Standard deviation is a measure of how spread out data values are from the mean, representing the typical distance of data points from the average. A small standard deviation means data clusters tightly around the mean; a large one means data is widely spread.
If the mean is 'home base,' standard deviation tells you how far data points typically wander from home. Small SD = data clusters close to the mean (like a tight group of friends). Large SD = data is scattered (friends spread all over town).
Showing a random 20 of 50 problems.
Example 1
hard
What is the SD of a,a (only two equal values)?
Example 2
medium
A set has population SD 4. Each value is divided by 2. What is the new SD?
Example 3
medium
Calculate the population standard deviation of: 10, 12, 14.
Example 4
challenge
Two data sets each have n=4 values with mean 5 and population SD 2. Must the two sets have the same values?
Example 5
challenge
Show why adding a value far above the mean increases the SD more than adding a value near the mean (one sentence reason).
Example 6
easy
Standard deviation is the square root of which other statistic?
Example 7
hard
For data {1,2,3,4,5}, compute the population SD.
Example 8
easy
Which data set is more spread out: A={5,5,5} or B={1,5,9}?Set B has values 1, 5, 9 — spread widely from low to high. Set A
Example 9
easy
A set has population variance 36. What is its standard deviation?
Example 10
easy
Can a standard deviation be −3?
Example 11
medium
Compute the population standard deviation of 2,4,4,4,5,5,7,9.The 8 data values {2, 4, 4, 4, 5, 5, 7, 9} plotted in order. The mean is 5 and σ
Example 12
medium
Find the population SD of 1,3,5,7.
Example 13
easy
A constant data set has SD equal to what?
Example 14
medium
For population variance σ2 and sample variance s2, which divides by n−1?
Example 15
easy
Find the mean of 2,4,6.
Example 16
easy
SD has the same units as which quantity?
Example 17
medium
A sample 3,5,7 has mean 5. Compute the SAMPLE standard deviation (divide by n−1).
Example 18
easy
Compute the variance of 2,4 (population).
Example 19
medium
A data set has SD 6. Each value gets 10 added. What is the new SD?
Example 20
easy
A data set with values tightly clustered near the mean has a (small / large) standard deviation?