Question

Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1

\(S=\sqrt{\frac{n\left[\sum\left(1 \cdot x^{2}\right)\right]-\left[\sum(t+x)\right]^{2}}{n(n-1)}}\)

Interval	30.36	37-43	44.50	51-57	53.84	65-71	72.78
Frequency	2	2	1	1	13	28	30

Standard deviations=

(Round to one decimal place as needed.)

Consider a difference of 20% between two values of a standard deviation to be significant. How does this computer values compare with the given standard deviation 11.1?

the computer values is not significantly different from the given value

the computer values is significantly greater than the given value

the computer values is significantly less than the given values

Answer 1

Interval	Midpoint (X)	Frequency (f)	f * X	f * X2
30 - 36	33	2	66	2178
37 - 43	40	2	80	3200
44 - 50	47	1	47	2209
51 - 57	54	1	54	2916
58 - 64	61	13	793	48373
65 - 71	68	29	1972	134096
72 - 78	75	30	2250	168750

We want to find, the standard deviation ( s ),

Therefore, standard deviation = 9.4