[填空题]
The London National Theatre iqwt9wnsj7m 0,s presenting the famous Shakespearean play Hamlei+xsn;79a fucpfs4e: t. Matthew is interested ;uc9p ei:s4f sanxf7+in the age range of the audience attendees and collects data by standing at the entrance and sampling every fifth audience member as they enter the theatre. Using this data, he constructs a box-and-whisker diagram to represent the data, as shown below.
1. State the sampling method Matthew used in his study.
2. Write down the median age of the sample.
3. Calculate the interquartile range.
The youngest audience member sampled, Rosie, is just 15 years old. Matthew believes that Rosie is an outlier and is considering excluding her from the sample data set. years
4. Determine if Matthew is correct. Give a reason to your answer.
When asking their ages, Matthew also asks how many other Shakespearean plays they have watched in their lifetime ( y ). The following scatter diagram shows this data, paired with their age (x) .
5. Describe the correlation between the two variables.
Matthew used the data to calculate the equation of the regression line y on x as
y=0.458 x-5.76
Matthew used this equation to estimate the number of Shakespearean plays a 65 year old audience attendee would have previously watched.
6. 1. Determine Matthew's estimate.≈
2. State whether it is valid to use the line of regression equation for this estimate. Give a reason for your answer.
Matthew, an avid Shakespearean fan, wants to understand if there is a relationship between his favourite Shakespearean plays and their length, measured by total run time in minutes. He creates a table, shown below, and ranks 8 Shakespearean plays (A-H), their run time length, and his rating out of all the Shakespearean plays he has seen ( 1 being his favourite).
For this analysis, Matthew uses the Spearman's rank correlation coefficient, r s to understand the relationship between the variables. A rank table is created.
7. Copy and complete the rank table.
8. 1. Calculate the value of $r_{s}$ .
2. Interpret the result.
