lesson
Choose a chart that fits the values
1 · Learn
A discrete variable takes separate count values. In a fictional pet-count survey, the table is 0 pets: 3 homes; 1 pet: 5; 2 pets: 4; 3 pets: 2. There are 14 homes, not 6: add the frequencies, not the different pet counts. Plot pet counts at their numerical positions with a vertical line or separated bar for each count.
The modal number of pets is 1, because its frequency is 5. To find the median, use cumulative frequencies: positions 1–3 have 0 pets, positions 4–8 have 1 pet, positions 9–12 have 2 and positions 13–14 have 3. Both middle observations, positions 7 and 8, are 1, so the median is 1 pet.
A SEPARATE fictional time survey has groups 0 <= t < 10 minutes: 3; 10 <= t < 20: 5; 20 <= t < 30: 4; 30 <= t < 40: 2. Times are continuous; grouping loses exact individual values. Draw the equal-width intervals in their numerical order. The supplied adjacent bars have width 10 minutes and heights equal to frequency. This simple height rule assumes equal group widths.
Use each interval midpoint to estimate a grouped mean: (3×5 + 5×15 + 4×25 + 2×35)/14 = 260/14, about 18.57 minutes. The largest-frequency group is 10 to under 20 minutes, but the exact modal time and exact median time are unknown. A bar's height counts observations; it is not a measured duration.
2 · Worked example
A time of exactly 10 minutes belongs in 10 <= t < 20, not the first group. Exactly 20 belongs in 20 <= t < 30. The inequalities stop values being counted twice. No observation in this dataset reaches 40 minutes because every group excludes its upper endpoint.
3 · Your turn
In the pet survey, how many homes have at least 2 pets? In the grouped time survey, how many observations are under 20 minutes? Can you recover the exact longest time from the grouped chart?
Check your answer
6 homes: 4+2. There are 8 times under 20 minutes: 3+5. No: the longest lies from 30 up to, but not including, 40 minutes; its exact value was not retained.
4 · Apply your learning
Draw the two supplied charts on separate grids and label their different horizontal axes and units. Compare why the same frequency heights do not make the datasets interchangeable. Mark the interval containing 25 minutes without inventing an individual observation at the midpoint.
Adult guidance and safety
Use the supplied fictional datasets, not pupil personal records. Check frequency totals, axis scales, keys and denominators. Provide squared paper, a ruler and protractor. A chart supports an interpretation only within the dataset and collection method stated.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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