Question

7 from unit 1, lesson 3 the histogram represents the distribution of the number of seconds it took for each of 50 students to find the answer to a trivia question using the internet. which interval contains the median? a. 0 to 5 seconds b. 5 to 10 seconds c. 10 to 15 seconds d. 15 to 20 seconds

Explanation:

Step1: Determine position of median

There are $n = 50$ data - points. For a set of $n$ data - points (where $n$ is even), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered data - points. Here, $\frac{n}{2}=\frac{50}{2}=25$ and $\frac{n}{2}+1 = 26$. So, we need to find the class interval that contains the 25th and 26th ordered data - points.

Step2: Calculate cumulative frequencies

The frequencies for the intervals are:

• For $0 - 5$ seconds: $22$
• For $5 - 10$ seconds: $6$
• For $10 - 15$ seconds: $8$
• For $15 - 20$ seconds: $10$
• For $20 - 25$ seconds: $4$
• For $25 - 30$ seconds: $0$

The cumulative frequency for the $0 - 5$ seconds interval is $22$. The cumulative frequency for the $5 - 10$ seconds interval is $22 + 6=28$.

Step3: Identify median - containing interval

Since the 25th and 26th data - points fall within the cumulative frequency range of the $5 - 10$ seconds interval (because the cumulative frequency up to the $0 - 5$ seconds interval is $22$ and up to the $5 - 10$ seconds interval is $28$), the median lies in the $5 - 10$ seconds interval.

Answer:

B. 5 to 10 seconds