Complete Question
The histogram from this question is shown on the first uploaded image
Answer:
The first quartile is [tex]1st Q = 19^{th} girl (subject ) = 1 \serving\ of\ fruit\ per\ day[/tex]
The median is [tex]Median = 38 ^{th} \ girl (subject) = 2 \serving\ of\ fruit\ per\ day [/tex]
The third quartile is [tex]3rd Q = 56^{th} \ girl (subject) = 4 \serving\ of\ fruit\ per\ day [/tex]
The mean is [tex]\= x = 2.62[/tex]
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
[tex]Median = \frac{\frac{n}{2} +[ \frac{n}{2} + 1] }{2}[/tex]
So
[tex]Median = \frac{\frac{74}{2} +[ \frac{74}{2} + 1] }{2}[/tex]
=> [tex]Median = \frac{37 +38 }{2}[/tex]
=> [tex]Median =37.5 \ girl [/tex]
From the histogram [tex]37.5 \approx 38^{th} \ girl[/tex] fall under 2 fruits per day
Generally the first quartile is mathematically represented as
[tex]1st \ Q = \frac{\frac{n}{4} + [\frac{n}{4} + 1] }{2}[/tex]
=> [tex]1st \ Q = \frac{\frac{74}{4} + [\frac{74}{4} + 1] }{2}[/tex]
=> [tex]1st \ Q = 19 \ girl [/tex]
From the histogram [tex]19^{th} [/tex]girl fall under 1 fruit per day
Generally the third quartile is mathematically represented as
[tex]3rd\ Q = \frac{\frac{n}{2} + n }{2}[/tex]
=> [tex]3rd\ Q = \frac{\frac{74}{2} + 74 }{2}[/tex]
=> [tex]3rd\ Q = 55.5 [/tex]
From the histogram [tex]55.5 \approx 56^{th} \ girl[/tex] 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 [tex]\sum f = 74[/tex]
xf 0 11 30 33 32 25 18 21 24 [tex]\sum xf = 194[/tex]
Generally the mean is mathematically represented as
[tex]\= x = \frac{1}{ \sum f} * [\sum xf][/tex]
=> [tex]\= x = \frac{1}{ 74} *194[/tex]
=> [tex]\= x = 2.62[/tex]
