Hod do you put this calculator into statistical mode?

Put the calculator in STATistics mode (maybe called SD). Enter the data then use a key called sigma_d.

The statistical display menu choices depend on the type of statistical calculations you intend to do. Please Read the manual. Note: When you finish entering data press AC key and renter the stat mode.

Scientific calculator
The most basic scientific calculator can do simple 1-variable statistics. Usually you put the calculator in STATistics Mode, then CLEAR all statistics data that may already be stored.
You enter a data value by typing in the number then pressing a key marked DATA. The calculator may display the number 1 for the 1st point. Then as you enter more values, the display shows number that increase by 1.
Once you finish entering data values, you may have to press AC button to exit the data entry phase.
Then you look for the second function (2nd 2ndF, or SHIFT) of some keys. The one marked with an x with a bar on top give the average, the one with marked n give the number of data entered. You may have other keys with the Greek Capital Letter SIGMA. They give various results such as sum of squares, etc. Check your manual for more details.
Newer calculators allow you to use the frequency if there are repeated values. I cannot say more because I do n ot have the make and model of the calculator.

There must be an error in what you report. You pressed MODE then 4: Base-N and now your calculator is in base-N calculation mode (the DEC, Hex, BIN, OCT) numeration keys are active.
To do statistics you must put the calculator in STATS mode.
Press MODE: You have 6 computational modes to choose from
1: COMP, the general computational mode
2:CMPLX, for calculation s with complex numbers,
3: STAT for statistics,
4: Base-N, binary, octal, decimal, and hexadecimal numeration
5: Equation, solving mode, etc..
For statistics, choose 3:STAT

The TI-30Xa does not have a statistics mode. That statistics operations are available at all times, just like addition and subtraction. Just enter the data with Sigma-plus and then calculate the desired statistics---mean, standard deviation, and so forth.

Full details are in the "One-Variable Statistics" section of the guidebook (page 9 in my copy). If you need the guidebook, you can download one from
http://education.ti.com/calculators/downloads/US/Guidebooks/Detail?id=6132

This will show you how to do statistics (calculate average, standard deviation, regressions etc.) as to the mode and median refer to the definitions.

TO COMPUTE STANDARD DEVIATION AND 2-VAR STATISTICS.

I assume you know the theory. I will show you the key strokes

For 1-Var statistics
Press [MODE][3:STAT] [1:1-VAR]. You are ready to enter values in the X column.
Enter a number and press [=]. Cursor jumps to second number to enter.
Keep entering numbers and pressing [=] till all numbers are in. Press the [=] key after the last one.
Press [AC] key to clear the screen.
Press [SHIFT] [STAT] (above digit 1.) then [5:Var]. Screen displays the statistical variables 1:n ;2: x bar; 3: x sigma n; 4:x sigma n-1.
Press the number corresponding to the statistical value you want, ex 1:n . The variable appears on screen. Press [=] and it will be displayed.
To display another variable press [SHIFT][STAT][5:Var][ 1,2, 3, or 4] .

To access the sum of squares sigma x^2 and the sum of data sigma x press[SHIFT][STAT][4:SUM] then [1: for sigma x^2] or [2: for sigma x]. Press [SHIFT][STAT][6:MinMax] to access minX and maxX.

For 2-var statistics
To perform 2 variable statistics you press [MODE][3:STAT] and any of the other regression options (except 1:1-Var). A two column template opens where you enter the X and Y values. When finished entering data, press [SHIFT][STAT][5:Var]. to access the different statistics. As I assumed above, you should be able to recognize what each variable means.

The TI-30XA does not have to be switched to a statistics mode, the operations are available all the time. The choice of operations are somewhat limited; the calculator offers statistics functions for one dimensional data sets only (no linear interpolation of (x,y) value pairs, for example):

• [2nd] [CSR] - erase statistics data
• [] - add a number to the sample set
• [2nd] [] - remove a number from the sample set
• [2nd] [FRQ] - multiple entry of the same sample value
• [2nd] [n] - sample set size
• [2nd] [] - sum of all sample elements
• [2nd] [] - sum of the squares of all sample elements
• [2nd] [] - average of the sample set
• [2nd] [] - standard deviation (sample set is a complete set)
• [2nd] [] - standard deviation (sample set is a subset of a larger set)

The calculator displays "STAT" if the current sample set is non-empty.

Example: calculate the average and standard deviation of the set { 3, 4, 5, 5, 5, 5, 6 }.

1. [2nd] [CSR] - erase stat memory
   
2. 3 [] 4 [] 5 [2nd] [FRQ] 4 [] 6 [] - enter the data, note the use of [2nd] [FRQ] to enter the four occurrences of "5". Entering 5 [] four times would have done the same.
3. [2nd] [] - display the average of the set, (4.714...)
4. [2nd] [] - display the standard deviation of the set (0.8806...)
   

The truth of the matter is that there is no statistical mode per se. You just start entering data in a specific sequence.
If there is data in the statistics register (remnant of and old calculation) you must start by clearing old values :[2nd][CSR].
Here is a screen capture with an example that uses frequencies.

The [MODE] key can be used to select the modes described below.
Important! The following is a general explanation of Scientific Calculator modes. Note that your calculator may not include all of the modes described here.
1) Calculation Modes
Before performing a calculation, you first need to select the appropriate calculation mode.
COMP: Basic arithmetric calculations
(arithmetic operations, trigonometric functions, etc.)
COMPLEX: Complex number calculations
SD: Single-variable statistical calculations
(sample standard deviation, etc.)
LR or REG: Paired-variable statistical calculations
(linear regression statistical calculations, etc.)
BASE or BASE-n: Binary, octal, decimal, hexadecimal number system calculations
MAT: Matrix calculations (determinants, etc.)
VCT: Vector calculations
EQU: nth degree equations, simultaneous equations
2) Display Settings
Use these settings to control how calculation results are displayed.
Note that changing the Fix and Sci settings does not affect internal calculation results.
Norm: Exponential display format and cancels the currently configured Fix and Sci settings.
Fix: Specifies a fixed number of digits to the right of the decimal place.
Sci: Specifies a fixed number of significant digits.
3) Angle Unit Setting
(90°=?/2 radians=100 grads)
Deg: Degrees
Rad: Radians
Gra: Grads
4) Engineering Mode
Use this mode when you want to input and perform calculations using engineering symbols.
Please rate this response . .

Click on the Mode button twice until you see “SD”. Select 1. This puts the calculator in Statistics Mode. Enter the first number, 1.
Hit the M+. (n= 1 will appear in the window)
Enter the second number, 1.
Hit the M+ key. (n=2 will appear in the window)
. . . . .
Enter the last number, 7.
Hit the M+ key. (n=7 will appear in the window)
Hit shift, 2. (This invokes the S-Var option.)
Hit 1 for the sample mean. Hit Enter.
Hit 3 for the sample standard deviation that we will use in class. Hit Enter. here you can also ffind the sum of all numbers