Compare Two Populations Using Data - 7th Grade Math
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Identify the better evidence of a population difference: one sample or many random samples?
Identify the better evidence of a population difference: one sample or many random samples?
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Many random samples. Multiple samples provide more reliable population estimates.
Many random samples. Multiple samples provide more reliable population estimates.
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Identify the median of the ordered data $2, 4, 6, 8, 10$.
Identify the median of the ordered data $2, 4, 6, 8, 10$.
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$6$. With 5 values, the 3rd position is the median.
$6$. With 5 values, the 3rd position is the median.
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What should you compare to decide which population is more consistent (less spread out)?
What should you compare to decide which population is more consistent (less spread out)?
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Compare measures of variability (such as range or $\text{IQR}$). Lower variability means more predictable values.
Compare measures of variability (such as range or $\text{IQR}$). Lower variability means more predictable values.
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Identify the median of the ordered data $1, 3, 5, 7, 9, 11$.
Identify the median of the ordered data $1, 3, 5, 7, 9, 11$.
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$\frac{5+7}{2} = 6$. With 6 values, average the 3rd and 4th positions.
$\frac{5+7}{2} = 6$. With 6 values, average the 3rd and 4th positions.
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Which population is generally larger if sample medians are $12$ (A) and $9$ (B)?
Which population is generally larger if sample medians are $12$ (A) and $9$ (B)?
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Population A. Higher median suggests generally larger values.
Population A. Higher median suggests generally larger values.
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Which sample shows greater variability if $\text{IQR}_A = 4$ and $\text{IQR}_B = 9$?
Which sample shows greater variability if $\text{IQR}_A = 4$ and $\text{IQR}_B = 9$?
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Sample B. Larger IQR indicates more spread in the data.
Sample B. Larger IQR indicates more spread in the data.
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What is a random sample in a population comparison?
What is a random sample in a population comparison?
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A sample chosen so each member of the population has an equal chance. Ensures unbiased representation of the population.
A sample chosen so each member of the population has an equal chance. Ensures unbiased representation of the population.
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Which measure of center is most affected by extreme values (outliers)?
Which measure of center is most affected by extreme values (outliers)?
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Mean. Outliers pull the mean toward extreme values.
Mean. Outliers pull the mean toward extreme values.
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Which measure of center is usually preferred for skewed data or outliers?
Which measure of center is usually preferred for skewed data or outliers?
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Median. Less affected by extreme values than the mean.
Median. Less affected by extreme values than the mean.
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What does a measure of variability describe about a data set?
What does a measure of variability describe about a data set?
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How spread out the data values are (such as range or $\text{IQR}$). Indicates whether values cluster together or spread widely.
How spread out the data values are (such as range or $\text{IQR}$). Indicates whether values cluster together or spread widely.
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What does a measure of center describe about a data set?
What does a measure of center describe about a data set?
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A typical value (such as mean or median) for the distribution. Represents where the data is centered or clustered.
A typical value (such as mean or median) for the distribution. Represents where the data is centered or clustered.
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What does the interquartile range (IQR) measure?
What does the interquartile range (IQR) measure?
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Variability of the middle $50%$ of the data: $\text{IQR} = Q_3 - Q_1$. Shows spread of the middle half, excluding outliers.
Variability of the middle $50%$ of the data: $\text{IQR} = Q_3 - Q_1$. Shows spread of the middle half, excluding outliers.
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What is the median of a data set?
What is the median of a data set?
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The middle value when data are ordered; average of two middles if even. For odd counts, it's the middle; for even, average the two middle values.
The middle value when data are ordered; average of two middles if even. For odd counts, it's the middle; for even, average the two middle values.
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What is the mean of a data set?
What is the mean of a data set?
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The sum of values divided by the number of values. Add all values and divide by how many there are.
The sum of values divided by the number of values. Add all values and divide by how many there are.
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What is the range of a data set?
What is the range of a data set?
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Maximum value minus minimum value. Measures the full spread from smallest to largest value.
Maximum value minus minimum value. Measures the full spread from smallest to largest value.
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What should you compare first to decide which population has generally larger values?
What should you compare first to decide which population has generally larger values?
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Compare measures of center (median or mean) of the two samples. Centers show which population typically has higher values.
Compare measures of center (median or mean) of the two samples. Centers show which population typically has higher values.
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What is an informal comparative inference using samples?
What is an informal comparative inference using samples?
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A conclusion about which population tends to be larger based on sample stats. Uses sample statistics to compare population characteristics.
A conclusion about which population tends to be larger based on sample stats. Uses sample statistics to compare population characteristics.
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Which option best supports a real population difference: similar centers or clearly different centers?
Which option best supports a real population difference: similar centers or clearly different centers?
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Clearly different centers. Large center differences suggest distinct populations.
Clearly different centers. Large center differences suggest distinct populations.
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Find $\text{IQR}$ if $Q_1 = 7$ and $Q_3 = 19$.
Find $\text{IQR}$ if $Q_1 = 7$ and $Q_3 = 19$.
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$12$. IQR = third quartile - first quartile = $19 - 7 = 12$.
$12$. IQR = third quartile - first quartile = $19 - 7 = 12$.
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What does a larger IQR usually indicate when comparing two populations?
What does a larger IQR usually indicate when comparing two populations?
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More variability in the population. The data values are more spread out.
More variability in the population. The data values are more spread out.
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What does a larger difference in medians usually indicate when comparing two populations?
What does a larger difference in medians usually indicate when comparing two populations?
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A difference in typical value (center). The populations have different typical values.
A difference in typical value (center). The populations have different typical values.
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Which measure of center is less affected by extreme values: mean or median?
Which measure of center is less affected by extreme values: mean or median?
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Median. Outliers pull the mean but not the median.
Median. Outliers pull the mean but not the median.
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Which measure of variability is less affected by extreme values: range or IQR?
Which measure of variability is less affected by extreme values: range or IQR?
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IQR. Range includes extremes; IQR focuses on the middle.
IQR. Range includes extremes; IQR focuses on the middle.
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What is an informal comparative inference about two populations based on samples?
What is an informal comparative inference about two populations based on samples?
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A cautious conclusion about populations using sample center and spread. We use samples to estimate population characteristics.
A cautious conclusion about populations using sample center and spread. We use samples to estimate population characteristics.
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Identify the better comparison for “generally larger”: mean, median, range, or IQR.
Identify the better comparison for “generally larger”: mean, median, range, or IQR.
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Median (a measure of center). Center measures typical size, not spread.
Median (a measure of center). Center measures typical size, not spread.
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