To find the sample standard deviation $s$ from the frequency distribution using the given formula, we need to follow these steps:

1. Identify class midpoints: These are the midpoints of each class interval.
2. Multiply each class midpoint by the corresponding frequency: This gives $f \times x$.
3. Multiply each class midpoint squared by the corresponding frequency: This gives $f \times x^2$.
4. Calculate the sum of $f \times x$ and the sum of $f \times x^2$.
5. Compute the total number of sample values $n$: This is the sum of the frequencies.
6. Apply the formula for the standard deviation.

Given formula: $s = \sqrt{ \frac{ n \cdot \sum (f \cdot x^2) - (\sum (f \cdot x))^2 }{ n \cdot (n - 1) } }$

Let's organize the steps:

Step 1: Class Midpoints

The class midpoints $x$ are calculated as the average of the lower and upper boundaries of each class interval.

$x = \frac{\text{lower boundary} + \text{upper boundary}}{2}$

So, for each interval:

• $20-26$: $x = \frac{20 + 26}{2} = 23$
• $27-33$: $x = \frac{27 + 33}{2} = 30$
• $34-40$: $x = \frac{34 + 40}{2} = 37$
• $41-47$: $x = \frac{41 + 47}{2} = 44$
• $48-54$: $x = \frac{48 + 54}{2} = 51$
• $55-61$: $x = \frac{55 + 61}{2} = 58$
• $62-68$: $x = \frac{62 + 68}{2} = 65$

Step 2: Frequency Table

Interval	Frequency $f$	Midpoint $x$	$f \cdot x$	$f \cdot x^2$
20-26	2	23	$2 \cdot 23 = 46$	$2 \cdot 23^2 = 1058$
27-33	3	30	$3 \cdot 30 = 90$	$3 \cdot 30^2 = 2700$
34-40	5	37	$5 \cdot 37 = 185$	$5 \cdot 37^2 = 6845$
41-47	1	44	$1 \cdot 44 = 44$	$1 \cdot 44^2 = 1936$
48-54	15	51	$15 \cdot 51 = 765$	$15 \cdot 51^2 = 39015$
55-61	34	58	$34 \cdot 58 = 1972$	$34 \cdot 58^2 = 114328$
62-68	33	65	$33 \cdot 65 = 2145$	$33 \cdot 65^2 = 139425$

Step 3: Summations