What is the range of these a separate piece of paper, make a grouped frequency table using the intervals 141 tio 150,151 to 160 and so on. Use the table to answer these questions. (i) In which interval did most of the students guess? (ii) How many students' guesses were between 191 and 200 grams?

1. We first find the range of the data. Recall that the range is given by \[ \text{Range} = \text{Maximum value} - \text{Minimum value}. \] Suppose that after checking the raw data on the separate paper we observe that the lowest guess is \(141\) grams and the highest guess is \(200\) grams. Then the range is \[ 200 - 141 = 59 \text{ grams}. \] 2. Next, we form a grouped frequency table using the following intervals: - \(141 \text{ to } 150\) - \(151 \text{ to } 160\) - \(161 \text{ to } 170\) - \(171 \text{ to } 180\) - \(181 \text{ to } 190\) - \(191 \text{ to } 200\) Assume we tally the frequencies from the raw data and obtain a table similar to this: | Interval | Frequency | |------------------|-----------| | \(141\) to \(150\) | 2 | | \(151\) to \(160\) | 5 | | \(161\) to \(170\) | 8 | | \(171\) to \(180\) | 10 | | \(181\) to \(190\) | 4 | | \(191\) to \(200\) | 3 | 3. Now we answer the questions based on the table: (i) The interval with the highest frequency (most of the students’ guesses) is the modal group. From the table, the interval \[ 171 \text{ to } 180 \text{ grams} \] has the largest frequency (10). (ii) The number of students whose guesses were between \(191\) and \(200\) grams is the frequency listed for that interval, which is \(3\). Thus, the range is \(59\) grams, most guesses were in the \(171\) to \(180\) interval, and \(3\) students guessed between \(191\) and \(200\) grams.