1.1. Hattie’s homeroom teacher decides to summarise the number of minutes, t, she has been late to school during the last year in preparation for a parents’ meeting.  The results are shown in the table below.

Write down, in the context of the question, what the time interval -10 ≤ t < -5  represents.

1.2. (i) Using $x$ to represent the mid-point of each class, write an expression in terms of a for  $\Sigma fx$, giving your answer in simplified form. 

 (ii) Given that  $\Sigma fx$= 2132.5  and  $\Sigma f{x}^{2}$= 53568.75,  calculate the estimated mean and standard deviation of the amount of time Hattie was late for school last year.

1.3. Hattie happens to notice that on three of the days she was recorded as being 40 minutes late for school, she had actually arrived 40 minutes early.  Calculate the corrected estimate for the mean amount of time she was late for school last year.