A simple random sample consists of four observations 1, 3, 5 ,7. The point estimate of population standard deviation is :

2.58

The correct answer is Option (3) → 2.58

Sample mean $\bar x=\frac{1+3+5+7}{4}=\frac{16}{4}=4$

Squared deviation = $(1-4)^2=9,(3-4)^2=1,(5-4)^2=1,(7-4)^2=9$

Sum of squared deviation = $∑(x_i-\bar x)^2=9+1+1+9=20$

Sample variance = $\frac{∑(x_i-\bar x)^2}{n-1}$

$=\frac{20}{3}≈6.67$

Sample standard deviation = $\sqrt{\text{Sample variance}}=\sqrt{6.67}≈2.58$