Question

A veterinarian weighed a sample of 666 puppies. Here are each of their weights (in kilograms): 1, 2, 7, 7, 10, 151,2,7,7,10,151, comma, 2, comma, 7, comma, 7, comma, 10, comma, 15 The mean of these weights is \bar x=7\text{ kg} x ˉ =7 kgx, with, \bar, on top, equals, 7, start text, space, k, g, end text. What is the standard deviation? Round your answer to two decimal places. s_x\approxs x ​ ≈s, start subscript, x, end subscript, approximately equals \text{kg}kgstart text, k, g, end text

Answer 1

Answer:

The standard deviation of the weight, σ, is approximately 4.73 kg

Step-by-step explanation:

The weights of the six puppies are;

$x_i$ = 1, 2, 7, 7, 10, and 15

The number of puppies, n = 6

Therefore, we have;

The mean = μ = ∑x/n = (1 + 2 + 7 + 7 + 10 + 15)/6 = 7

The standard deviation, σ, is given as follows;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n}}$

By substituting, we have;

$\sigma =\sqrt{\dfrac{ \left (1-7 \right )^{2} + \left (2-7 \right )^{2} + \left (7-7 \right )^{2} + \left (7-7 \right )^{2} + \left (10-7 \right )^{2} + \left (15-7 \right )^{2} }{6}}$

Simplifying gives;

$\sigma =\sqrt{\dfrac{ \left (-6 \right )^{2} + \left (-5 \right )^{2} + \left (0 \right )^{2} + \left (0 \right )^{2} + \left (3 \right )^{2} + \left (8 \right )^{2} }{6}} =\sqrt{\dfrac{ 36 + 25 + 0 +0+ 9 + 64 }{6}}$

$\sigma =\sqrt{\dfrac{ 134 }{6}} = \sqrt{\dfrac{67}{3} } \approx 4.72582$

The standard deviation of the weight, σ ≈ 4.73 kg to two decimal places.

Answer 2

Answer:

It’s actually 5.18 kg on khan

Step-by-step explanation: