Answer
350.1k+ views
Hint: To prepare the frequency chart of the above data, we have to count the number of times a particular temperature appears. The maximum and the minimum temperature is the highest and the lowest value of the temperature recorded. And the range of temperature is writing the lowest and highest value together with (hyphen) separating them. Now, the mean temperature of the month is calculated by using the following formula: $Mean=\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$.
Complete step by step answer:
The table of the temperatures given in the above problem is as follows:
Solving part (a) of the above problem we get,
We are going to make a table of the temperature and the frequency of that particular temperature. Now, frequency is the number of times a particular observation occurs.
Hence, we have solved part (a).
Solving the part (b) we get,
The maximum temperature recorded in the month of September is ${{38}^{\circ }}C$.
Solving the part (c) we get,
The minimum temperature recorded in the month of September is ${{30}^{\circ }}C$.
Solving the part (d) we get,
The range of the temperature recorded in the month of September is equal to: $\left( {{30}^{\circ }}C-{{38}^{\circ }}C \right)$.
Solving the part (e) we get,
We are asked to find the mean temperature recorded in the month of September which we are going to find by using the following formula of the mean:
$Mean=\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$
Total number of observations is calculated by adding the frequencies which we have written above. Adding the frequencies of the temperatures we get,
From the above, we got the total number of the observations as 30.
Now, we are going to find the sum of all the observations by adding all the observations:
We are going to add the above observations by multiplying frequency of the given temperature from the table which we have drawn above:
$\begin{align}
& 30\left( 3 \right)+31\left( 5 \right)+32\left( 5 \right)+33\left( 2 \right)+34\left( 4 \right)+35\left( 5 \right)+36\left( 2 \right)+37\left( 1 \right)+38\left( 3 \right) \\
& =90+155+160+66+136+175+72+37+114 \\
& =1005 \\
\end{align}$
Now, we are going to substitute the value of sum of all observations and the total number of observations in the formula for mean and we get,
$\begin{align}
& Mean=\dfrac{1005}{30} \\
& \Rightarrow Mean={{33.5}^{\circ }}C \\
\end{align}$
Hence, we have found the mean of the temperatures recorded in the month of September.
Note: Instead of the way we have added the observations in the above solution, we can just add all the observations one by one. We did the addition which we have shown above in that manner because it will reduce the time needed to do the addition.
Complete step by step answer:
The table of the temperatures given in the above problem is as follows:
31 | 35 | 32 | 31 | 38 | 30 | 36 | 35 | 32 | 35 | 38 | 33 | 33 | 34 | 38 |
32 | 30 | 31 | 32 | 36 | 37 | 34 | 31 | 34 | 35 | 30 | 32 | 31 | 34 | 35 |
Solving part (a) of the above problem we get,
We are going to make a table of the temperature and the frequency of that particular temperature. Now, frequency is the number of times a particular observation occurs.
Temperature$\left( ^{\circ }C \right)$ | Frequency |
30 | 3 |
31 | 5 |
32 | 5 |
33 | 2 |
34 | 4 |
35 | 5 |
36 | 2 |
37 | 1 |
38 | 3 |
Hence, we have solved part (a).
Solving the part (b) we get,
The maximum temperature recorded in the month of September is ${{38}^{\circ }}C$.
Solving the part (c) we get,
The minimum temperature recorded in the month of September is ${{30}^{\circ }}C$.
Solving the part (d) we get,
The range of the temperature recorded in the month of September is equal to: $\left( {{30}^{\circ }}C-{{38}^{\circ }}C \right)$.
Solving the part (e) we get,
We are asked to find the mean temperature recorded in the month of September which we are going to find by using the following formula of the mean:
$Mean=\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$
Total number of observations is calculated by adding the frequencies which we have written above. Adding the frequencies of the temperatures we get,
Frequency |
3 |
5 |
5 |
2 |
4 |
5 |
2 |
1 |
3 |
Total:30 |
From the above, we got the total number of the observations as 30.
Now, we are going to find the sum of all the observations by adding all the observations:
We are going to add the above observations by multiplying frequency of the given temperature from the table which we have drawn above:
$\begin{align}
& 30\left( 3 \right)+31\left( 5 \right)+32\left( 5 \right)+33\left( 2 \right)+34\left( 4 \right)+35\left( 5 \right)+36\left( 2 \right)+37\left( 1 \right)+38\left( 3 \right) \\
& =90+155+160+66+136+175+72+37+114 \\
& =1005 \\
\end{align}$
Now, we are going to substitute the value of sum of all observations and the total number of observations in the formula for mean and we get,
$\begin{align}
& Mean=\dfrac{1005}{30} \\
& \Rightarrow Mean={{33.5}^{\circ }}C \\
\end{align}$
Hence, we have found the mean of the temperatures recorded in the month of September.
Note: Instead of the way we have added the observations in the above solution, we can just add all the observations one by one. We did the addition which we have shown above in that manner because it will reduce the time needed to do the addition.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)