Question

each of 8 students reported the number of movies they saw in the past year. this is what they reported.
4, 18, 14, 13, 11, 15, 19, 8
find the median and mean number of movies that the students saw.
if necessary, round your answers to the nearest tenth.

(a) median: \\(\square\\) movies

(b) mean: \\(\square\\) movies

Explanation:

Step1: Find the Median

First, we need to order the data set from least to greatest. The data set is \(4, 18, 14, 13, 11, 15, 19, 8\). Ordering it gives: \(4, 8, 11, 13, 14, 15, 18, 19\). Since there are 8 (an even number) data points, the median is the average of the two middle numbers. The two middle numbers are the 4th and 5th values. The 4th value is \(13\) and the 5th value is \(14\). So, the median is \(\frac{13 + 14}{2}=\frac{27}{2} = 13.5\).

Step2: Find the Mean

The mean is calculated by summing all the data points and dividing by the number of data points. First, sum the data: \(4+8 + 11+13+14+15+18+19\). Let's calculate the sum: \(4+8=12\), \(12 + 11=23\), \(23+13 = 36\), \(36+14=50\), \(50+15 = 65\), \(65+18=83\), \(83+19 = 102\). There are 8 data points, so the mean is \(\frac{102}{8}=12.75\), which rounds to \(12.8\) (to the nearest tenth).

Answer:

(a) Median: \(13.5\) movies
(b) Mean: \(12.8\) movies