We all know that fruit is good for us. Below is a histogram of the number of servings of fruit per day claimed by $74$seventeen-year-old girls in a study in Pennsylvania?

(a) With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them?

(b) Estimate the mean of the distribution. Explain your method clearly.

Given graph :

The mean of a data set is determined by adding all of the numbers in the set and dividing by the number of values in the set. The median is the value in the middle of a data set when it is arranged from smallest to largest. The mode is the number that appears the most frequently in a data set.

According to a study in Pennsylvania, the median amount of servings of fruit per day claimed by $74$seventeen-year-old females is$2$, the first quartile is $1$and the third quartile is $4$To find the median and quartiles, use the formulas below:

The median can be calculated as follows:

$$\begin{gathered} M=\frac{N+1}{2} \\ N=Cumilativefrequency \\ M=\frac{74+1}{2} \\ M=37.5thitem \\ =2 \\ {Q}_1=\frac{N+1}{4}thitem \\ {Q}_1=\frac{75}{4}thitem \\ {Q}_1=18.75thitem \\ =1 \\ {Q}_3=\frac{3(N+1)}{4}thitem \\ =\frac{3\left(75\right)}{4}thitem \\ =56.25thitem \\ =4 \end{gathered}$$

Therefore, the median is $2$and the quartiles are $1$and $4$respectively.

From the given histogram of number of servings of fruit per day claimed by $74$ seventeen years old girls is a study in Pennsylvania the mean

The mean of the distribution is $$\begin{gathered} \overline{X}=\frac{\Sigma fx}{\Sigma f} \\ =\frac{194}{74} \\ \overline{X}=2.59 \end{gathered}$$

Therefore, mean is $2.59$