Question

With a little care, you can find the median and the quartiles from the histogram. what are these numbers? you can also find the mean number of servings of fruit claimed per day from the histogram. first use the information in the histogram to compute the sum of the 74 observations, and then use this to compute the mean.

Answer 1

Complete Question

The histogram from this question is shown on the first uploaded image

Answer:

The first quartile is  $1st Q = 19^{th} girl (subject ) = 1 \serving\ of\ fruit\ per\ day$

The median is   $Median = 38 ^{th} \ girl (subject) = 2 \serving\ of\ fruit\ per\ day$

The third quartile  is $3rd Q = 56^{th} \ girl (subject) = 4 \serving\ of\ fruit\ per\ day$  

The  mean is  $\= x = 2.62$

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

       $Median = \frac{\frac{n}{2} +[ \frac{n}{2} + 1] }{2}$

So

          $Median = \frac{\frac{74}{2} +[ \frac{74}{2} + 1] }{2}$

=>         $Median = \frac{37 +38 }{2}$

=>         $Median =37.5 \ girl$    

From the histogram $37.5 \approx 38^{th} \ girl$ fall under 2 fruits per day

Generally the first quartile is mathematically represented as

      $1st \ Q = \frac{\frac{n}{4} + [\frac{n}{4} + 1] }{2}$

=>    $1st \ Q = \frac{\frac{74}{4} + [\frac{74}{4} + 1] }{2}$

=>     $1st \ Q = 19 \ girl$

From the histogram $19^{th}$girl fall under 1 fruit per day

 Generally the third quartile is mathematically represented as

     $3rd\ Q = \frac{\frac{n}{2} + n }{2}$

=>    $3rd\ Q = \frac{\frac{74}{2} + 74 }{2}$

=>    $3rd\ Q = 55.5$

From the histogram $55.5 \approx 56^{th} \ girl$ 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    $\sum f = 74$

xf                                       0    11    30   33   32  25   18   21     24    $\sum xf = 194$

Generally the mean is mathematically represented as

      $\= x = \frac{1}{ \sum f} * [\sum xf]$

=>     $\= x = \frac{1}{ 74} *194$

=>      $\= x = 2.62$