Complete Question
The histogram from this question is shown on the first uploaded image
Answer:
The first quartile is ![1st Q = 19^{th} girl (subject ) = 1 \serving\ of\ fruit\ per\ day](https://tex.z-dn.net/?f=1st%20Q%20%3D%2019%5E%7Bth%7D%20girl%20%28subject%20%29%20%3D%201%20%5Cserving%5C%20of%5C%20fruit%5C%20per%5C%20day)
The median is ![Median = 38 ^{th} \ girl (subject) = 2 \serving\ of\ fruit\ per\ day](https://tex.z-dn.net/?f=Median%20%20%3D%2038%20%5E%7Bth%7D%20%5C%20girl%20%28subject%29%20%3D%20%202%20%5Cserving%5C%20of%5C%20fruit%5C%20per%5C%20day%20)
The third quartile is
The mean is ![\= x = 2.62](https://tex.z-dn.net/?f=%5C%3D%20x%20%3D%202.62)
Step-by-step explanation:
From the question we are told that
The total number of girls is n = 74
Generally the median is mathematically represented as
![Median = \frac{\frac{n}{2} +[ \frac{n}{2} + 1] }{2}](https://tex.z-dn.net/?f=Median%20%20%3D%20%20%5Cfrac%7B%5Cfrac%7Bn%7D%7B2%7D%20%20%2B%5B%20%5Cfrac%7Bn%7D%7B2%7D%20%2B%201%5D%20%20%7D%7B2%7D)
So
![Median = \frac{\frac{74}{2} +[ \frac{74}{2} + 1] }{2}](https://tex.z-dn.net/?f=Median%20%20%3D%20%20%5Cfrac%7B%5Cfrac%7B74%7D%7B2%7D%20%20%2B%5B%20%5Cfrac%7B74%7D%7B2%7D%20%2B%201%5D%20%20%7D%7B2%7D)
=> ![Median = \frac{37 +38 }{2}](https://tex.z-dn.net/?f=Median%20%20%3D%20%20%5Cfrac%7B37%20%20%2B38%20%7D%7B2%7D)
=>
From the histogram
fall under 2 fruits per day
Generally the first quartile is mathematically represented as
![1st \ Q = \frac{\frac{n}{4} + [\frac{n}{4} + 1] }{2}](https://tex.z-dn.net/?f=1st%20%5C%20Q%20%3D%20%20%5Cfrac%7B%5Cfrac%7Bn%7D%7B4%7D%20%2B%20%5B%5Cfrac%7Bn%7D%7B4%7D%20%2B%201%5D%20%20%7D%7B2%7D)
=> ![1st \ Q = \frac{\frac{74}{4} + [\frac{74}{4} + 1] }{2}](https://tex.z-dn.net/?f=1st%20%5C%20Q%20%3D%20%20%5Cfrac%7B%5Cfrac%7B74%7D%7B4%7D%20%2B%20%5B%5Cfrac%7B74%7D%7B4%7D%20%2B%201%5D%20%20%7D%7B2%7D)
=> ![1st \ Q = 19 \ girl](https://tex.z-dn.net/?f=1st%20%5C%20Q%20%3D%2019%20%5C%20%20girl%20)
From the histogram
girl fall under 1 fruit per day
Generally the third quartile is mathematically represented as
![3rd\ Q = \frac{\frac{n}{2} + n }{2}](https://tex.z-dn.net/?f=3rd%5C%20%20Q%20%3D%20%20%5Cfrac%7B%5Cfrac%7Bn%7D%7B2%7D%20%20%2B%20n%20%7D%7B2%7D)
=> ![3rd\ Q = \frac{\frac{74}{2} + 74 }{2}](https://tex.z-dn.net/?f=3rd%5C%20%20Q%20%3D%20%20%5Cfrac%7B%5Cfrac%7B74%7D%7B2%7D%20%20%2B%2074%20%7D%7B2%7D)
=> ![3rd\ Q = 55.5](https://tex.z-dn.net/?f=3rd%5C%20%20Q%20%3D%20%2055.5%20)
From the histogram
fall under 4 fruits per day
Generally from the histogram table the frequency [number of subjects (girls) ] and the servings of fruit per day can be represented as
Total
x(servings per day ) 0 1 2 3 4 5 6 7 8
f (number of subjects ) 15 11 15 11 8 5 3 3 3 ![\sum f = 74](https://tex.z-dn.net/?f=%5Csum%20f%20%20%3D%20%2074)
xf 0 11 30 33 32 25 18 21 24 ![\sum xf = 194](https://tex.z-dn.net/?f=%5Csum%20xf%20%3D%20%20194)
Generally the mean is mathematically represented as
![\= x = \frac{1}{ \sum f} * [\sum xf]](https://tex.z-dn.net/?f=%5C%3D%20x%20%3D%20%5Cfrac%7B1%7D%7B%20%5Csum%20f%7D%20%20%2A%20%5B%5Csum%20xf%5D)
=>
=> ![\= x = 2.62](https://tex.z-dn.net/?f=%5C%3D%20x%20%3D%202.62)