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Statistics

One-variable statistics (mean, median, standard deviation)

Instant summary statistics from a list - no formulas to compute by hand.

In short: One-variable statistics gives the key summary values of a data set in a single step: the mean, standard deviation, median, quartiles, minimum and maximum. You enter the data in a list, with frequencies if it is grouped, run the one-variable analysis and read the results. Use it for any question about centre or spread.

When you'd use this

TI-84 Plus CECasio fx-CG50 and fx-CG100TI-Nspire CX

At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared

 TI-84 Plus CECasio fx-CG50 and fx-CG100TI-Nspire CX
Key sequenceSTAT → Edit → type values into L1. Then STAT → CALC → 1:1-Var Stats, choose L1, Calculate.Statistics menu → enter data in List 1 → CALC (F2) → 1-VAR.Add a Lists & Spreadsheet page, name a column and enter data; then a Calculator page → menu → Statistics → Stat Calculations → One-Variable Statistics.

On a TI-84 Plus CE

  1. Enter the data into a list.
  2. STAT → Edit → type values into L1. Then STAT → CALC → 1:1-Var Stats, choose L1, Calculate.
  3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max).
  4. For frequency data, put values in one list and frequencies in another and set the frequency list.

Tip: Sx vs σx: use σx (population) for a complete data set, Sx (sample) for a sample. IB usually wants σx.

On a Casio fx-CG50 and fx-CG100

  1. Enter the data into a list.
  2. Statistics menu → enter data in List 1 → CALC (F2) → 1-VAR.
  3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max).
  4. For frequency data, put values in one list and frequencies in another and set the frequency list.

Tip: Sx vs σx: use σx (population) for a complete data set, Sx (sample) for a sample. IB usually wants σx.

On a TI-Nspire CX

  1. Enter the data into a list.
  2. Add a Lists & Spreadsheet page, name a column and enter data; then a Calculator page → menu → Statistics → Stat Calculations → One-Variable Statistics.
  3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max).
  4. For frequency data, put values in one list and frequencies in another and set the frequency list.

Tip: Sx vs σx: use σx (population) for a complete data set, Sx (sample) for a sample. IB usually wants σx.

Related guides

Try it yourself

Here's a real IB-style question that uses exactly this technique.

Easy Calculator Paper 2 [3 marks]

The data set is 4, 5, 5, 6, 7, 8, 9, 10. Find the mean and the population standard deviation, each to 3 significant figures.

Mean = 6.75, σ = 1.98
Mark it
Correct 3 / 3 marks
Worked solution & mark scheme:
M1 Enter the data as a one-variable list
A1 Mean = 6.75
A1 σ = 1.98

Common questions

When would I need to find the mean, median and standard deviation of a data set in IB Maths?

Instant summary statistics from a list - no formulas to compute by hand. A question gives a list or frequency table of data and asks for the mean, median or standard deviation. Comparing the spread (standard deviation) of two data sets, not just their averages.

How do I find the mean, median and standard deviation of a data set on a TI-84 Plus CE?

1. Enter the data into a list. 2. STAT → Edit → type values into L1. Then STAT → CALC → 1:1-Var Stats, choose L1, Calculate. 3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max). 4. For frequency data, put values in one list and frequencies in another and set the frequency list.

How do I find the mean, median and standard deviation of a data set on a Casio fx-CG50 and fx-CG100?

1. Enter the data into a list. 2. Statistics menu → enter data in List 1 → CALC (F2) → 1-VAR. 3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max). 4. For frequency data, put values in one list and frequencies in another and set the frequency list.

How do I find the mean, median and standard deviation of a data set on a TI-Nspire CX?

1. Enter the data into a list. 2. Add a Lists & Spreadsheet page, name a column and enter data; then a Calculator page → menu → Statistics → Stat Calculations → One-Variable Statistics. 3. Read x̄ (mean), Sx (sample sd) or σx (population sd), and the five-number summary (min, Q1, median, Q3, max). 4. For frequency data, put values in one list and frequencies in another and set the frequency list.

What should I watch out for when I find the mean, median and standard deviation of a data set?

Sx vs σx: use σx (population) for a complete data set, Sx (sample) for a sample. IB usually wants σx.

How are marks awarded when I find the mean, median and standard deviation of a data set in an IB exam?

In the worked example on this page (3 marks, Paper 2), the marks are: M1: Enter the data as a one-variable list; A1: Mean = 6.75; A1: σ = 1.98.

Practise with your calculator

Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.