Question

3.2.37 Question Help 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. [(*•x?)]-[><*• x)]? n(n-1) Interval 30-36 1 37-43 4 4-50 51-57 58-64 65-71 72-78 Frequency T2T2T 4T 3 T 10 | 35 | 39 O Standard deviation = (Round to one decimal place as needed.) Enter your answer in the answer box and then click Check Answer 1 part 1 pantaining - remaining Clear All Check Answer Pearson

Answer 1

Interval	f	x(Midpoint)	x*f	$x^2*f$
30-36	2	(30+36)/2 = 33	66	2178
37-43	2	(37+43)/2 = 40	80	3200
44-50	4	(44+50)/2 = 47	188	8836
51-57	3	(51+57)/2 = 54	162	8748
58-64	10	(58+64)/2 = 61	610	37210
65-71	35	(65+71)/2 = 68	2380	161840
72-78	39	(72+78) = 75	2925	219375
	$\sum f=95$		$\sum x*f=6411$	$\sum x^2*f=441387$

n = $\sum f=95$

Standard deviation:

|n-Σf r')]-Σ )]? n* (n – 1) Π

$s=\sqrt{\frac{95*[441387]-[6411]^2}{95*(95-1)}}$

$s=\sqrt{\frac{830844}{8930}}$

s = 9.6             (Round to one decimal)

Standard deviation = 9.6