Question

Below is a data set of the length of times, in seconds, that it took for nine boys to find Waldo.
10 7 29 8 13 12 13 11 8
1. Write the numbers in order and circle the median.
a. About what part of the values in a data set are BELOW the median? How do you
know this?
b. About what percent of values in a data set are ABOVE the median? How do you know
this?

Answer 1

First, let's arrange the provided times in ascending order:

**Ordered data set:**
7, 8, 8, 10, 11, 12, 13, 13, 29

Next, we need to find the median. The median is the middle number in a sorted list. Since we have 9 values (an odd number), the median is the 5th number in this ordered list.

**Median:**
- The 5th value is **11**.

Now, to circle the median, you can visualize it as follows:
- Ordered data set: 7, 8, 8, 10, **11**, 12, 13, 13, 29

### a. About what part of the values in a data set are BELOW the median?

To find the part of the values that are below the median:

- Values below 11: **7, 8, 8, 10**
- There are 4 values below the median (11).

Since there are a total of 9 values in the data set, the part that is below the median is:
\[
\frac{4}{9} \approx 0.444 \text{ or } 44.4\%
\]

### b. About what percent of values in a data set are ABOVE the median?

Now, to determine the values above the median:

- Values above 11: **12, 13, 13, 29**
- There are 4 values above the median (11).

Similarly, the part that is above the median is:
\[
\frac{4}{9} \approx 0.444 \text{ or } 44.4\%
\]

### Summary:
- Median: 11
- Approximately 44.4% of the values are below the median.
- Approximately 44.4% of the values are above the median.

Finally, in the case of a data set with an odd number of observations:
- There is always exactly one median with equal numbers of values on either side (in this case, 4 values below and 4 values above).