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Standard Error worksheet

Grade 12 to college

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Start from: Raw data
- Data set: 3, 4, 3, 3, 5, 4, 6, 10
Find: Standard error of the mean
Answer
2.
Problem 2.
- Start from: Raw data
- Data set: 2, 4, 4, 4, 5, 5, 7, 9
Find: Standard error of the mean
Answer
3.
Problem 3.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 11
- Sample size (n): 32
Find: Standard error of the mean
Answer
4.
Problem 4.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 10
- Sample size (n): 42
Find: Standard error of the mean
Answer
5.
Problem 5.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 18
- Sample size (n): 54
Find: Standard error of the mean
Answer
6.
Problem 6.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 15
- Sample size (n): 40
Find: Standard error of the mean
Answer
7.
Problem 7.
- Start from: Raw data
- Data set: 2, 4, 4, 3, 4, 3, 7, 8
Find: Standard error of the mean
Answer
8.
Problem 8.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 18
- Sample size (n): 32
Find: Standard error of the mean
Answer
9.
Problem 9.
- Start from: Standard deviation and sample size
- Sample standard deviation (s): 14
- Sample size (n): 24
Find: Standard error of the mean
Answer
10.
Problem 10.
- Start from: Raw data
- Data set: 3, 4, 3, 4, 5, 5, 7, 9
Find: Standard error of the mean
Answer

Answer key: Standard Error worksheet

1. Standard error of the mean: 0.84
1. Find the average (mean, x̄) of the 8 values
  $x̄$ $= \frac{3 + 4 + 3 + 3 + 5 + 4 + 6 + 10}{8}$ $= 4.75$
2. Find the sample standard deviation s, the typical distance from the average. Square each value's gap from the average, add them, divide by n − 1, then take the square root
  $s$ $= \sqrt{\frac{39.5}{7}}$ $= 2.37547$
3. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
4. Put in your values of s and n
  $SE$ $= \frac{2.37547}{\sqrt{8}}$ $= \frac{2.37547}{2.828427}$ $= 0.839855$
2. Standard error of the mean: 0.76
1. Find the average (mean, x̄) of the 8 values
  $x̄$ $= \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8}$ $= 5$
2. Find the sample standard deviation s, the typical distance from the average. Square each value's gap from the average, add them, divide by n − 1, then take the square root
  $s$ $= \sqrt{\frac{32}{7}}$ $= 2.13809$
3. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
4. Put in your values of s and n
  $SE$ $= \frac{2.13809}{\sqrt{8}}$ $= \frac{2.13809}{2.828427}$ $= 0.755929$
3. Standard error of the mean: 1.94
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{11}{\sqrt{32}}$ $= \frac{11}{5.656854}$ $= 1.944544$
4. Standard error of the mean: 1.54
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{10}{\sqrt{42}}$ $= \frac{10}{6.480741}$ $= 1.543033$
5. Standard error of the mean: 2.45
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{18}{\sqrt{54}}$ $= \frac{18}{7.348469}$ $= 2.44949$
6. Standard error of the mean: 2.37
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{15}{\sqrt{40}}$ $= \frac{15}{6.324555}$ $= 2.371708$
7. Standard error of the mean: 0.73
1. Find the average (mean, x̄) of the 8 values
  $x̄$ $= \frac{2 + 4 + 4 + 3 + 4 + 3 + 7 + 8}{8}$ $= 4.375$
2. Find the sample standard deviation s, the typical distance from the average. Square each value's gap from the average, add them, divide by n − 1, then take the square root
  $s$ $= \sqrt{\frac{29.875}{7}}$ $= 2.065879$
3. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
4. Put in your values of s and n
  $SE$ $= \frac{2.065879}{\sqrt{8}}$ $= \frac{2.065879}{2.828427}$ $= 0.730399$
8. Standard error of the mean: 3.18
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{18}{\sqrt{32}}$ $= \frac{18}{5.656854}$ $= 3.181981$
9. Standard error of the mean: 2.86
1. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
2. Put in your values of s and n
  $SE$ $= \frac{14}{\sqrt{24}}$ $= \frac{14}{4.898979}$ $= 2.857738$
10. Standard error of the mean: 0.73
1. Find the average (mean, x̄) of the 8 values
  $x̄$ $= \frac{3 + 4 + 3 + 4 + 5 + 5 + 7 + 9}{8}$ $= 5$
2. Find the sample standard deviation s, the typical distance from the average. Square each value's gap from the average, add them, divide by n − 1, then take the square root
  $s$ $= \sqrt{\frac{30}{7}}$ $= 2.070197$
3. Averages vary less than single values, so divide the standard deviation s by the square root of the sample size n
  $SE$ $= \frac{s}{\sqrt{n}}$
4. Put in your values of s and n
  $SE$ $= \frac{2.070197}{\sqrt{8}}$ $= \frac{2.070197}{2.828427}$ $= 0.731925$