Question

A popular streaming service surveyed all of the students at a school about the number of TV shows they streamed

last Friday night, then recorded the results.
Let M = the number of TV shows streamed last Friday night.
Number of Shows Streamed
0
1
2
3
Probability
0.095 0.203 0.326 0.187
Calculate the median of M. Use the histogram to corroborate your choice of the distribution's shape.
Since the shape of the distribution for number of TV shows streamed is
we expect the median
to be
the mean number of TV-shows streamed. This is confirmed when we calculate the
median to be compared to the mean of 2.187 TV shows streamed. The shape of the histogram supports the
relationship of the mean and the median because the mean is
4
0.174
5
0.015

Answer 1

Explanation:

To find the median, we need to find the middle value when the data is arranged in increasing order. We can use the cumulative probability to do this:

Number of Shows Streamed Probability Cumulative Probability

0 0.095 0.095

1 0.203 0.298

2 0.326 0.624

3 0.187 0.811

Since the cumulative probability for 2 is the smallest value greater than 0.5, the median is 2. Therefore, the median number of TV shows streamed is 2.

The histogram appears to have a roughly symmetric shape, which supports the assumption that the distribution is approximately normal.