AP Statistics · TI-84 Plus CE

Unit 1A Calculator Guide

Four things you need to be able to do without thinking about it: put data in a list, sort it, get the summary statistics, and build a histogram. Every keystroke is here. Work through it with your calculator in your hand — reading it is not the same as doing it.

↓ Printable version (PDF) — 9 pages with practice and answer key

1 Start clean
2 Enter data
3 Sort it
4 1-Var Stats
5 Histogram
Practice
When it breaks

Start clean

Old numbers left in a list are the single most common reason an answer comes out wrong. Do this before every new problem.

1

Open the memory menu. mem is the blue label above the + key.

2nd +
2
Choose 4: ClrAllLists and press enter.

4: ClrAllLists → enter
NORMAL FLOAT AUTO REAL RADIAN MP
```
ClrAllLists
                Done
```
Every list is now empty. That is what you want.

If L1 has disappeared Sometimes L1 is missing from the editor entirely. Press stat, choose 5: SetUpEditor, then enter. L1 through L6 come back.

The reset — learn this one When the calculator is behaving strangely and you cannot work out why, put it back to factory settings. It is five keys, and it is worth memorising:

2nd + → 7: Reset… → 1: All RAM… → 2: Reset

Say it as 2nd + 7 1 2. The screen answers RAM cleared. Every list, variable, window setting and mode goes back to how it came out of the box, which is exactly why it fixes so much.

It also deletes any program stored in RAM. Anything you archived survives, but if you have programs you care about, try everything else first — this is the last resort, not the first.

Put the data into L1

Everything else in this guide reads from L1, so this step has to be right.

1

Open the list editor.

stat → 1: Edit…
2
Make sure the cursor is in the L1 column. Type your first value and press enter. The cursor drops down a row. Keep going until every value is in.
NORMAL FLOAT AUTO REAL RADIAN MP
```
L1     L2     L3     1
------ ------ ------
160
34
360
28
80
------------------------
L1(6)=
```
Five values in, cursor waiting on the sixth.
3

When the last value is in, leave the editor.

2nd mode

Fixing mistakes Wrong number? Arrow onto it, type the correct one, press enter.
Typed an extra value? Arrow onto it and press del — the row disappears and everything below shifts up.
Skipped a value? Arrow to where it belongs, press 2nd del (that is ins), type it, press enter.

Clearing one list To empty just L1, arrow up onto the L1 heading itself, press clear, then press the down arrow. Do not press del while the heading is highlighted — that removes L1 from the editor instead of emptying it, and it looks like you deleted your list. If it happens, see the note in step 1.

Sort it with SortA(

SortA( means sort ascending — smallest to largest. It is how you check your typing, and how you find the median and quartiles by hand.

1

Open the STAT menu and choose the sort.

stat → 2: SortA(
2
Tell it which list. L1 is the blue label above the 1 key.

2nd 1 → ) → enter
NORMAL FLOAT AUTO REAL RADIAN MP
```
SortA(L1)
                Done
```
Done is the whole confirmation. Nothing else happens on this screen.
3

Go look at it. This is the point of sorting.

stat → 1: Edit…

Why this is worth doing Once the list is in order you can read the minimum and maximum straight off the ends, and you can count in to find the median and quartiles without the calculator doing it for you. It is also the fastest way to catch a typo: sort it, and compare against the sorted answer.

There is no undo SortA( rearranges the list permanently. If your data is paired — values in L1 and their frequencies in L2, or x in L1 and y in L2 — then sorting L1 by itself scrambles the pairing and every answer after that is wrong. Sort them together instead: SortA(L1,L2). L1 gets sorted and L2 is carried along to match.

Worth noticing Run 1-Var Stats before you sort and again after. Nothing changes. The mean, the standard deviation, the quartiles, the histogram — all identical. Sorting changes the order, not the distribution. The order data arrives in is not part of what you are describing.

Summary statistics with 1-Var Stats

One command gives you the mean, the standard deviation and the whole five-number summary.

1

Open STAT, then move right to the CALC tab.

stat → ▶ → 1: 1-Var Stats
2
Set List to L1. Leave FreqList completely blank. Then arrow down to Calculate and press enter.

2nd 1 → Calculate → enter
NORMAL FLOAT AUTO REAL RADIAN MP
```
1-Var Stats
List:L1
FreqList:
Calculate
```
If anything is sitting in FreqList, clear it out.
3
Read the first screen.
NORMAL FLOAT AUTO REAL RADIAN MP
```
1-Var Stats
 x̄=112.75
 Σx=2255
 Σx²=458665
 Sx=103.7237602
 σx=101.0974159
 n=20
↓minX=0
```
That little ↓ on the last line means there is more below.
4
Press the down arrow to reach the five-number summary. Most people forget this step and then say the calculator does not give quartiles.

▼
NORMAL FLOAT AUTO REAL RADIAN MP
```
↑n=20
 minX=0
 Q₁=36
 Med=64.5
 Q₃=200
 maxX=360
```

Sx or σx? Use Sx. That is the sample standard deviation, and it is what AP Statistics wants any time your data is a sample — which in this course is essentially always. σx is the population standard deviation. The two numbers are always close, which is exactly why picking the wrong one is easy to miss. Look for the S.

Getting the IQR and the range The calculator does not display these. Do them yourself from the screen above: IQR = Q₃ − Q₁ and range = maxX − minX. For this data that is 200 − 36 = 164, and 360 − 0 = 360.

Build a histogram

More steps than the others, and the one place things go wrong quietly. Follow it in order.

1

Check for leftover equations. Press y=. If anything is typed on any line, put the cursor on that line and press clear.

y= → clear

Skip this and a random curve gets drawn across your histogram.
2

Open STAT PLOT — the blue label above y= — and pick Plot1.

2nd y= → 1: Plot1
3
Highlight On and press enter. Then arrow down to Type and move across to the third icon on the top row — that is the histogram. Press enter on it.
NORMAL FLOAT AUTO REAL RADIAN MP
```
Plot1  Plot2  Plot3
 On   Off
Type: ●  ●  ■
      ●  ●  ●
Xlist:L1
Freq:1
```
The six icons are two rows of three. Histogram is top row, far right.
4

Set Xlist to L1, and set Freq to the number 1.

2nd 1 then Freq → 1

Freq must be the digit 1, not a list, unless you were given a frequency table.
5

Let the calculator find a starting window.

zoom → 9: ZoomStat

You get a histogram, but with awkward bar widths. That is normal — fix it next.
6
Press window and set the numbers yourself. Xscl is the bar width — it is the one that decides what your histogram looks like.

window
NORMAL FLOAT AUTO REAL RADIAN MP
```
WINDOW
 Xmin=0
 Xmax=400
 Xscl=50
 Ymin=-3
 Ymax=11
 Yscl=1
 Xres=1
```
Ymax has to be taller than your tallest bar. Ymin goes slightly negative so the trace readout does not sit on top of the bars.
7

Draw it.

graph
8
Press trace, then use left and right to step from bar to bar. Each bar tells you its interval and how many values are in it.

trace → ◀ ▶
NORMAL FLOAT AUTO REAL RADIAN MP
```
min=0
max<50
n=9
```
Nine values land in the first bar. Read it as 0 ≤ x < 50 — the left edge is included, the right edge belongs to the next bar. That is how a value of exactly 50 gets counted.

Try this before you move on Go back into window and change Xscl to 100, then to 25, pressing graph each time. Same data, three genuinely different-looking pictures. Bar width is a choice you are making, and it changes the story the graph tells.

Practice

Do the whole sequence start to finish, twice. Write your answers down before you open the key.

Set A — caffeine, 20 drinks

Milligrams of caffeine per serving. The same data we used in class.

160 34 360 28 80 210 0 75 200 41 205 22 300 47 150 54 200 5 46 38

Enter all 20 into L1, then sort with SortA(L1).
Write down the mean, Sx, and all five numbers of the five-number summary.
Work out the IQR and the range by hand.
Make a histogram with Xmin = 0, Xmax = 400, Xscl = 50. Trace it and record how many values are in each bar.
Describe the shape. Is there one clump or two?

Check your answers — Set A

Sorted list

0 5 22 28 34 38 41 46 47 54 75 80 150 160 200 200 205 210 300 360

x̄ (mean)	112.75
Sx	103.7237602 → round to 103.72
σx	101.0974159 (not the one you want)
n	20
minX	0
Q₁	36
Med	64.5
Q₃	200
maxX	360
IQR	164 (200 − 36)
Range	360 (360 − 0)

Histogram counts at Xscl = 50

Bar	Count	Bar	Count
0 – 50	9	200 – 250	4
50 – 100	3	250 – 300	0
100 – 150	0	300 – 350	1
150 – 200	2	350 – 400	1

Shape Two clumps, not one. Sodas and teas pile up below 100 mg; coffee and energy drinks cluster again around 200 mg, with almost nothing in between. A distribution with two peaks is called bimodal.

This is why the mean of 112.75 is a bad summary: no drink on the list is anywhere near 112.75 mg. Neither is the median of 64.5. Always graph the data before you trust a single number to describe it.

Set B — hours of sleep, 10 students

Smaller and with decimals, so you get practice with the . key.

5 8 6.5 7 9 6 7.5 8 4 7

Clear L1 first, then enter these ten values and sort them.
Find the mean, Sx, and the five-number summary.
Find the IQR.
With only ten values you can check the calculator by hand — count in from each end to find the median and quartiles yourself. Do they match?

Check your answers — Set B

Sorted list

4 5 6 6.5 7 7 7.5 8 8 9

x̄ (mean)	6.8
Sx	1.494434118 → round to 1.49
σx	1.417744688
n	10
minX	4
Q₁	6
Med	7
Q₃	8
maxX	9
IQR	2 (8 − 6)

Checking it by hand Ten values, so the median sits between the 5th and 6th: both are 7, so Med = 7. The bottom half is 4, 5, 6, 6.5, 7 — its middle value is Q₁ = 6. The top half is 7, 7.5, 8, 8, 9 — its middle value is Q₃ = 8. Same answers the calculator gave you.

When it breaks

Every one of these has happened to every student in the class. None of them means your calculator is broken.

What you see	What it means and how to fix it
`ERR: INVALID DIM`	A stat plot is switched on but pointing at a list that is empty or misnamed. Press `2nd` `y=` and choose 4: PlotsOff, then set Plot1 up again from step 5.2.
`ERR: DIM MISMATCH`	Two lists of different lengths are being used together. Usually Freq is set to a list instead of the number 1. Set Freq back to 1.
`ERR: SYNTAX`	Almost always the wrong minus. `(−)` next to enter makes a number negative; the tall `−` on the right is subtraction. They are not interchangeable. Also check for a missing `)`.
A curve or line across my histogram	There is an equation left in `y=`. Go there and `clear` every line.
Blank graph, or bars off the screen	The window does not match the data. Press `zoom` then 9: ZoomStat to jump back to something sensible, then re-set Xscl.
L1 is not in the editor	You pressed `del` on the list heading. Press `stat`, choose 5: SetUpEditor, press `enter`.
My numbers are all wrong	Old data is still in the list, or you have more values than you think. Check n on the 1-Var Stats screen — if n is not what you expected, that is your answer. Clear the lists and start over.
Everything is in tiny fractions	The calculator is in a different answer mode. Press `mode` and make sure the answer row is set to DEC and NORMAL FLOAT.
Nothing in this table fixes it	Reset the whole calculator: `2nd` `+`, then 7: Reset → 1: All RAM → 2: Reset — 2nd + 7 1 2. Everything returns to factory settings, including any program stored in RAM, so work down this list before you reach for it.

AP Statistics · Unit 1A · Written for the TI-84 Plus CE. Older TI-84 and TI-83 Plus models use the same keys; a few menus look slightly different, and 1-Var Stats may want you to type 1-Var Stats L1 on the home screen instead of filling in a form.