The number that is closest to the mean of the considered distribution is given by: Option C: 6
How to find the mean of the observations from their frequency distribution?
A frequency distribution lists the observations along with the number of times they appear in the data set(the frequency).
The mean is calculated as:
[tex]\overline{x} = \dfrac{\sum^n_{i=1} (x_i \times f_i)}{\sum_{i=1}^n(f_i)}[/tex]
where [tex]x_i[/tex] is the ith unique observation with its frequency [tex]f_i[/tex]
Histogram is a graphical way to represent the unique observations (on horizontal axis) and their respective frequency(on the vertical axis).
From the considered histogram, we get the frequency distribution as:
[tex]\begin{array}{ccc}i&x_i&f_i\\1&3&1\\2&4&4\\3&5&5\\4&6&4\\5&7&2\\6&8&1\\7&9&1\\8&10&1\\9&11&1\\\text{Total} & & 20\\\end{array}\\[/tex]
Thus, we get:
[tex]\overline{x} = \dfrac{\sum^n_{i=1} (x_i \times f_i)}{\sum_{i=1}^n(f_i)} = \dfrac{3 \times 1 + 4 \times 4 + \cdots + 11 \times 1}{20} =\dfrac{130}{20} = 6.5[/tex]
Thus, the number that is closest to the mean of the considered distribution is given by: Option C: 6
Learn more about mean of frequency distributions here:
https://brainly.com/question/12954518
