Find the percentile for the data point.
-The weights (in pounds)of 30 newborn babies are listed below. Find $\mathrm { Q } _ { 1 }$ $$\begin{array} { l l l l l l l l l l }
5.5 & 5.7 & 5.8 & 6.0 & 6.1 & 6.1 & 6.3 & 6.4 & 6.5 & 6.6 \
6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \
7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7
\end{array}$$
A)6.4
B)5.8
C)7.5
D)6.3

Question

Find the percentile for the data point.
-The weights (in pounds)of 30 newborn babies are listed below. Find $\mathrm { Q } _ { 1 }$ $$\begin{array} { l l l l l l l l l l } 
5.5 & 5.7 & 5.8 & 6.0 & 6.1 & 6.1 & 6.3 & 6.4 & 6.5 & 6.6 \
6.7 & 6.7 & 6.7 & 6.9 & 7.0 & 7.0 & 7.0 & 7.1 & 7.2 & 7.2 \
7.4 & 7.5 & 7.7 & 7.7 & 7.8 & 8.0 & 8.1 & 8.1 & 8.3 & 8.7
\end{array}$$
A)6.4
B)5.8
C)7.5
D)6.3

Quizplus · Accepted Answer

To find the first quartile ($Q_1$), which represents the 25th percentile, we arrange the data in ascending order (which it already is) and then find the value below which 25% of the data fall. With 30 data points, the position of $Q_1$ is found using the formula $P = \frac{1 + N}{4}$, where $P$ is the position and $N$ is the total number of data points. Substituting $N = 30$, we get $P = \frac{1 + 30}{4} = 7.75$. This means $Q_1$ is between the 7th and 8th data points. The 7th data point is 6.3 and the 8th is 6.4. Since the position is not a whole number, $Q_1$ is a value between these two, but since we are looking for the closest value in the options provided, 6.4 is the correct answer because it is the value that 25% of the data points do not exceed.

Find the Percentile for the Data Point Q1\mathrm { Q } _ { 1 }Q1​

Find the Percentile for the Data Point $\mathrm { Q } _ { 1 }$