The table gives some information about the ages of 100 people visiting a museum. In which class interval is the median? Circle your answer.
The table tells us there were 17 people greater than zero years of age but less than or equal to 15. There were 35 people greater than 15 but less than or equal to 30. There were 22 people between the ages of 30 and 60. And finally, there were 26 people between the ages of 60 and 90. We were asked to work out which of the four class intervals is the median.
The median is the middle number when all of our data is in order from smallest to largest. In this question, we need to work out which group the middle person’s age lies in. We can work out who the median person is using the following expression: 𝑛 plus one divided by two, where 𝑛 is the total number of people, in this case 100.
We could check this value by adding 17, 35, 22, and 26, the four frequencies from the table. We need to add one to 100 and then divide by two. 100 plus one is equal to 101. We need to halve this answer or divide it by two. 101 divided by two is equal to 50.5. We can therefore say that the median lies between the 50th and 51st person.
As the table is already in order of age, our next step is to calculate the cumulative frequencies. The cumulative frequency is the running total. The first number in our cumulative frequency column is the same as the frequency, 17, as there are 17 people less than or equal to 15 years of age.
To calculate the number of people less than or equal to 30 years of age, we need to add 17 and 35. This is equal to 52. Therefore, 52 people are less than or equal to 30 years of age.
We can repeat this process for the next group by adding 52 and 22. This is equal to 74. Therefore, 74 people who visited the museum are less than or equal to 60 years of age. Finally, we need to add 74 and 26, which gives us a total of 100. All 100 people who visited the museum were less than or equal to 90 years of age.
We worked out earlier that the median was between the 50th and 51st person. As 50 and 51 are less than 52, we know that the median will lie in the second group. The median age is greater than 15 but less than or equal to 30.
We can therefore conclude that, of the 100 people who visited the museum, the class interval, that is, the median, is 𝑦 is greater than 15 but less than or equal to 30.