the results of a random sample of the number of pets per household in a region are shown in the histogram…

Explanation:

Step1: Identify mid - points and frequencies

Let the number of pets be grouped as (0 - 1), (1 - 2), (2 - 3), (3 - 4). Mid - points (x_i) are (0.5), (1.5), (2.5), (3.5) and frequencies (f_i) are (4), (12), (8), (6) respectively.

Step2: Calculate the sample mean (\bar{x})

The formula for the sample mean (\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{\sum_{i=1}^{n}f_i}). (\sum_{i = 1}^{n}f_ix_i=4\times0.5 + 12\times1.5+8\times2.5 + 6\times3.5=2+18 + 20+21 = 61). (\sum_{i=1}^{n}f_i=4 + 12+8 + 6=30). (\bar{x}=\frac{61}{30}\approx2.0) (already given).

Step3: Calculate (\sum_{i = 1}^{n}f_i(x_i-\bar{x})^2)

((x_1-\bar{x})^2=(0.5 - 2.0)^2=(-1.5)^2 = 2.25), (f_1(x_1-\bar{x})^2=4\times2.25 = 9). ((x_2-\bar{x})^2=(1.5 - 2.0)^2=(-0.5)^2 = 0.25), (f_2(x_2-\bar{x})^2=12\times0.25 = 3). ((x_3-\bar{x})^2=(2.5 - 2.0)^2=(0.5)^2 = 0.25), (f_3(x_3-\bar{x})^2=8\times0.25 = 2). ((x_4-\bar{x})^2=(3.5 - 2.0)^2=(1.5)^2 = 2.25), (f_4(x_4-\bar{x})^2=6\times2.25 = 13.5). (\sum_{i = 1}^{n}f_i(x_i-\bar{x})^2=9 + 3+2+13.5 = 27.5).

Step4: Calculate the sample standard deviation (s)

The formula for the sample standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}f_i(x_i-\bar{x})^2}{n - 1}}), where (n=\sum_{i=1}^{n}f_i = 30). (s=\sqrt{\frac{27.5}{30 - 1}}=\sqrt{\frac{27.5}{29}}\approx0.97\approx1.0).

Answer:

The sample standard deviation is (s = 1.0)