Question

thirty - six students at a large university were given a test to measure their intelligence quotient (iq). a histogram of the iq test scores is shown below. in each interval, the left endpoint is included in the interval, but not the right endpoint. iq scores in which interval is the median located? 99 - 102 102 - 105 105 - 108 108 - 111

Explanation:

Step1: Determine total number of data points

There are $n = 36$ students. Since $n$ is even, the median is the average of the $\frac{n}{2}=18$ - th and $(\frac{n}{2}+ 1)=19$ - th ordered data - points.

Step2: Calculate cumulative frequencies

Starting from the left - hand side of the histogram:

• For the interval $90 - 93$: frequency $f_1=1$
• For the interval $93 - 96$: frequency $f_2 = 2$
• For the interval $96 - 99$: frequency $f_3=3$
• For the interval $99 - 102$: frequency $f_4 = 5$
• Cumulative frequency up to $99 - 102$ is $1 + 2+3 + 5=11$
• For the interval $102 - 105$: frequency $f_5 = 8$
• Cumulative frequency up to $102 - 105$ is $11+8 = 19$

The 18 - th and 19 - th ordered data - points fall within the interval $102 - 105$.

Answer:

$102 - 105$