Suppose 240 nursing students took a certification test that is worth 140 points. The five-number summary for the scores is shown here:

[tex]\[
\begin{aligned}
\text{min value} & = 68 \\
Q_1 & = 110 \\
\text{median} & = 125 \\
Q_3 & = 130 \\
\max \text{value} & = 138
\end{aligned}
\][/tex]

About how many students had a score of 130 or less?



Answer :

To determine the number of students out of 240 who had a score of 130 or less given the five-number summary, we need to consider what the third quartile (Q3) represents.

1. Understanding Q3: The third quartile (Q3) is the score below which 75% of the data falls. In other words, Q3 represents the 75th percentile.

2. Interpreting Q3: In this case, Q3 value is given as 130. This means that 75% of the students scored 130 or less on the certification test.

3. Calculate the number of students: To find how many students scored 130 or less, we calculate 75% of 240.
[tex]\[ \text{Number of students who scored 130 or less} = 0.75 \times 240 \][/tex]

4. Perform the multiplication:
[tex]\[ 0.75 \times 240 = 180 \][/tex]

Therefore, about 180 students had a score of 130 or less.