Solution:
a. original [tex]\bar{x} =70,000 =\frac{\sum x}{n}[/tex]
[tex]\therefore \sum x = 70,000 \times 10 =700,000[/tex]
[tex]modified \sum x = 700,000 - 100,000 + 1,000,000 = 1,600,000[/tex]
[tex]modified \bar{x} = \frac{1,600,000}{10} =160,000[/tex]
b. Median remains the same.
c. [tex]original s^{2}=(20,000)^{2}=400000000=\frac{1}{n-1}[\sum x^{2}- n\bar{x}^{2}][/tex]
[tex]\therefore orig. \sum x^{2} = (10-1)(20000)^{2} + 10(70000)^{2}[/tex]
[tex]=52600000000[/tex]
[tex]mod. \sum x^{2} = 52600000000-100000^{2} +1000000^{2}[/tex]
[tex]=1.0426E+12[/tex]
[tex]mod.s^{2} = \frac{1}{n-1} [\sum x^{2} - n\bar{x}^{2}][/tex]
[tex]=\frac{1}{9} [1.0426E+12 - 10 \times 160000^{2}][/tex]
[tex]=87400000000[/tex]
[tex]modified s= \sqrt{s^{2}} =\sqrt{87400000000} =295634.91[/tex]
