3. James recorded the times, in minutes, for 20 students to complete a test. The information about these times is shown in the table. Time (t mins) & Frequency & & 0<t leq 4 & 4 & & 4<t leq 8 & 11 & & 8<t leq 12 & 4 & & 12<t leq 16 & 1 & & (a) Write down the modal class interval.

## Step1: Understand the TableFirst, we understand the structure of the given table. Each row represents an interval of time and the number of students, referred to as frequency, who completed the test in that interval of time. ## Step2: Modal Class IntervalThe modal class interval is the interval of time that has the highest frequency.## Step3: Mean calculationTo estimate the mean test time, we need to first calculate the total test time, and then divide that by the number of students. To find this total test time, the frequency is first multiplied by the midpoint of each specific sub-interval and these results are then summed. The midpoint of each sub-interval can be found by adding the lower and upper bounds of that sub-interval and dividing by 2. ### Midpoints:The midpoints are:for : \(\frac{(4 + 0)}{2} = 2\)for : \(\frac{(8 + 4)}{2} = 6\)for : \(\frac{(12 + 8)}{2} = 10\)for : \(\frac{(16 + 12)}{2} = 14\)By multiplying these by their respective frequencies we can estimate the total test times: 2 * 4 + 6 * 11 + 10 * 4 + 14 * 1 = 132 minutesThen, this total is divided by the total number of students. The total number of students is found by summing the frequencies: this totals 20.### The estimation of mean time:The estimation of mean time is: minutes, considering you rounded up to the tenths.