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?

1 answer

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).