Answer:
![Range = 16](https://tex.z-dn.net/?f=Range%20%3D%2016)
![Inter\ Quartile\ Range = 6.75](https://tex.z-dn.net/?f=Inter%5C%20Quartile%5C%20Range%20%3D%206.75)
![Variance = 20.44](https://tex.z-dn.net/?f=Variance%20%3D%2020.44)
![Standard\ Deviation = 4.52](https://tex.z-dn.net/?f=Standard%5C%20Deviation%20%3D%204.52)
Step-by-step explanation:
Given
4, 17, 12, 9, 6, 10, 1, 5, 9, 3
Calculating the range;
![Range = Highest - Lowest](https://tex.z-dn.net/?f=Range%20%3D%20Highest%20-%20Lowest)
From the given data;
Highest = 17 and Lowest = 1
Hence;
![Range = 17 - 1](https://tex.z-dn.net/?f=Range%20%3D%2017%20-%201)
![Range = 16](https://tex.z-dn.net/?f=Range%20%3D%2016)
Calculating the Inter-quartile Range
Inter quartile range (IQR) is calculates as thus
![IQR = Q_3 - Q_1](https://tex.z-dn.net/?f=IQR%20%3D%20Q_3%20-%20Q_1)
Where
Q3 = Upper Quartile and Q1 = Lower Quartile
<em />
<em>Start by arranging the data in ascending order</em>
1, 3, 4, 5, 6, 9, 9, 10, 12, 17
N = Number of data; N = 10
---------------------------------------------------------------------------------
Calculating Q3
![Q_3 = \frac{3}{4}(N+1) th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%20%5Cfrac%7B3%7D%7B4%7D%28N%2B1%29%20th%5C%20item)
<em>Substitute 10 for N</em>
![Q_3 = \frac{3}{4}(10+1) th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%20%5Cfrac%7B3%7D%7B4%7D%2810%2B1%29%20th%5C%20item)
![Q_3 = \frac{3}{4}(11) th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%20%5Cfrac%7B3%7D%7B4%7D%2811%29%20th%5C%20item)
![Q_3 = \frac{33}{4} th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%20%5Cfrac%7B33%7D%7B4%7D%20th%5C%20item)
![Q_3 = 8.25 th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%208.25%20th%5C%20item)
Express 8.25 as 8 + 0.25
![Q_3 = (8 + 0.25) th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%20%288%20%2B%200.25%29%20th%5C%20item)
![Q_3 = 8th\ item + 0.25 th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%208th%5C%20item%20%2B%200.25%20th%5C%20item)
Express 0.25 as fraction
![Q_3 = 8th\ item +\frac{1}{4} th\ item](https://tex.z-dn.net/?f=Q_3%20%3D%208th%5C%20item%20%2B%5Cfrac%7B1%7D%7B4%7D%20th%5C%20item)
![Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)](https://tex.z-dn.net/?f=Q_3%20%3D%208th%5C%20item%20%2B%5Cfrac%7B1%7D%7B4%7D%20%289th%5C%20item%20-%208th%5C%20item%29)
From the arranged data;
and ![9th\ item = 12](https://tex.z-dn.net/?f=9th%5C%20item%20%3D%2012)
![Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)](https://tex.z-dn.net/?f=Q_3%20%3D%208th%5C%20item%20%2B%5Cfrac%7B1%7D%7B4%7D%20%289th%5C%20item%20-%208th%5C%20item%29)
![Q_3 = 10 +\frac{1}{4} (12 - 10)](https://tex.z-dn.net/?f=Q_3%20%3D%2010%20%2B%5Cfrac%7B1%7D%7B4%7D%20%2812%20-%2010%29)
![Q_3 = 10 +\frac{1}{4} (2)](https://tex.z-dn.net/?f=Q_3%20%3D%2010%20%2B%5Cfrac%7B1%7D%7B4%7D%20%282%29)
![Q_3 = 10 +0.5](https://tex.z-dn.net/?f=Q_3%20%3D%2010%20%2B0.5)
![Q_3 = 10.5](https://tex.z-dn.net/?f=Q_3%20%3D%2010.5)
Calculating Q1
![Q_1 = \frac{1}{4}(N+1) th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%20%5Cfrac%7B1%7D%7B4%7D%28N%2B1%29%20th%5C%20item)
<em>Substitute 10 for N</em>
![Q_1 = \frac{1}{4}(10+1) th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%20%5Cfrac%7B1%7D%7B4%7D%2810%2B1%29%20th%5C%20item)
![Q_1 = \frac{1}{4}(11) th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%20%5Cfrac%7B1%7D%7B4%7D%2811%29%20th%5C%20item)
![Q_1 = \frac{11}{4} th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%20%5Cfrac%7B11%7D%7B4%7D%20th%5C%20item)
![Q_1 = 2.75 th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%202.75%20th%5C%20item)
Express 2.75 as 2 + 0.75
![Q_1 = (2 + 0.75) th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%20%282%20%2B%200.75%29%20th%5C%20item)
![Q_1 = 2nd\ item + 0.75 th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%202nd%5C%20item%20%2B%200.75%20th%5C%20item)
Express 0.75 as fraction
![Q_1 = 2nd\ item +\frac{3}{4} th\ item](https://tex.z-dn.net/?f=Q_1%20%3D%202nd%5C%20item%20%2B%5Cfrac%7B3%7D%7B4%7D%20th%5C%20item)
![Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)](https://tex.z-dn.net/?f=Q_1%20%3D%202nd%5C%20item%20%2B%5Cfrac%7B3%7D%7B4%7D%20%283rd%5C%20item%20-%202nd%5C%20item%29)
From the arranged data;
and ![3rd\ item = 4](https://tex.z-dn.net/?f=3rd%5C%20item%20%3D%204)
![Q_1 = 3 +\frac{3}{4} (4 - 3)](https://tex.z-dn.net/?f=Q_1%20%3D%203%20%2B%5Cfrac%7B3%7D%7B4%7D%20%284%20-%203%29)
![Q_1 = 3 +\frac{3}{4} (1)](https://tex.z-dn.net/?f=Q_1%20%3D%203%20%2B%5Cfrac%7B3%7D%7B4%7D%20%281%29)
![Q_1 = 3 +0.75](https://tex.z-dn.net/?f=Q_1%20%3D%203%20%2B0.75)
![Q_1 = 3 .75](https://tex.z-dn.net/?f=Q_1%20%3D%203%20.75)
---------------------------------------------------------------------------------
Recall that
![IQR = Q_3 - Q_1](https://tex.z-dn.net/?f=IQR%20%3D%20Q_3%20-%20Q_1)
![IQR = 10.5 - 3.75](https://tex.z-dn.net/?f=IQR%20%3D%2010.5%20-%203.75)
![IQR = 6.75](https://tex.z-dn.net/?f=IQR%20%3D%206.75)
Calculating Variance
Start by calculating the mean
![Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7B1%2B3%2B4%2B5%2B6%2B9%2B9%2B10%2B12%2B17%7D%7B10%7D)
![Mean = \frac{76}{10}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7B76%7D%7B10%7D)
![Mean = 7.6](https://tex.z-dn.net/?f=Mean%20%3D%207.6)
Subtract the mean from each data, then square the result
![(1 - 7.6)^2 = (-6.6)^2 = 43.56](https://tex.z-dn.net/?f=%281%20-%207.6%29%5E2%20%3D%20%28-6.6%29%5E2%20%3D%2043.56)
![(3 - 7.6)^2 = (-4.6)^2 = 21.16](https://tex.z-dn.net/?f=%283%20-%207.6%29%5E2%20%3D%20%28-4.6%29%5E2%20%3D%2021.16)
![(4 - 7.6)^2 = (-3.6)^2 = 12.96](https://tex.z-dn.net/?f=%284%20-%207.6%29%5E2%20%3D%20%28-3.6%29%5E2%20%3D%2012.96)
![(5 - 7.6)^2 = (-2.6)^2 = 6.76](https://tex.z-dn.net/?f=%285%20-%207.6%29%5E2%20%3D%20%28-2.6%29%5E2%20%3D%206.76)
![(6 - 7.6)^2 = (-1.6)^2 = 2.56](https://tex.z-dn.net/?f=%286%20-%207.6%29%5E2%20%3D%20%28-1.6%29%5E2%20%3D%202.56)
![(9 - 7.6)^2 = (1.4)^2 = 1.96](https://tex.z-dn.net/?f=%289%20-%207.6%29%5E2%20%3D%20%281.4%29%5E2%20%3D%201.96)
![(9 - 7.6)^2 = (1.4)^2 = 1.96](https://tex.z-dn.net/?f=%289%20-%207.6%29%5E2%20%3D%20%281.4%29%5E2%20%3D%201.96)
![(10 - 7.6)^2 = (2.4)^2 = 5.76](https://tex.z-dn.net/?f=%2810%20-%207.6%29%5E2%20%3D%20%282.4%29%5E2%20%3D%205.76)
![(12 - 7.6)^2 = (4.4)^2 = 19.36](https://tex.z-dn.net/?f=%2812%20-%207.6%29%5E2%20%3D%20%284.4%29%5E2%20%3D%2019.36)
![(17 - 7.6)^2 = (9.4)^2 = 88.36](https://tex.z-dn.net/?f=%2817%20-%207.6%29%5E2%20%3D%20%289.4%29%5E2%20%3D%2088.36)
Sum the result
![43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4](https://tex.z-dn.net/?f=43.56%20%2B%2021.16%20%2B%2012.96%20%2B%206.76%20%2B%202.56%20%2B%201.96%20%2B%201.96%20%2B%205.76%20%2B%2019.36%20%2B%2088.36%20%3D%20204.4)
Divide by number of observation;
![Variance = \frac{204.4}{10}](https://tex.z-dn.net/?f=Variance%20%3D%20%5Cfrac%7B204.4%7D%7B10%7D)
![Variance = 20.44](https://tex.z-dn.net/?f=Variance%20%3D%2020.44)
Calculating Standard Deviation (SD)
![SD = \sqrt{Variance}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7BVariance%7D)
![SD = \sqrt{20.44}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B20.44%7D)
<em>(Approximated)</em>