Answer:
It equals 10.5
Step-by-step explanation:
Answer:
a) 4.60 (2 dp)
b) 1.31 (2 dp)
c) 8.8
Step-by-step explanation:
The "Frequency" part of a frequency table is the measure of how often the data value occurs.
To calculate the mean of data presented in a frequency table, we need to multiply each data value by its given frequency, sum these, then divide by the sum of the frequency.
The formula for mean is:
![\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}](https://tex.z-dn.net/?f=%5Ctextsf%7Bmean%7D%3D%5Coverline%7Bx%7D%3D%5Cdfrac%7B%5Cdisplaystyle%20%5Csum%20fx%7D%7B%5Cdisplaystyle%5Csum%20f%7D)
<h3><u>Part (a)</u></h3>
Add a row showing the values of ![fx](https://tex.z-dn.net/?f=fx)
Add a column showing the totals of
and ![fx](https://tex.z-dn.net/?f=fx)
![\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7B%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%5Ccline%7B1-8%7D%20%26%20%26%20%26%20%26%20%26%20%26%20%26%20%5Csf%20Total%20%5C%5C%5Ccline%7B1-8%7D%20x%20%26%202%20%26%203%20%26%204%20%26%205%20%26%206%20%26%207%20%26%20%5C%5C%5Ccline%7B1-8%7D%20%5Ctextsf%7BFrequency%7D%5C%3Af%20%26%2011%20%26%2017%20%26%2024%20%26%2023%20%26%2018%20%26%2015%20%26%20108%5C%5C%5Ccline%7B1-8%7D%20fx%20%26%2022%20%26%2051%20%26%2096%20%26%20115%26%20108%20%26%20105%20%26497%20%5C%5C%5Ccline%7B1-8%7D%5Cend%7Barray%7D)
Now use the formula to calculate the mean:
![\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7Bmean%7D%3D%5Coverline%7Bx%7D%3D%5Cdfrac%7B497%7D%7B108%7D%3D4.60%5C%3A%5Ctextsf%7B%282%20dp%29%7D)
<h3><u>Part (b)</u></h3>
Add a column showing the values of ![fx](https://tex.z-dn.net/?f=fx)
Add a row showing the totals of
and ![fx](https://tex.z-dn.net/?f=fx)
![\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7B%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%5Ccline%7B1-3%7D%20x%20%26%20%5Ctextsf%7BFrequency%7D%5C%3A%20f%20%26%20fx%20%5C%5C%5Ccline%7B1-3%7D%200%20%26%2035%20%26%200%20%5C%5C%5Ccline%7B1-3%7D%201%20%26%2076%20%26%2076%5C%5C%5Ccline%7B1-3%7D%202%20%26%2048%20%26%2096%5C%5C%5Ccline%7B1-3%7D%203%20%26%2022%20%26%2066%20%5C%5C%5Ccline%7B1-3%7D%20%5Csf%20Total%20%26%20181%20%26%20238%20%5C%5C%5Ccline%7B1-3%7D%5Cend%7Barray%7D)
Now use the formula to calculate the mean:
![\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7Bmean%7D%3D%5Coverline%7Bx%7D%3D%5Cdfrac%7B238%7D%7B181%7D%3D1.31%5C%3A%5Ctextsf%7B%282%20dp%29%7D)
<h3><u>Part (c)</u></h3>
Add a column showing the values of ![fx](https://tex.z-dn.net/?f=fx)
Add a row showing the totals of
and ![fx](https://tex.z-dn.net/?f=fx)
![\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}](https://tex.z-dn.net/?f=%5Clarge%5Cbegin%7Barray%7D%7B%7C%20c%20%7C%20c%20%7C%20c%20%7C%7D%5Ccline%7B1-3%7D%20x%20%26%20%5Ctextsf%7BTally%7D%5C%3A%20f%20%26%20fx%20%5C%5C%5Ccline%7B1-3%7D%208%20%26%207%20%26%2056%5C%5C%5Ccline%7B1-3%7D%209%20%26%2010%20%26%2090%5C%5C%5Ccline%7B1-3%7D%2010%20%26%203%20%26%2030%5C%5C%5Ccline%7B1-3%7D%20%5Csf%20Total%20%26%2020%20%26%20176%5C%5C%5Ccline%7B1-3%7D%5Cend%7Barray%7D)
Now use the formula to calculate the mean:
![\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7Bmean%7D%3D%5Coverline%7Bx%7D%3D%5Cdfrac%7B176%7D%7B20%7D%3D8.8)
Y is 8
And X is -4 because 8 divide by -2 is -4
Answer:
Go on to photo math it's good for equations
C.the ant would be the most likely thing to have a mass of three grams.