thirty - six students at a large university were given a test to measure their intelligence quotient (iq). a…

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

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

Answer

Explanation:

Step1: Find the position of the median

There are $n = 36$ data - points. For a set of $n$ data - points, the position of the median is $\frac{n + 1}{2}=\frac{36+1}{2}=18.5$. This 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 90 - 93 is 1. The frequency of the interval 93 - 96 is 2. The frequency of the interval 96 - 99 is 3. The frequency of the interval 99 - 102 is 5. The cumulative frequency up to the interval 99 - 102 is $1 + 2+3 + 5=11$. The frequency of the interval 102 - 105 is 8. The cumulative frequency up to the interval 102 - 105 is $11 + 8=19$.

Step3: Locate the median interval

Since the 18th and 19th ordered data - points fall within the interval where the cumulative frequency first exceeds 18.5, the median is located in the 102 - 105 interval.

Answer:

102 - 105