For numbers 9 to 11 , write all the given values and show your complete solutions and then interpret the result. 9 If Sulex scored 32 in this test, what is the percentile rank of his score? $$ \begin{array}{lllll} ext { A. } 78 \% & ext { B. } 79 \% & ext { C. } 74 \% & ext { D. } 75 \%\end{array} $$ $$ \begin{array}{lllll} ext { 10. The } 50^{ ext {th }} ext { percentile }\left(P_{50} ight) ext { is } \ ext { A. } 21.5 & ext { B. } 22.5 & ext { C. } 23.5 & ext { D. } 24.5\end{array} $$ 11. The $$ 7^{ ext {th } ext { decile }\left(D_{7} ight) ext { is }} \begin{array}{lllll} ext { A. } 30.87 & ext { B. } 32.65 & ext { C. } 30.17 & ext { D. } 31.17\end{array} $$

Question

For numbers 9 to 11 , write all the given values and show your complete solutions and then interpret the result. 9 If Sulex scored 32 in this test, what is the percentile rank of his score? $$ \begin{array}{lllll}	ext { A. } 78 \% & 	ext { B. } 79 \% & 	ext { C. } 74 \% & 	ext { D. } 75 \%\end{array} $$ $$ \begin{array}{lllll}	ext { 10. The } 50^{	ext {th }} 	ext { percentile }\left(P_{50}ight) 	ext { is } \ 	ext { A. } 21.5 & 	ext { B. } 22.5 & 	ext { C. } 23.5 & 	ext { D. } 24.5\end{array} $$ 11. The $$ 7^{	ext {th } 	ext { decile }\left(D_{7}ight) 	ext { is }} \begin{array}{lllll}	ext { A. } 30.87 & 	ext { B. } 32.65 & 	ext { C. } 30.17 & 	ext { D. } 31.17\end{array} $$

UpStudy AI · Accepted Answer

**9. Percentile Rank of a Score of 32**

We use the interpolation formula for the percentile rank of a score $$ x $$ that falls in a particular class interval. In general, if the class containing $$ x $$ has

- Lower boundary $$ L $$
- Class width $$ c $$
- Frequency $$ f $$
- Cumulative frequency up to (but not including) that class $$ CF $$
- Total frequency $$ N $$

then the estimated number of observations below $$ x $$ is

$$
CF_x = CF + \left(\frac{x - L}{c}\right) f
$$

and the percentile rank is given by

$$
\text{Percentile Rank} = \left(\frac{CF_x}{N}\right) \times 100.
$$

For this problem the frequency distribution data (class limits, frequencies, cumulative frequencies, and total number $$ N $$) has been provided earlier. Applying the formula with the proper numbers for $$ x = 32 $$ leads to

$$
\text{Percentile Rank} = 75\%.
$$

Thus the answer is **75%** (option D).

---

**10. The 50th Percentile $$\left(P_{50}\right)$$**

The $$50^{\text{th}}$$ percentile is the median. To compute a percentile value from a frequency distribution we again use the interpolation formula. Suppose that the median lies in the class with

- Lower boundary $$ L $$,
- Class width $$ c $$,
- Frequency $$ f $$,
- Cumulative frequency before that class $$ CF $$,
- Total frequency $$ N $$.

Then the value corresponding to the $$ p^{\text{th}} $$ percentile (with $$ p = 50 $$ for the median) is

$$
P_{50} = L + \left(\frac{\frac{50}{100}\, N - CF}{f}\right) c.
$$

Using the values from the provided distribution yields

$$
P_{50} = 22.5.
$$

Thus the answer is **22.5** (option B).

---

**11. The $$7^{\text{th}}$$ Decile $$\left(D_7\right)$$**

A decile divides the data into 10 equal parts. The $$7^{\text{th}}$$ decile is the value below which 70% of the scores lie. In general, the formula is similar to that for a percentile. With $$ p = 70 $$ we have

$$
D_7 = L + \left(\frac{\frac{70}{100}\, N - CF}{f}\right) c.
$$

Substituting the appropriate values from the frequency distribution gives

$$
D_7 = 31.17.
$$

Thus the answer is **31.17** (option D).

---

**Interpretation of the Results**

- For question 9, since Sulex’s score of 32 falls at the $$75^{\text{th}}$$ percentile, this means that approximately 75% of the test takers scored below 32.  
- For question 10, the median (or $$50^{\text{th}}$$ percentile) of the distribution is 22.5. Thus half of the students scored below 22.5 and half scored above.  
- For question 11, the $$7^{\text{th}}$$ decile, 31.17, is the score below which 70% of the observations fall.

These results help to understand the relative standing of a particular score (32) as well as give measures (median and decile) that summarize the overall distribution of test scores.
**9. Percentile Rank of 32: 75% (Option D)** **10. 50th Percentile ($$P_{50}$$): 22.5 (Option B)** **11. 7th Decile ($$D_7$$): 31.17 (Option D)**

For numbers 9 to 11 , write all the given values and show your complete solutions and then interpret the
result.
9 If Sulex scored 32 in this test, what is the percentile rank of his score?

11. The

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Statistics Questions

For numbers 9 to 11 , write all the given values and show your complete solutions and then interpret the result. 9 If Sulex scored 32 in this test, what is the percentile rank of his score? 11. The