Practise IB Maths AI SL statistics and probability through data analysis, distributions, regression and technology-supported models with clear interpretation.
Elsie, a librarian, wants to investigate the length of time, T minutes, that people spent in her library on a particular day.
State whether the variable T is discrete or continuous.
Elsie's data for 160 people who visited the library on that particular day is shown in the following table.
Find the value of k.
Write down the modal class.
Write down the mid-interval value for this class.
Use Elsie's data to calculate an estimate of the mean time that people spent in the library.
Using the table, write down the maximum possible number of people who spent 35 minutes or less in the library on that day.
Elsie assumes her data to be representative of future visitors to the library.
Find the probability a visitor spends at least 60 minutes in the library.
The following box and whisker diagram shows the times, in minutes, that the 160 visitors spent in the library.
Write down the median time spent in the library.
Find the interquartile range.
Hence show that the longest time that a person spent in the library is not an outlier.
Elsie believes the box and whisker diagram indicates that the times spent in the library are not normally distributed.
Identify one feature of the box and whisker diagram which might support Elsie's belief.
The mean annual temperatures for Earth, recorded at fifty-year intervals, are shown in the table.
Tami creates a linear model for this data by finding the equation of the straight line passing through the points with coordinates (1708,8.73) and (1958,9.45).
Thandizo uses linear regression to obtain a model for the data.
Find the equation of the regression line y on x.
Find the value of r, the Pearson's product-moment correlation coefficient.
Use Thandizo's model to estimate the mean annual temperature in the year 2000.