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 โ spread widely from low to high. Set A = {5, 5, 5} has no spread at all.
Example 9
easy
A set has population variance 36. What is its standard deviation?
Example 10
easy
Can a standard deviation be โ3?
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 ฯ = 2.
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 ฯ2 and sample variance s2, which divides by nโ1?
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 nโ1).
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?