Five numbers you need: rate, average, spread, the bell curve, an interval

Thursday 5 November 2026. NQ opens the regular session at 09:30 ET (21:30 ICT, winter) at 28,203.25. By 16:00 ET it trades at 26,746.25: down 1,457 points from the open, a loss of $29,140 for one NQ contract held all day. In the other 57 sessions of our sample, open-to-close moves had a standard deviation of about 207 points. How rare was this day? And NQ closed above its open on only 25 of the 58 sessions: does it “tend to fall” during the day? Five numbers answer both, and you will use them on every page of this academy.

Key terms

Rate (tỷ lệ): how many times something happened, divided by how many chances it had Definition. 25 up sessions out of 58 is a rate of 43%.

Average or mean (trung bình): the sum of the values divided by how many there are Definition. Median (trung vị) is the middle value once you sort them.

Standard deviation, σ (độ lệch chuẩn, read “sigma”): the typical distance of a value from the average Definition. A big σ means the values are spread out.

Normal curve (phân phối chuẩn, the bell curve): a model of how values pile up around their average, symmetric, with fewer and fewer values far away Definition.

Percentile (bách phân vị): the value below which a given share of the data falls Definition. The 90th percentile has 90% of the values under it.

95% interval (khoảng tin cậy 95%): the range where the true value could plausibly sit, given the sample size Definition.

Terms you need: RTH is the regular trading session, 09:30–16:00 ET; M0.04 covers sessions. A point is one full unit of the NQ price: $20 on one NQ contract and $2 on one MNQ. A tick is a quarter point, $5 on NQ. M0.05 covers contracts.

Chart first: how days pile up under a bell curve

How it works

Rate: count, then divide

From our lab’s NQ tick history (ATAS backfill) across 58 full RTH sessions from 17 August to 6 November 2026, NQ closed above its open on 25 of them, below on 32, and flat on one Context. The up rate is 25 ÷ 58 = 43.1%.

A rate has two parts: what counts as a hit, and how many chances there were. Write both down before you count. “Price reached the level” means nothing until you say how close counts, and over what window.

Average and median: the centre

Here are five real sessions, open to close, in NQ points:

• Session (2026): Mon 26 Oct — Open: 29,230.50; Close: 29,439.25; Change: +208.75.

• Session (2026): Tue 27 Oct — Open: 29,561.25; Close: 29,813.25; Change: +252.00.

• Session (2026): Wed 28 Oct — Open: 29,930.00; Close: 29,992.75; Change: +62.75.

• Session (2026): Thu 29 Oct — Open: 29,612.25; Close: 29,566.00; Change: −46.25.

• Session (2026): Fri 30 Oct — Open: 28,798.50; Close: 28,527.25; Change: −271.25.

The sum is +206.00, so the average is 206.00 ÷ 5 = +41.2 points. Sorted, the middle value is +62.75: that is the median.

Over all 58 sessions the average change was −39.8 points and the median −25.9 Context. Drop 5 November alone: the average jumps to −14.9, the median barely moves (−24.0). One extreme day drags the average; the median resists it. Report both.

Spread: the standard deviation

The average hides how far days wander. To measure that:

1. Subtract the average from each value: +167.55, +210.80, +21.55, −87.45, −312.45.
2. Square each one, so minus signs stop cancelling: 28,073, 44,437, 464, 7,648, 97,625.
3. Add them (178,247) and divide by one less than the count: 178,247 ÷ 4 = 44,562.
4. Take the square root: σ ≈ 211 points.

For all 58 sessions σ was 279.5 points; without 5 November, 207.5 Context. In money, one σ of 280 points is $5,600 on one NQ and $560 on one MNQ: the size of an ordinary day, not a bad one.

The bell curve and percentiles

If days followed a normal curve, about 38% would land within ±0.5σ of the average, 68% within ±1σ and 95% within ±2σ Definition. That is arithmetic of the curve, not a fact about NQ.

Over all 58 sessions (σ = 279.5 points): 35 landed within ±0.5σ (60%), 47 within ±1σ (81%), and 55 within ±2σ (95%) Context. Why did 81% sit inside ±1σ? Because 5 November inflated σ from 207.5 to 279.5 points, stretching the ±1σ band wide enough to swallow ordinary days. Without 5 November, the other 57 sessions had 24 within ±0.5σ (42%), 42 within ±1σ (74%), and 54 within ±2σ (95%), much closer to the normal curve’s middle—while 5 November itself sat far outside in the tail. Published studies across many markets find both a sharper peak and fatter tails than the normal curve MeasuredOther market (box below).

Percentiles describe a list without assuming any curve. The RTH range (high minus low) of the 58 sessions had a median of 295 points, a 10th percentile of 202 and a 90th percentile of 579 Context. In words: half the sessions moved less than 295 points from high to low, and only one session in ten moved more than 579.

An interval: how sure is the number?

The up rate of 43% came from 58 sessions. Another 58 sessions would give a different rate. A 95% interval shows the range the true rate could plausibly sit in. For 25 of 58 it runs from 31% to 56% Definition. It includes 50%, so this sample cannot tell NQ’s intraday direction from a coin flip.

A quick rule for rates near 50%: the 95% interval is about ±1/√n. With 100 trades, ±10 points; with 1,000, about ±3.

The same idea works for an average. Divide σ by √n to get the standard error, then go about two standard errors each side. For the open-to-close average: 279.5 ÷ √58 = 36.7, so −39.8 ± 72, from −112 to +32 points. Zero is inside.

What the data says

Worked example: the open-to-close long, measured

Suppose you had bought one MNQ at every RTH open and sold at every close over the 58 sessions. Not a strategy: practice on a real outcome.

• Rate: 25 winners out of 58, 43.1%, interval 31% to 56%.
• Average: −39.8 points a session, −$79.60 on one MNQ before costs.
• Spread: σ of 279.5 points, $559 on one MNQ. The spread is seven times the size of the average.
• Interval for the average: −112 to +32 points. Zero is inside, so the sample cannot say whether the long side had a real disadvantage.

Fifty-eight sessions felt like a lot of screen time. Statistically they decide almost nothing about a result this small.

The mirror and the failure

The short side. Selling every open and buying back at the close gives the mirror: 32 winners of 58 (55%), average +39.8 points, interval from −32 to +112. It looks better, and it is just as undecided: zero is inside the interval. Costs cut both sides, because you pay them on every round trip.

Where the bell curve fails. On 5 November NQ fell 1,457 points open to close: −5.1σ when 5 November is included in the 58-session σ (279.5 points), or −7.0σ when measured against the other 57 sessions (σ = 207.5 points). Under a normal curve a 5σ day comes about once in 1.7 million trading days, and a 7σ day once in 1.5 billion years. It happened in our three-month sample. Use σ as a ruler for ordinary days, and size every position as if the extreme day can arrive tomorrow.

Do it on your platform

Prop-firm note. Many firms state a daily loss limit in dollars; check yours (see the PROP course). One σ changes with the market, so compare them before you choose a size (RSK1.05).

Common mistake: reading a rate without its interval. “NQ closed down on 55% of sessions, so I lean short in the afternoon” treats a coin-flip result as an edge. With 58 sessions, the interval for down days runs from 43% to 67% and includes 50%.

Common mistake: planning with the average when a few days are huge. The average range of 361 points is pulled up by a 1,510-point day; the median of 295 describes a normal session better.

Drill: your own five numbers

1. Take ten consecutive RTH sessions of NQ or ES from your platform.
2. For each, write the open, the close and the change in points.
3. Compute the up rate, the average, the median and the standard deviation.
4. Put a rough 95% interval around the up rate with ±1/√n.

Recap

• A rate is hits divided by chances; define the hit before you count.
• The average is pulled by extreme days; the median is not. Report both.
• σ is the size of an ordinary day; on our NQ sample it was about 280 points (207.5 without 5 November), $560 on one MNQ.
• The bell curve gives 38% inside ±0.5σ and 68% inside ±1σ; real market returns have fatter tails than the curve predicts MeasuredOther market.
• A 95% interval around a rate is about ±1/√n near 50%; if it includes 50% or zero, the sample has not decided.

Further reading

• Freedman, Pisani and Purves, Statistics (4th edition, 2007): chapters on the average and standard deviation, the normal curve and the accuracy of percentages.
• Cont (2001), “Empirical properties of asset returns: stylized facts and statistical issues”, Quantitative Finance 1, 223–236.
• Mandelbrot (1963), “The variation of certain speculative prices”, Journal of Business 36, 394–419.
• Our lab: open-to-close changes and RTH ranges of 58 NQ sessions (17 August to 6 November 2026), computed from the lab’s NQ tick history (ATAS backfill).

Next: EV1.02 uses the rate you just learned to ask what “it works 85% of the time” really means, and why every rate needs a baseline.

Educational content only — not financial advice. Futures trading involves substantial risk of loss.