Question

8. The following is the average daily temperature for Frederick, Maryland for the month of June:878989767575717384709484839071837391789280779177807577838171(a) Complete the frequency distribution for the data.TemperatureFrequencyRelative Frequency70-7475-7980-8485-8990-94(b) Which of the following is the correct histogram for this data?246810121416Temperature708090100Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(61,100,0,16);axes(186,2,1,null,2); fill="blue"; textabs([165,0],"Temperature","above");line([70,-0.32],[70,0.32]); text([70,0],"70","below");line([80,-0.32],[80,0.32]); text([80,0],"80","below");line([90,-0.32],[90,0.32]); text([90,0],"90","below");line([100,-0.32],[100,0.32]); text([100,0],"100","below");textabs([0,115],"Frequency","right",90);rect([70,0],[80,8]);rect([80,0],[90,16]);rect([90,0],[100,6]);]2468Temperature707580859095Frequency[Graphs generated by this script: setBorder(47,40,20,15); initPicture(65.5,95,0,8);axes(188,2,1,null,2); fill="blue"; textabs([165,0],"Temperature","above");line([70,-0.16],[70,0.16]); text([70,0],"70","below");line([75,-0.16],[75,0.16]); text([75,0],"75","below");line([80,-0.16],[80,0.16]); text([80,0],"80","below");line([85,-0.16],[85,0.16]); text([85,0],"85","below");line([90,-0.16],[90,0.16]); text([90,0],"90","below");line([95,-0.16],[95,0.16]); text([95,0],"95","below");textabs([0,115],"Frequency","right",90);rect([70,0],[75,6]);rect([75,0],[80,8]);rect([80,0],[85,8]);rect([85,0],[90,3]);rect([90,0],[95,5]);]2468101214Temperature708090100Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(61,100,0,14);axes(188,2,1,null,2); fill="blue"; textabs([165,0],"Temperature","above");line([70,-0.28],[70,0.28]); text([70,0],"70","below");line([80,-0.28],[80,0.28]); text([80,0],"80","below");line([90,-0.28],[90,0.28]); text([90,0],"90","below");line([100,-0.28],[100,0.28]); text([100,0],"100","below");textabs([0,115],"Frequency","right",90);rect([70,0],[80,14]);rect([80,0],[90,11]);rect([90,0],[100,5]);]2468Temperature707580859095Frequency

Answer 1

Part a

A frequency is the number of times a data value occurs. Then, in the frequency column, we will write the amount of data found in the intervals shown in the temperature column.

So, we have:

• Temperature 70 - 74: There are ,6, values in this interval

,

• Temperature 75 - 79: There are ,8 ,values in this interval

,

• Temperature 80 - 84: There are ,8, values in this interval

• Temperature 85 - 89: There are ,3, values in this interval

,

• Temperature 90 - 94: There are ,5, values in this interval

Now, the relative frequency is the proportion (or percent) of observations within a category and, it can be found using this formula:

`\begin{gathered} \text{relative frequency }=\frac{\text{ frequency}}{\text{ n}} \\ \end{gathered}`

Where n is the total data and also corresponds to the sum of all frequencies.

In this case, there are 30 data or values in total, then we have:

• Temperature 70 - 74:

`\text{relative frequency }=(6)/(30)=0.2`

• Temperature 75 - 79:

`\text{relative frequency }=(8)/(30)=0.27`

• Temperature 80 - 84:

`\text{relative frequency }=(8)/(30)=0.27`

• Temperature 85 - 89:

`\text{relative frequency }=(3)/(30)=0.1`

• Temperature 90 - 94:

`\text{relative frequency }=(5)/(30)=0.16`

Therefore, the table of the frequency distribution is

Part b

To o make the histogram associated with the given data set, on the x-axis, we put the intervals and the frequencies on the y-axis. So, we have:

Therefore, the correct histogram for this data is: