NAME _____________________________________________ DATE ____________________________ PERIOD _____________
12-2 Study Guide and Intervention
Statistics and Parameters
Statistics and Parameters A statistic is a measure that describes a characteristic of a sample. A parameter is a
measure that describes a characteristic of a population. Statistics can change from sample to sample while parameters
do not.
Example: Identify the sample and the population for each situation. Then describe the sample statistic and the
population parameter.
a. At a local supermarket, a random sample of 50 shoppers is selected. The median amount spent at the
supermarket is calculated for the sample.
Sample: the group of 50 shoppers
Population: all shoppers at the supermarket
Sample statistic: median amount of time spent by shoppers in the sample Population parameter: median amount by all
shoppers spent at the supermarket
b. Every 20 minutes at a furniture factory, a finished sofa is pulled from the assembly line and checked for
defects. The percentage of sofas in the sample which are defective is then calculated.
Sample: the sofas checked for defects
Population: all sofas manufactured
Sample statistic: percentage of defective sofas in the sample Population parameter: percentage of all sofas which are
defective
Exercises
Identify the sample and the population for each situation. Then describe the sample statistic and the population
parameter.
1. WEATHER A meteorologist places ten weather stations in a county to measure rainfall. The mean annual rainfall is
calculated for the sample.
2. BOTANY A scientist randomly selects 20 trees in a forest. The mean height of the 20 trees is then calculated.
3. POLITICS A political reporter randomly selects 25 congressional districts across the country. The mean number of
votes cast in the 25 congressional districts is calculated.
Chapter 12
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Glencoe Algebra 1
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
12-2 Study Guide and Intervention (continued)
Statistics and Parameters
Statistical Analysis The mean absolute deviation is the average of the absolute values of the differences between the
mean and each value in the data set. It is used to predict errors and judge how well the mean represents the data. The
standard deviation is the calculated value that shows how data deviate from the mean of the set of data. The variance
of data is the square of the standard deviation.
Example: EMPLOYMENT Employees at a law firm keep track of how many hours they work each week:
{44, 48, 44, 40, 59}.
a. Find and interpret the mean absolute deviation.
Step 1 Find the mean. For this set of data, the mean is 47.
Step 2 Find the sum of the absolute values of the differences between each value in the set of data and the mean.
|44 − 47|+ |48 − 47| + |44 − 47|+ |40 − 47| + |59 − 47| = 3 + 1 + 3 + 7 + 12 = 26
Step 3 Divide the sum by the number of values in the set of data:
26 ÷ 5 = 5.2
The mean absolute deviation of 5.2 indicates that the data, on average, are 5.2 hours away from the mean of 47 hours.
b. Find and interpret the standard deviation.
Step 1 To find the variance, square the difference between each number and the mean. Then divide by the number of
values.
𝜎2 =
=
(44 − 47)2 + (48 − 47)2 + (44 − 47)2 + (40 − 47)2 + (59 − 47)2
5
(−3)2 + (1)2 + (−3)2 + (−7)2 + (12)2
5
=
9 + 1 + 9 + 49 + 144
5
=
212
5
or 42.4
Step 2 The standard deviation is the square root of the variance.
√𝜎 2 = √42.4
σ ≈ 6.51
The standard deviation is approximately 6.51, which is small compared to the mean of 47. This suggests that most of the
employees work relatively close to 47 hours per week.
Exercises
Find and interpret the mean absolute deviation and standard deviation of each set of data.
1. {2, 4, 6, 5, 5, 3, 5, 4}
Chapter 12
2. {13, 10, 36, 48, 52}
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Glencoe Algebra 1