Questions: 26 randomly selected students were asked the number of movies they watched the previous week. The results are as follows: # of Movies 0 1 2 3 4 5 6 Frequency 7 4 3 4 2 4 2 Round all your answers to 4 decimal places where possible. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents watched at least 4 movies the previous week? % 43% of all respondents watched fewer than how many movies the previous week

26 randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

# of Movies 0 1 2 3 4 5 6
Frequency 7 4 3 4 2 4 2

Round all your answers to 4 decimal places where possible.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:

What percent of the respondents watched at least 4 movies the previous week? %
43% of all respondents watched fewer than how many movies the previous week

Transcript text: 26 randomly selected students were asked the number of movies they watched the previous week. The results are as follows: \begin{tabular}{|c|l|l|l|l|l|l|l|} \hline \# of Movies & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 7 & 4 & 3 & 4 & 2 & 4 & 2 \\ \hline \end{tabular} Round all your answers to 4 decimal places where possible. The mean is: $\square$ The median is: $\square$ The sample standard deviation is: $\square$ The first quartile is: $\square$ The third quartile is: $\square$ What percent of the respondents watched at least 4 movies the previous week? $\square$ \% 43\% of all respondents watched fewer than how many movies the previous week $\square$

Solution

Solution Steps

Step 1: Mean Calculation

The mean is calculated as the sum of each category's value multiplied by its frequency, divided by the total number of observations. Thus, the mean is 2.385.

Step 2: Median Calculation

The median is found based on the cumulative frequency distribution. For our data, the median is 1.

Step 3: Sample Standard Deviation Calculation

The sample standard deviation is calculated using the formula for the square root of the sum of squared differences between each category's midpoint and the mean, each weighted by the category's frequency, divided by n-1. The standard deviation is 2.080.

Step 4: Quartiles Calculation

The first quartile (Q1) is the value below which 25% of the data falls, and it is 0. The third quartile (Q3) is the value below which 75% of the data falls, and it is 4.