$
> where $l$ = lower boundary of the class containing $P_k$ (found by locating $\frac{kN}{100}$ in the cumulative-frequency column), $cf$ = cumulative frequency of the class just before it, $f$ = frequency of the $P_k$-class, $h$ = class width.

1. From Example 43's cumulative-frequency ($cf$) column, compute the two target ranks: $\dfrac{70N}{100}=0.70N$ and $\dfrac{80N}{100}=0.80N$.
2. Locate the class-interval in which each rank falls: the class whose cumulative frequency first **equals or exceeds** $0.70N$ contains $PR_{70}$; similarly for $0.80N$ and $PR_{80}$.
3. For $PR_{70}$: read off that class's lower boundary $l$, the cumulative frequency $cf$ of the class immediately before it, its own frequency $f$, and the class width $h$; substitute into $P_{70}=l+\dfrac{0.70N-cf}{f}	imes h$.
4. For $PR_{80}$: repeat step 3 with the class containing $0.80N$, substituting into $P_{80}=l+\dfrac{0.80N-cf}{f}	imes h$.
5. Since $80\% > 70\%$, expect $P_{80} > P_{70}$ as a self-check (a higher percentile rank must correspond to a value further up the distribution) — if the arithmetic gives $P_{80}\le P_{70}$, re-check the class-location step. …

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Q.Calculate reasonable value for $PR_{70}$ and $PR_{80}$ for example no. 43 (given in Percentile rank of grouped data).

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Q.Calculate reasonable value for PR70PR_{70}PR70​ and PR80PR_{80}PR80​ for example no. 43 (given in Percentile rank of grouped data).

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Q.Calculate reasonable value for $PR_{70}$ and $PR_{80}$ for example no. 43 (given in Percentile rank of grouped data).

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