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. in which interval is the median located? 99 - 102 102 - 105 105 - 108 108 - 111 iq scores

Explanation:

Step1: Find the position of the median

Since there are $n = 36$ data - points, the position of the median is $\frac{n+1}{2}=\frac{36 + 1}{2}=18.5$, which means the median is the average of the 18th and 19th ordered data - points.

Step2: Calculate cumulative frequencies

Starting from the left - hand side of the histogram:
The frequency of the interval 93 - 96 is 1, cumulative frequency $CF_1=1$.
The frequency of the interval 96 - 99 is 3, cumulative frequency $CF_2=1 + 3=4$.
The frequency of the interval 99 - 102 is 5, cumulative frequency $CF_3=4 + 5=9$.
The frequency of the interval 102 - 105 is 8, cumulative frequency $CF_4=9+8 = 17$.
The frequency of the interval 105 - 108 is 6, cumulative frequency $CF_5=17 + 6=23$.

Step3: Locate the median

The 18th and 19th ordered data - points fall within the interval 105 - 108 because the cumulative frequency up to the 102 - 105 interval is 17 and the cumulative frequency up to the 105 - 108 interval is 23.

Answer:

105 - 108