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### High School Mathematics - 211.7 Standard Deviation - Grouped Data

Example: Find the standard deviation for the data: 20, 23, 25, 26, 26, 23, 25, 25
The data can be grouped as follows:
 f Data 1 20 2 23 3 25 2 26
1. The arithmetic mean of the data (1*20+2*23+3*25+2*26)/8 = 24.125
The deviations from the mean are respectively:
24.125 - 20 = 4.125
24.125 - 23 = 1.125
25 - 24.125 = 0.875
26 - 24.125 = 1.875
The squares of these deviations are:
4.1252 = 17.015625
1.1252 = 1.265625
0.8752 = 0.765625
1.8752 = 3.515625
2. The sum of the squared results from step 1 are now multiplied by their associated f. This gives us:
for 20, 1 * 17.015625 = 17.015625
for 23, 2 * 1.265625 = 2.53125
for 25, 3 * 0.765625 = 2.296875
for 26, 2 * 3.515625 = 7.03125
3. The sum of the resulting products is 17.015625 + 2.53125 + 2.296875 + 7.03125 = 28.875.
Now divided by (n-1), which is 7
28.875/7 = 4.125
4. The square root of 4.125 is approximately 2.031
Answer: The Standard Deviation of the set of numbers {20, 23, 25, 26, 26, 23, 25, 25} is 2.031

Directions: Answer the following question. Also write an example of your own and try working out the standard deviation of the data.
 Q 1: Find the standard deviation for the data: 100 200 300 400 500 600Answer: Q 2: Find the standard deviation for the data: 1 2 2 3 3 4 4 5 Answer: Q 3: Find the standard deviation for the data: 5 2 3 4 1 2 6 5Answer: Q 4: Find the standard deviation for the data: 5 10 10 5 10 10 15 4 Answer: Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!