Introduction to Data Analysis and Sampling

Decide whether each of the following is discrete or continuous data and justify your choice: (i) the number of goals scored by a team in a season, (ii) the time (in minutes) it takes students to finish a quiz, (iii) the height of plants (in cm) after four weeks.

Answer explanation

(i) Discrete: goals are whole numbers. (ii) Continuous: time can take any value within a range. (iii) Continuous: height can vary and take any value within a range.

A class survey about favourite ice cream flavours produced this frequency table out of 40 students: Strawberry 3, Sweet Corn 9, Chocolate 12, Durian 6, Vanilla 10. Explain which flavour is the least popular and justify your choice using the table values.

Answer explanation

The least popular flavour is Strawberry, with only 3 votes. This is the lowest value in the frequency table compared to Sweet Corn (9), Chocolate (12), Durian (6), and Vanilla (10).

A compound bar chart shows the waiting times of shoppers for a free shuttle bus on a weekday. For each number of stops (1 to 6), both women and men are represented. Describe how to determine the total number of shoppers who used the shuttle bus from the chart and explain the steps you would take to find this total.

Answer explanation

To find the total number of shoppers, sum the heights of the bars for both women and men for each number of stops (1 to 6). Add these sums together to get the overall total of shoppers who used the shuttle bus.

A school team surveys 180 tourists about their country of origin. The pie chart shows sectors labeled: China 80°, Malaysia 70°, United Kingdom 40°, Australia 30°, Thailand 40°, and Other Countries 100°. Use the chart to determine which country contributed the largest number of tourists and calculate how many tourists that represents.

Answer explanation

The largest sector is China with 80°. To find the number of tourists, calculate the fraction of the total: (80/360) * 180 = 40 tourists from China.

Find the mode(s), median, and range for each data set: (a) 5, 2, 6, 4, 5, 3, 5; (b) 88, 86, 87, 90, 88, 82, 88, 98; (c) 1.9, 1.4, 1.1, 1.3, 1.5, 1.4, 1.4, 1.2, 1.3. Show your working.

Answer explanation

(a) Mode: 5, Median: 5, Range: 4; (b) Mode: 88, Median: 88, Range: 16; (c) Mode: 1.4, Median: 1.4, Range: 0.8. Calculated by sorting data and finding values accordingly.