Assess Visual Overlap of Distributions - 7th Grade Math
Card 1 of 25
What does $k=\frac{|\Delta|}{\text{MAD}}\approx 2$ suggest about overlap?
What does $k=\frac{|\Delta|}{\text{MAD}}\approx 2$ suggest about overlap?
Tap to reveal answer
Noticeable separation; overlap is smaller. When $k=2$, centers differ by twice the typical spread.
Noticeable separation; overlap is smaller. When $k=2$, centers differ by twice the typical spread.
← Didn't Know|Knew It →
Find $k$ if $\Delta=6$ and $\text{MAD}=3$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Find $k$ if $\Delta=6$ and $\text{MAD}=3$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Tap to reveal answer
$k=2$. $k=\frac{|6|}{3}=\frac{6}{3}=2$
$k=2$. $k=\frac{|6|}{3}=\frac{6}{3}=2$
← Didn't Know|Knew It →
Which statement best matches "similar variabilities" for two groups?
Which statement best matches "similar variabilities" for two groups?
Tap to reveal answer
Their MAD values are about the same size. Similar variabilities means the spreads are approximately equal.
Their MAD values are about the same size. Similar variabilities means the spreads are approximately equal.
← Didn't Know|Knew It →
Identify the correct unit for $k=\frac{|\Delta|}{\text{MAD}}$ (units or unitless).
Identify the correct unit for $k=\frac{|\Delta|}{\text{MAD}}$ (units or unitless).
Tap to reveal answer
Unitless (the units cancel). Both numerator and denominator have same units, which cancel out.
Unitless (the units cancel). Both numerator and denominator have same units, which cancel out.
← Didn't Know|Knew It →
What does a larger value of $k=\frac{|\Delta|}{\text{MAD}}$ indicate?
What does a larger value of $k=\frac{|\Delta|}{\text{MAD}}$ indicate?
Tap to reveal answer
Less overlap and a stronger difference between groups. Higher $k$ means centers are farther apart relative to variability.
Less overlap and a stronger difference between groups. Higher $k$ means centers are farther apart relative to variability.
← Didn't Know|Knew It →
What is the "center" of a numerical distribution in this standard?
What is the "center" of a numerical distribution in this standard?
Tap to reveal answer
A typical value such as the mean or the median. The center represents where most data values cluster in a distribution.
A typical value such as the mean or the median. The center represents where most data values cluster in a distribution.
← Didn't Know|Knew It →
What measure of variability is named in CCSS.7.SP.3 as an example?
What measure of variability is named in CCSS.7.SP.3 as an example?
Tap to reveal answer
Mean absolute deviation (MAD). MAD measures average distance from the mean, showing spread.
Mean absolute deviation (MAD). MAD measures average distance from the mean, showing spread.
← Didn't Know|Knew It →
What does $k=\frac{|\Delta|}{\text{MAD}}\approx 0$ suggest about overlap?
What does $k=\frac{|\Delta|}{\text{MAD}}\approx 0$ suggest about overlap?
Tap to reveal answer
Heavy overlap; centers are nearly the same. When $k$ is near 0, the difference is tiny relative to spread.
Heavy overlap; centers are nearly the same. When $k$ is near 0, the difference is tiny relative to spread.
← Didn't Know|Knew It →
Identify the correct conclusion if $|\Delta|=2$ and $\text{MAD}=8$ for two groups.
Identify the correct conclusion if $|\Delta|=2$ and $\text{MAD}=8$ for two groups.
Tap to reveal answer
Strong overlap because $k=\frac{2}{8}=0.25$ is small. $k=\frac{2}{8}=0.25$ is close to 0, indicating minimal separation.
Strong overlap because $k=\frac{2}{8}=0.25$ is small. $k=\frac{2}{8}=0.25$ is close to 0, indicating minimal separation.
← Didn't Know|Knew It →
If $\text{MAD}=5$ and $k=1.2$, what is $|\Delta|$ from $k=\frac{|\Delta|}{\text{MAD}}$?
If $\text{MAD}=5$ and $k=1.2$, what is $|\Delta|$ from $k=\frac{|\Delta|}{\text{MAD}}$?
Tap to reveal answer
$|\Delta|=6$. Rearrange: $|\Delta|=k \times \text{MAD}=1.2 \times 5=6$
$|\Delta|=6$. Rearrange: $|\Delta|=k \times \text{MAD}=1.2 \times 5=6$
← Didn't Know|Knew It →
If $\Delta=12$ and $k=3$, what is $\text{MAD}$ from $k=\frac{|\Delta|}{\text{MAD}}$?
If $\Delta=12$ and $k=3$, what is $\text{MAD}$ from $k=\frac{|\Delta|}{\text{MAD}}$?
Tap to reveal answer
$\text{MAD}=4$. Rearrange: $\text{MAD}=\frac{|\Delta|}{k}=\frac{12}{3}=4$
$\text{MAD}=4$. Rearrange: $\text{MAD}=\frac{|\Delta|}{k}=\frac{12}{3}=4$
← Didn't Know|Knew It →
Choose the pair with more overlap: Pair A $k=\frac{3}{6}$ or Pair B $k=\frac{6}{3}$.
Choose the pair with more overlap: Pair A $k=\frac{3}{6}$ or Pair B $k=\frac{6}{3}$.
Tap to reveal answer
Pair A, because $\frac{3}{6}=0.5$ is smaller than $\frac{6}{3}=2$. Smaller $k$ means more overlap: $0.5 < 2$.
Pair A, because $\frac{3}{6}=0.5$ is smaller than $\frac{6}{3}=2$. Smaller $k$ means more overlap: $0.5 < 2$.
← Didn't Know|Knew It →
Choose the larger separation: Pair 1 $k=\frac{8}{4}$ or Pair 2 $k=\frac{9}{6}$.
Choose the larger separation: Pair 1 $k=\frac{8}{4}$ or Pair 2 $k=\frac{9}{6}$.
Tap to reveal answer
Pair 1, because $\frac{8}{4}=2$ is larger than $\frac{9}{6}=1.5$. Compare: $\frac{8}{4}=2$ vs $\frac{9}{6}=1.5$; 2 > 1.5.
Pair 1, because $\frac{8}{4}=2$ is larger than $\frac{9}{6}=1.5$. Compare: $\frac{8}{4}=2$ vs $\frac{9}{6}=1.5$; 2 > 1.5.
← Didn't Know|Knew It →
If $\bar{x}_A=15$, $\bar{x}_B=20$, what is $|\Delta|$ for $\Delta=\bar{x}_A-\bar{x}_B$?
If $\bar{x}_A=15$, $\bar{x}_B=20$, what is $|\Delta|$ for $\Delta=\bar{x}_A-\bar{x}_B$?
Tap to reveal answer
$|\Delta|=5$. $\Delta=15-20=-5$, so $|\Delta|=|-5|=5$
$|\Delta|=5$. $\Delta=15-20=-5$, so $|\Delta|=|-5|=5$
← Didn't Know|Knew It →
Find $\Delta$ if $\bar{x}_A=72$ and $\bar{x}_B=68$ using $\Delta=\bar{x}_A-\bar{x}_B$.
Find $\Delta$ if $\bar{x}_A=72$ and $\bar{x}_B=68$ using $\Delta=\bar{x}_A-\bar{x}_B$.
Tap to reveal answer
$\Delta=4$. $\Delta=72-68=4$
$\Delta=4$. $\Delta=72-68=4$
← Didn't Know|Knew It →
Find $k$ if $\Delta=4$ and $\text{MAD}=8$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Find $k$ if $\Delta=4$ and $\text{MAD}=8$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Tap to reveal answer
$k=0.5$. $k=\frac{|4|}{8}=\frac{4}{8}=0.5$
$k=0.5$. $k=\frac{|4|}{8}=\frac{4}{8}=0.5$
← Didn't Know|Knew It →
Find $k$ if $\Delta=10$ and $\text{MAD}=5$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Find $k$ if $\Delta=10$ and $\text{MAD}=5$ using $k=\frac{|\Delta|}{\text{MAD}}$.
Tap to reveal answer
$k=2$. $k=\frac{|10|}{5}=\frac{10}{5}=2$
$k=2$. $k=\frac{|10|}{5}=\frac{10}{5}=2$
← Didn't Know|Knew It →
Find the multiple if $|\bar{x}_A-\bar{x}_B|=10$ and $\text{MAD}=5$.
Find the multiple if $|\bar{x}_A-\bar{x}_B|=10$ and $\text{MAD}=5$.
Tap to reveal answer
$2$. $\frac{10}{5}=2$
$2$. $\frac{10}{5}=2$
← Didn't Know|Knew It →
What does a separation multiple of at least $3$ usually suggest about overlap?
What does a separation multiple of at least $3$ usually suggest about overlap?
Tap to reveal answer
Little overlap; centers are far apart compared with variability. Large multiples indicate minimal distribution overlap.
Little overlap; centers are far apart compared with variability. Large multiples indicate minimal distribution overlap.
← Didn't Know|Knew It →
What does a separation multiple around $2$ suggest about visual overlap on a dot plot?
What does a separation multiple around $2$ suggest about visual overlap on a dot plot?
Tap to reveal answer
Noticeable separation; overlap is reduced compared with variability. Centers separated by 2 MADs show clear distinction.
Noticeable separation; overlap is reduced compared with variability. Centers separated by 2 MADs show clear distinction.
← Didn't Know|Knew It →
What does a separation multiple near $0$ suggest about visual overlap on a dot plot?
What does a separation multiple near $0$ suggest about visual overlap on a dot plot?
Tap to reveal answer
Heavy overlap; centers are very close compared with variability. Small multiples mean centers are close relative to spread.
Heavy overlap; centers are very close compared with variability. Small multiples mean centers are close relative to spread.
← Didn't Know|Knew It →
Compute $\text{MAD}$ for data ${5,5,9}$ using $\text{MAD}=\frac{\sum |x-\bar{x}|}{n}$.
Compute $\text{MAD}$ for data ${5,5,9}$ using $\text{MAD}=\frac{\sum |x-\bar{x}|}{n}$.
Tap to reveal answer
$\frac{16}{9}$. $\bar{x}=\frac{19}{3}$; sum of absolute deviations is $\frac{16}{3}$
$\frac{16}{9}$. $\bar{x}=\frac{19}{3}$; sum of absolute deviations is $\frac{16}{3}$
← Didn't Know|Knew It →
Compute $\text{MAD}$ for data ${2,4,6}$ using $\text{MAD}=\frac{\sum |x-\bar{x}|}{n}$.
Compute $\text{MAD}$ for data ${2,4,6}$ using $\text{MAD}=\frac{\sum |x-\bar{x}|}{n}$.
Tap to reveal answer
$\frac{4}{3}$. $\bar{x}=4$; deviations: $2,0,2$; MAD=\frac{4}{3}$
$\frac{4}{3}$. $\bar{x}=4$; deviations: $2,0,2$; MAD=\frac{4}{3}$
← Didn't Know|Knew It →
Which option indicates the most overlap: multiple $0.2$, $1.4$, $2.1$, or $3.0$?
Which option indicates the most overlap: multiple $0.2$, $1.4$, $2.1$, or $3.0$?
Tap to reveal answer
$0.2$. Smallest multiple means greatest overlap.
$0.2$. Smallest multiple means greatest overlap.
← Didn't Know|Knew It →
Which option indicates the least overlap: multiple $0.5$, $1$, $2$, or $3$?
Which option indicates the least overlap: multiple $0.5$, $1$, $2$, or $3$?
Tap to reveal answer
$3$. Largest multiple means greatest separation.
$3$. Largest multiple means greatest separation.
← Didn't Know|Knew It →