Standard Deviation exam prep
Standard deviation - correct answersIt indicates the difference between a group of values and their
mean, taking all of the data into account.
The standard deviation plays an important role in many tests of statistical significance.
The larger the standard deviation, the more the values differ from the mean, and therefore the more
widely they are spread out.
How to compute standard deviation - correct answersa.Calculate the mean.
b. Find the difference of each observations from the mean.
c. Square the differences of observations from the mean.
d. Add the squared values to get the sum of squares of the deviation.
e. Divide this sum by the number of observations minus one to get mean-squared deviation, called
Variance (σ2).
f. Find the square root of this variance to get root-mean squared deviation, called standard deviation.
Having squared the original, reverse the step of taking square root.
** go back to slide for formula and in depth explination
Calculation of standard deviation for grouped series - correct answersWithout finding the mean, SD can
be calculated in grouped series also by almost the same steps as for mean.
i. Make the frequency table.
ii. Place 0 opposite the middle group (working mean).
iii. Reduce the values to working units as in the case of mean dividing the differences from working
mean by class interval.
iv. Just as frequency is multiplied by working units for finding mean, similarly multiplied frequency by
squares of working units for finding the standard deviation.
v. Then apply the formula and find the mean and SD in working units as before.
vi. Convert this value of SD in real units. Multiply SD in working units by the size of class interval.
Uses of standard deviation - correct answersIt summarizes the deviations of a large distribution from
mean in one figure used as a unit of variation.
, Indicates whether the variation of difference of an individual from the mean is by chance, i.e. natural or
real due to some special reasons.
Helps in finding the standard error which determines whether the difference between means of two
similar samples is by chance or real.
It also helps in finding the suitable size of sample for valid conclusions
Range - correct answersThe range of distribution is the difference between the largest and the smallest
values in a set of observations.
Range = highest value in the series of data - lowest value of that series
Range of grouped data - correct answers= upper true limit of the highest class - lower true limit of the
lowest class
Mean deviation - correct answersEvery value of the variable differs from the sample mean by some
specific amount which is called its deviation.
Mean deviation is an average mean of the deviations of values from central value or central tendency.
Thus, the mean deviation can be defined 'as the mean of all the deviations in a given set of data
obtained from an average.
If the deviation is greater than the mean, the deviation is positive, but if it is less than the mean, the
deviation is negative.
Computation of mean deviation of ungrouped data - correct answersCalculate the mean from the data.
Calculate the deviation from the mean.
Sum up all deviations. All deviations are treated as positive.
Divide sum of all deviations by the total number of observations.
** go back to slides (29-30)
Mean deviation of grouped data - correct answersM.D. = ∑ IfdI/ ∑fWhich formula is used to calculate the
standard deviation of sample data? - correct answersA
A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3.
What does a z-score of 1.3 mean? - correct answersThe data point is 1.3 standard deviations away from
12.
A missing data value from a set of data has a z-score of -2.1. Fred already calculated the mean and
standard deviation to be mc025-1.jpg and mc025-2.jpg. What was the missing data value? Round the
answer to the nearest whole number. - correct answers39
Standard deviation - correct answersIt indicates the difference between a group of values and their
mean, taking all of the data into account.
The standard deviation plays an important role in many tests of statistical significance.
The larger the standard deviation, the more the values differ from the mean, and therefore the more
widely they are spread out.
How to compute standard deviation - correct answersa.Calculate the mean.
b. Find the difference of each observations from the mean.
c. Square the differences of observations from the mean.
d. Add the squared values to get the sum of squares of the deviation.
e. Divide this sum by the number of observations minus one to get mean-squared deviation, called
Variance (σ2).
f. Find the square root of this variance to get root-mean squared deviation, called standard deviation.
Having squared the original, reverse the step of taking square root.
** go back to slide for formula and in depth explination
Calculation of standard deviation for grouped series - correct answersWithout finding the mean, SD can
be calculated in grouped series also by almost the same steps as for mean.
i. Make the frequency table.
ii. Place 0 opposite the middle group (working mean).
iii. Reduce the values to working units as in the case of mean dividing the differences from working
mean by class interval.
iv. Just as frequency is multiplied by working units for finding mean, similarly multiplied frequency by
squares of working units for finding the standard deviation.
v. Then apply the formula and find the mean and SD in working units as before.
vi. Convert this value of SD in real units. Multiply SD in working units by the size of class interval.
Uses of standard deviation - correct answersIt summarizes the deviations of a large distribution from
mean in one figure used as a unit of variation.
, Indicates whether the variation of difference of an individual from the mean is by chance, i.e. natural or
real due to some special reasons.
Helps in finding the standard error which determines whether the difference between means of two
similar samples is by chance or real.
It also helps in finding the suitable size of sample for valid conclusions
Range - correct answersThe range of distribution is the difference between the largest and the smallest
values in a set of observations.
Range = highest value in the series of data - lowest value of that series
Range of grouped data - correct answers= upper true limit of the highest class - lower true limit of the
lowest class
Mean deviation - correct answersEvery value of the variable differs from the sample mean by some
specific amount which is called its deviation.
Mean deviation is an average mean of the deviations of values from central value or central tendency.
Thus, the mean deviation can be defined 'as the mean of all the deviations in a given set of data
obtained from an average.
If the deviation is greater than the mean, the deviation is positive, but if it is less than the mean, the
deviation is negative.
Computation of mean deviation of ungrouped data - correct answersCalculate the mean from the data.
Calculate the deviation from the mean.
Sum up all deviations. All deviations are treated as positive.
Divide sum of all deviations by the total number of observations.
** go back to slides (29-30)
Mean deviation of grouped data - correct answersM.D. = ∑ IfdI/ ∑fWhich formula is used to calculate the
standard deviation of sample data? - correct answersA
A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3.
What does a z-score of 1.3 mean? - correct answersThe data point is 1.3 standard deviations away from
12.
A missing data value from a set of data has a z-score of -2.1. Fred already calculated the mean and
standard deviation to be mc025-1.jpg and mc025-2.jpg. What was the missing data value? Round the
answer to the nearest whole number. - correct answers39
