Final Answer:
The mean height of six women is 1.64m. The heights of five of the women are 1.60m, 1.62m, 1.64m, 1.61m, and 1.62. So the correct option is a. 1.62m
Step-by-step explanation:
The mean height is calculated by summing up all individual heights and then dividing by the number of individuals. In this case, the mean height is given as 1.64m for six women. The sum of the heights of the five known women is 1.60m + 1.62m + 1.64m + 1.61m + 1.x (height of the sixth woman) = 1.64m * 6.
To find the height of the sixth woman, subtract the sum of the known heights from the product of the mean height and the number of women: 1.64m * 6 - (1.60m + 1.62m + 1.64m + 1.61m) = 1.x. Solving this equation gives the height of the sixth woman as 1.62m.
The mean height is the total height divided by the number of individuals. In this case, it's (1.60m + 1.62m + 1.64m + 1.61m + 1.62m) / 6 = 1.64m. This ensures that the sum of all heights equals the mean height multiplied by the number of individuals.
The calculated value of 1.62m for the sixth woman's height completes the dataset and satisfies the condition.
This method of calculation is fundamental in statistics, where the mean provides a central measure in a set of values. In practical terms, it helps to understand the average or typical height in a given group. So the correct option is a. 1.62m