The data list shows the scores of ten students th Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100
What is the standard deviation, to the nearest tenth, of the data If the scores represent a sample of Mr. Smith's students?
What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr.
Smith's students?
Sample:
Entire population:

Sample SD = 12.3

Population SD = 11.7.

Step-by-step explanation:

The mean of the scores

= The sum of the ten numbers  / 10

= 84.4

Now work out the differences of each score from this mean

61 - 84.4 = -23.4 ;  67 - 84.4 = -17.4

The other 8 differences are -3.4, -1.4, 2.6, 3.6, 4.6, 5.6, 13.6 and 15.6

Squares of these differences are :

547.56, 302.76, 11.56, 1.96, 6.76, 12.96, 21.16, 31.36, 184.96 and 243.36.

The Sum of these squares = 1364.4

The Sample Standard Deviation = √(sum of the squared difference/ (n-1)]

= √[1364.4/9]

= 12.3.

The Population Standard Deviation = √(sum of the squared difference/ (n)]

= √[1364.4/10]

= 11.7.

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the correct answer is c