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High School Mathematics - 2
11.7 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:
fData
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:
1 2
2 3
3 4
4 5

Answer:

Q 2: Find the standard deviation for the data:
4 5
3 5
4 6
7 8
9 12

Answer:

Q 3: Find the standard deviation for the data:
10 12
13 8
4 11

Answer:

Q 4: Find the standard deviation for the data:
100 200
300 400
500 600

Answer:

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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