Practice Maths

L56 — Measures Using Technology

Key Terms

=AVERAGE(range)
Calculates the mean of all values in the selected range of cells (e.g., =AVERAGE(A1:A10)).
=MEDIAN(range)
Returns the median — the middle value when the data is sorted — for the selected range.
=MODE(range)
Returns the most frequently occurring value. Returns an error if no value repeats.
=MAX(range)
Returns the largest value in the selected range.
=MIN(range)
Returns the smallest value in the selected range. Range = =MAX − =MIN.
estimation
Before applying any formula, estimate the answer by inspection. If technology gives a wildly different result, check for data entry errors.

How to Estimate the Mean

Look at the data and identify a rough "middle" value. The mean should be close to this. If technology gives you a mean outside the range of your data, you have almost certainly entered a value incorrectly.

Hot Tip: Technology can give wrong answers if you enter data incorrectly — a misplaced decimal or extra digit is easy to miss. Always estimate the mean first and compare it to the technology output. If they differ significantly, re-check your data entry.

Worked Example

Dataset: {12, 15, 8, 22, 11, 18, 9, 14, 16, 13}

Step 1 — Estimate the mean.
Values range from 8 to 22. A rough middle is around 13–15. The mean should be somewhere in that range.

Step 2 — Calculate using spreadsheet formulas.
Sum = 12 + 15 + 8 + 22 + 11 + 18 + 9 + 14 + 16 + 13 = 138
Mean = =AVERAGE(A1:A10) = 138 ÷ 10 = 13.8  ✓ (matches estimate)

Step 3 — Median.
Sorted: {8, 9, 11, 12, 13, 14, 15, 16, 18, 22}
=MEDIAN gives the average of the 5th and 6th values: (13 + 14) ÷ 2 = 13.5

Step 4 — Mode and Range.
Mode = none (all values are unique; =MODE returns an error)
Range = =MAX − =MIN = 22 − 8 = 14

Why Use Technology for Statistics?

When you have a small dataset of 5 or 6 values, calculating the mean by hand is quick and easy. But what if you had 200 values — the test scores for every student in your school? Adding those up by hand and dividing would take forever, and the chance of making an arithmetic error would be very high. This is where technology comes in. A spreadsheet like Google Sheets or Excel can calculate the mean, median, mode, and range of hundreds of values in under a second, with no arithmetic errors (as long as you enter the data correctly!).

Entering Data into a Spreadsheet

The key skill is entering data accurately. In Google Sheets or Excel, type each data value into its own cell in a single column (for example, cells A1 to A20 for 20 values). Double-check your entries before applying any formula — a mistyped value (like typing 100 instead of 10) will produce a wrong answer that looks completely plausible.

It's good practice to estimate the mean before using technology. Glance at your data and identify a rough "middle" value. If the formula gives you an answer far outside the range of your data, you've probably entered a value incorrectly.

Spreadsheet Formulas for Statistics

If your data is in cells A1 to A10, use these formulas:

  • =AVERAGE(A1:A10) — calculates the mean
  • =MEDIAN(A1:A10) — finds the median
  • =MODE(A1:A10) — finds the mode (returns an error if no value repeats)
  • =MAX(A1:A10) — largest value in the dataset
  • =MIN(A1:A10) — smallest value in the dataset
  • =MAX(A1:A10)-MIN(A1:A10) — calculates the range

The colon (:) in the formula means "from ... to ..." — so A1:A10 means "all cells from A1 through to A10." If you add a new value in A11, you would update your formulas to A1:A11.

What Technology Can and Cannot Do

Technology is fast and accurate for calculations, but it cannot choose which measure of centre is most appropriate for your data — that's your job. It also cannot write conclusions or identify whether the mean is being distorted by an outlier. You still need to understand what the numbers mean. Think of technology as a powerful calculator: it handles the arithmetic, but you handle the thinking.

Always estimate first: Before you trust any technology output, estimate the answer yourself. For the mean, add up the rough values in your head or on paper and divide. If technology gives you a mean of 145 but your values are all between 10 and 20, something is wrong — probably a data entry error. A quick estimate catches mistakes before they become part of your answer.

  1. For each dataset, first estimate the mean, then calculate the mean, median, mode, and range. Show all working. Fluency

    1. Dataset A: {23, 18, 31, 27, 24, 19, 35, 22, 28, 26, 21, 33, 17, 29, 25}
    2. Dataset B: {8, 12, 8, 15, 9, 8, 11, 14, 10, 8, 13, 12, 9, 11, 8}
    3. Dataset C: {105, 98, 112, 107, 95, 110, 103, 99, 108, 101, 96, 115, 102, 97, 106}
    4. Dataset D: {3.2, 4.5, 2.8, 5.1, 3.7, 4.2, 3.9, 5.5, 2.5, 4.8, 3.4, 4.0, 2.9, 5.2, 3.6}

  2. Identifying technology errors Understanding

    1. A student enters the dataset {14, 18, 21, 16, 19, 15, 20, 17} into a spreadsheet and gets a mean of 142. What has most likely gone wrong? What should the correct mean be?
    2. Another student uses a dataset of values all between 40 and 60 but gets a mean of 7.2 from the spreadsheet. Explain two possible causes of this error.
    3. Explain in your own words why estimating the mean before using technology is a useful habit. Give a specific example of an error it could help you catch.
    4. A dataset of exam scores (out of 100) has a mean of 103.5. Is this possible? Explain.

  3. Applied statistical problems Problem Solving

    1. Canteen sales: The number of sandwiches sold at the school canteen each day for 3 weeks (15 school days) was:
      {34, 41, 38, 29, 45, 37, 43, 31, 40, 36, 44, 28, 39, 42, 33}
      1. Calculate the mean, median, mode, and range.
      2. The canteen manager wants to order enough bread for an "average" week. Which measure would you recommend she use and why?
      3. On the day with the lowest sales, the tuckshop was closed early. How might this affect your measures and what would you do about it?
    2. Sports team statistics: A basketball team recorded the points scored by their star player over 12 games:
      {18, 24, 15, 31, 22, 19, 27, 14, 28, 21, 25, 20}
      1. Calculate all four measures.
      2. The player missed two games due to injury and scored 0 points. If those 0s are included in the dataset, how do the mean and range change?
      3. Explain whether you would include or exclude the 0s when describing the player's typical performance.
    3. Comparing two teams: Over 10 games, Team A scored: {55, 62, 48, 71, 58, 67, 53, 74, 60, 52} and Team B scored: {63, 63, 64, 62, 65, 61, 64, 63, 62, 63}.
      1. Calculate the mean and range for each team.
      2. Which team would you rather manage? Use the statistics to justify your answer.

  4. Write the spreadsheet formula for each task. Fluency

    Assume data is entered in cells A1 to A20.

    1. Find the mean of the dataset.
    2. Find the median of the dataset.
    3. Find the mode of the dataset.
    4. Calculate the range of the dataset using a single formula.

  5. Estimate and check Fluency

    For each dataset, estimate the mean by inspection (no calculation), then calculate the exact mean and check your estimate.

    1. {50, 52, 48, 51, 49, 53, 47, 50} — estimate first, then calculate.
    2. {200, 250, 180, 230, 210, 190, 220, 240} — estimate first, then calculate.
    3. {1.1, 1.3, 0.9, 1.2, 1.0, 1.4, 0.8, 1.1} — estimate first, then calculate.
    4. {72, 68, 75, 71, 69, 74, 70, 73} — estimate first, then calculate.

  6. Choosing and interpreting measures Understanding

    1. A dataset has mean = 45, median = 38, and mode = 35. What does the fact that the mean is much higher than the median suggest about the data?
    2. A dataset has all four values (mean, median, mode, range) equal to 10. Is this possible? Give an example of such a dataset.
    3. Two datasets both have a mean of 50. Dataset X has a range of 5; Dataset Y has a range of 40. What does this tell you about the spread of each dataset?
    4. A teacher calculates the mean mark for two classes. Class A: mean = 68. Class B: mean = 72. She concludes "Class B is better at maths." Is this conclusion justified based only on the mean? What other statistics would help?

  7. Missing values problems Understanding

    1. The mean of five numbers is 14. Four of the numbers are 11, 16, 13, and 18. Find the fifth number.
    2. The mean of six test scores is 72. Five scores are 68, 75, 70, 80, and 65. What is the sixth score?
    3. A dataset of seven values has a mean of 30. The sum of six of the values is 185. What is the seventh value?
    4. The range of a dataset is 24. The smallest value is 13. What is the largest value?

  8. Using technology to detect and correct errors Problem Solving

    1. A student records the daily temperatures (°C) for two weeks:
      {24, 27, 23, 260, 25, 22, 28, 26, 24, 27, 23, 25, 26, 27}
      1. Calculate the mean with all values included. Does it seem reasonable? Explain.
      2. Identify the likely data entry error and correct it (assume 260 should be 26).
      3. Recalculate the mean, median, and range with the corrected data.
    2. A spreadsheet formula =AVERAGE(A1:A10) returns 15.3 for a dataset about student ages (which should all be between 11 and 14). Identify two possible sources of error and explain how you would find and fix them.
    3. A student enters 12 values into a spreadsheet and gets: Mean = 45.2, Median = 44.5, Mode = 44, Range = 18.
      She then realises she forgot to include one more value: 62.
      Without recalculating everything, predict: (a) Will the mean go up or down? (b) Will the range increase? Explain your reasoning, then verify by recalculating.

  9. Statistics in context Understanding

    The table below shows the number of goals scored per match by two football teams over a season of 10 matches.

    Match 12345678910
    Team Eagles 2415324623
    Team Tigers 3343343343
    1. Calculate the mean, median, mode, and range for each team.
    2. Which team scored more goals on average?
    3. Which team was more consistent in their scoring? Use a specific statistic to justify your answer.
    4. Write a formula in spreadsheet notation to calculate Team Eagles' mean if their data is in cells B2 to K2.

  10. Extended technology investigation Problem Solving

    A class of 18 students recorded how many minutes they spent on homework last night:

    {45, 60, 30, 75, 50, 45, 90, 35, 60, 45, 80, 55, 40, 65, 50, 45, 70, 55}

    1. Before calculating, estimate the mean. Show your reasoning.
    2. Calculate the mean, median, mode, and range. Show all working.
    3. Write the spreadsheet formula you would use to find each measure if the data is in cells A1 to A18.
    4. The teacher claims: "The typical student spent about an hour on homework." Does the data support this claim? Use two different measures in your answer.
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