Question

section 2, module 2—hard
10 mark for review
two data sets, o and p, are shown in the table. each data set consists of 31 values, and the table shows the frequencies of the values for each data set. which of the following best relates the medians of data set o and data set p?
(a) there is not enough information to compare the medians of data set o and data set p.
(b) the median of data set o is greater than the median of data set p.
(c) the median of data set o is less than the median of data set p.
(d) the median of data set o is equal to the median of data set p.

Explanation:

Step1: Find the position of the median

Since each data - set has $n = 31$ values, the position of the median is $\frac{n + 1}{2}=\frac{31+1}{2}=16$th value when the data is arranged in ascending order.

Step2: Calculate the cumulative frequencies for data set O

For data set O:

• For value 15, cumulative frequency $CF_1=11$.
• For value 18, cumulative frequency $CF_2=11 + 9=20$. Since $11<16<20$, the median of data set O is 18.

Step3: Calculate the cumulative frequencies for data set P

For data set P:

• For value 15, cumulative frequency $CF_1 = 3$.
• For value 18, cumulative frequency $CF_2=3 + 7 = 10$.
• For value 21, cumulative frequency $CF_3=10+9 = 19$. Since $10<16<19$, the median of data set P is 21.

Answer:

C. The median of data set O is less than the median of data set P.