NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
← Back to practice

Data displays and distributions

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

A class of 24 students recorded their heights in centimetres. The data collected were: 152, 155, 156, 158, 158, 159, 160, 160, 161, 162, 162, 163, 164, 165, 165, 166, 167, 168, 169, 170, 171, 172, 175, 180.

Construct a stem-and-leaf plot and determine the exact value of the median height.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The data set contains 24 heights in centimetres, listed in ascending order. The task is to construct a stem-and-leaf plot and find the exact median height.
  2. Group the data by tens digit (stem) and units digit (leaf). The stems range from 15 to 18, as the smallest height is 152 cm and the largest is 180 cm.
  3. Construct the stem-and-leaf plot: for stem 15, leaves are 2, 5, 6, 8, 8, 9; for 16: 0, 0, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9; for 17: 0, 1, 2, 5; for 18: 0.
  4. The median is the average of the 12th and 13th values in an ordered list of 24 values.
  5. List the data in order: 152, 155, 156, 158, 158, 159, 160, 160, 161, 162, 162, 163, 164, 165, 165, 166, 167, 168, 169, 170, 171, 172, 175, 180.
  6. The 12th value is 163 cm (count from the start: 1st=152, 2nd=155, ..., 12th=163).
  7. The 13th value is 164 cm.
  8. Calculate the median: (163 + 164) / 2 = 327 / 2 = 163.5 cm.
  9. The median height is 163.5 cm. This value lies between the 12th and 13th data points, confirming the correct method for even-sized data sets.
  10. The distribution is slightly skewed right due to the outlier at 180 cm, which pulls the mean higher than the median.
  11. The mode is 158 cm and 162 cm (both appear twice), so the distribution is bi-modal.
  12. The range is 180 - 152 = 28 cm. The median is 163.5 cm, which is consistent with the data and correct for an even-numbered list.

Reference answer: 163.5 cm

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.