What is the standard deviation of students math test scores? 12 18 27 31 40 42...

What is the standard deviation of students math test scores? 12 18 27 31 40 42 14 20 27 32 40 51 14 20 27 32 40 56 14 21 29 32 40 60 16 23 31 36 40 65

Solutions

Expert Solution

Standard deviation - s

s =

s is standard deviation

x are the data individual values

xbar or x? is mean

n is the number of data values

Step 1 - calculate mean

n= 30

= 12+18+27+31+40+42+14+20+27+32+40+51+14+20+27+32+40+56+14+21+29+32+40+60+16+23+31+36+40+65

=950

x? or mean = 950÷30 = 31.66

Step2?- Subtract mean 31.66 from each value of x

we get these values -

-19.66,-13.66, -4.66, -0.66, 8.33, 10.33, -17.66, -11.66, -4.66, 0.33, 8.33, 19.33, -17.66, -11.66, -4.66, 0.33, 8.33, 24.33, -17.66, -10.66, -2.66, 0.33, 8.33, 28.33, -15.66, -8.66, -0.66, 4.33, 8.33, 33.33

Step 3- Squaring the above given values, we obtain

386.77, 186.77, 21.77, 0.44, 69.44, 106.77, 312.11, 136.11, 21.77, 0.11, 69.44, 373.77, 312.11, 136.12, 21.77, 0.11, 69.44, 592.11, 312.11, 113.77, 7.11, 0.11, 69.44, 802.77, 245.44, 75.11, 0.44, 18.77, 69.44, 1111.11

Step 4- Sum of the squared differences

386.77+ 186.77+ 21.77+ 0.44+ 69.44+ 106.77+ 312.11+ 136.11+ 21.77+ 0.11+ 69.44+ 373.77+ 312.11+ 136.12+ 21.77+ 0.11+ 69.44+ 592.11+ 312.11+ 113.77+ 7.11+ 0.11+ 69.44+ 802.77+ 245.44+ 75.11+ 0.44+ 18.77+ 69.44+ 1111.11

=5642.66

putting all the values in formuls we get

s =

s= 13.94

Hayet Jeridi answered 5 months ago

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