Question

This list represents the number of children for the first six​ "first ladies" of a certain country.

Complete parts​ (a) through​ (d) below.

First Lady​ #1 2

First Lady​ #2 6

First Lady​ #3 7

First Lady​ #4 1

First Lady​ #5 2

First Lady​ #6 4

a. Find the mean number of​ children, rounding to the nearest tenth. Interpret the mean in this context. The mean number of children birthed by first ladies is ___children. Interpret the mean. Select the correct answer below. A.The mean is the typical or average number of children birthed by these first ladies. B.The mean represents the number of children birthed such that half of all these first ladies gave fewer births than the​ mean, and the other half gave more births than the mean. C.The mean represents the most common number of children birthed by these first ladies. D.The mean is the difference between the largest and smallest number of births by these first ladies. b. A statistic states that women living around that time period tended to have between 7 and 8 children. How does the mean of these first ladies compare to​ that? A.The mean number of children birthed by these first ladies is greater than the mean number of children birthed by women living around that time period. B.The means cannot be compared because they are from different time periods. C.The means are roughly equal. D.The mean number of children birthed by these first ladies is less than the mean number of children birthed by women living around that time period. c. Which of the first ladies listed here had the number of children that is farthest from the mean and therefore contributes most to the standard​ deviation? First lady ​#___ had the number of children that is farthest from the mean. d. Find the standard​ deviation, rounding to the nearest tenth. The standard deviation is ___ children.

Answer 1

a. Mean number of children = Total no of children/n = 2+6+..+4/6 = 22/4 = 5.4

This mean is the average no of children that a first lady has.

So the correct option is A.

B is incorrect because we don't know whether the distribution of the number of children follows a normal distribution. C is incorrect because mean is the average value we cannot say if it's the most common value. D is telling us about the range and not the mean so it's incorrect.

b) The mean of 5.4 < statistic value which states that avert is 7 or 8

So option D here is correct.

c) The first lady 4 has only 1 child, so it is farthest from the mean compared to the other values given in the data above. So first lady 4 had the number of children that is farthest from the mean.

d) SD = √Variance

Variance =( (2-5.4)^2 +.....+(4-5.4)^2 )/5 = 9.472

So required SD = √9.472 = 3.1 (rounded to the nearest tenth)