6th Grade Math Flashcards: Give Measures Of Center And Variability

What this deck covers

This deck focuses on Give Measures Of Center And Variability, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the interquartile range (IQR) in terms of $Q_1$ and $Q_3$?

Answer: $\text{IQR}=Q_3-Q_1$. Measures spread of the middle 50% of data.

Flashcard 2: What does a larger MAD tell you about a data set compared to a smaller MAD?

Answer: Values are farther from the mean on average (more variability). Larger MAD indicates data points deviate more from center.

Flashcard 3: Find the mean of the data set $2, 4, 6, 8$.

Answer: $5$. $\frac{2+4+6+8}{4} = \frac{20}{4} = 5$

Flashcard 4: Identify the striking deviation (outlier) in the data set $4,5,5,6,6,7,30$.

Answer: $30$. Much larger than other values ($4-7$).

Flashcard 5: What is the median of a data set after the values are put in order?

Answer: The middle value, or the mean of the two middle values. For odd count, take middle; for even, average the two middle values.

Flashcard 6: What is the median of the ordered data set $2,4,7,9,10$?

Answer: $7$. Middle value of 5 ordered numbers is the 3rd one.

Flashcard 7: What is the median of an ordered data set with an even number of values?

Answer: Average of the two middle values. With even count, median is between the two center values.

Flashcard 8: What does $Q_1$ represent in an ordered data set?

Answer: Median of the lower half of the data. First quartile: 25% of data falls below this value.

Flashcard 9: What is the mean absolute deviation (MAD) from the mean $\bar{x}$ for $n$ values?

Answer: $\text{MAD} = \frac{\sum |x-\bar{x}|}{n}$. Average distance of data points from the mean.

Flashcard 10: A data set has $Q_1=12$ and $Q_3=20$. What is the IQR?

Answer: $8$. $\text{IQR} = Q_3 - Q_1 = 20 - 12 = 8$.

Flashcard 11: What does $Q_3$ represent in an ordered data set?

Answer: Median of the upper half of the data. Third quartile: 75% of data falls below this value.

Flashcard 12: What does a larger IQR indicate about a data set compared to a smaller IQR?

Answer: Greater variability in the middle $50\%$. Larger IQR means more spread in the middle half.

Flashcard 13: What does a larger IQR tell you about a data set compared to a smaller IQR?

Answer: The middle $50\%$ of the data are more spread out. Larger IQR means greater spread in the middle half.

Flashcard 14: Identify $Q_1$ for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.

Answer: $4$. Median of lower half: $\{2,3,5,8\}$ is $\frac{3+5}{2}=4$.

Flashcard 15: Find the MAD for the data set $1, 2, 3$ (use mean absolute deviation from the mean).

Answer: $\frac{2}{3}$. Mean is $2$; deviations: $1,0,1$; MAD = $\frac{2}{3}$.

Flashcard 16: Which measure of center is more resistant to outliers: mean or median?

Answer: Median. Outliers affect mean but not median position.

Flashcard 17: Find $Q_3$ for the ordered data $1,2,3,4,5,6,7,8$ using the median-of-halves method.

Answer: $Q_3=\frac{6+7}{2}=6.5$. Median of upper half: $5,6,7,8$.

Flashcard 18: Find the median of the ordered data set $1, 4, 6, 10$.

Answer: $5$. $\frac{4+6}{2} = \frac{10}{2} = 5$ (average of middle two).

Flashcard 19: Which measure of center is usually pulled toward extreme values: mean or median?

Answer: Mean. Extreme values affect the sum, changing the average.

Flashcard 20: What does a larger MAD indicate about a data set compared to a smaller MAD?

Answer: Values are farther from the mean on average. Larger MAD means data is more spread out.

Flashcard 21: What is the interquartile range (IQR) in terms of quartiles $Q_1$ and $Q_3$?

Answer: $\text{IQR} = Q_3 - Q_1$. Measures spread of the middle 50% of data.

Flashcard 22: Which description best indicates a striking deviation: a value far from the rest or a value near the center?

Answer: A value far from the rest (an outlier). Outliers are striking deviations from the pattern.

Flashcard 23: What is the MAD for the data $2,4,6$ (mean $\bar{x}=4$)?

Answer: $\text{MAD}=\frac{|2-4|+|4-4|+|6-4|}{3}=\frac{4}{3}$. Deviations are $2,0,2$; average is $\frac{4}{3}$.

Flashcard 24: Identify the first step to find the median of $6$ numbers.

Answer: Order the data from least to greatest. Must arrange values to find the middle position.

Flashcard 25: Find $Q_1$ for the ordered data $1,2,3,4,5,6,7,8$ using the median-of-halves method.

Answer: $Q_1=\frac{2+3}{2}=2.5$. Median of lower half: $1,2,3,4$.

Flashcard 26: Which measure of center is usually more resistant to outliers: mean or median?

Answer: Median. Outliers don't affect the middle position value.

Flashcard 27: What is the IQR for the ordered data $1,2,3,4,5,6,7,8$ using $Q_1=2.5$ and $Q_3=6.5$?

Answer: $\text{IQR}=6.5-2.5=4$. Subtract first quartile from third quartile.

Flashcard 28: What is the MAD for the data $1,1,1,5$ (mean $\bar{x}=2$)?

Answer: $\text{MAD}=\frac{1+1+1+3}{4}=1.5$. Deviations from $2$ are $1,1,1,3$.

Flashcard 29: Which data set has greater variability by IQR: Set A $\text{IQR}=6$ or Set B $\text{IQR}=2$?

Answer: Set A. Higher IQR indicates more variability.

Flashcard 30: A data set has mean $10$. What is $|x-\bar{x}|$ when a value is $x=6$?

Answer: $4$. Absolute deviation = $|6-10| = 4$.

Flashcard 31: Find the IQR for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.

Answer: $7$. $Q_3 - Q_1 = 11 - 4 = 7$ (from previous quartiles).

Flashcard 32: Which data set has greater variability by MAD: Set A $\text{MAD}=1.2$ or Set B $\text{MAD}=2.0$?

Answer: Set B. Higher MAD indicates more variability.

Flashcard 33: Find the median of the ordered data set $3, 7, 9, 12, 20$.

Answer: $9$. Middle value of 5 ordered values is the 3rd one.

Flashcard 34: Identify $Q_3$ for the ordered data set $2, 3, 5, 8, 9, 10, 12, 15$.

Answer: $11$. Median of upper half: $\{9,10,12,15\}$ is $\frac{10+12}{2}=11$.

Flashcard 35: What is the mean of a data set in terms of the total sum $S$ and number of values $n$?

Answer: Mean $= \frac{S}{n}$. Divide the sum of all values by the count of values.

Flashcard 36: What is the median of the ordered data set $3,5,8,12$?

Answer: $\frac{5+8}{2}=6.5$. Even count: average the 2nd and 3rd values.

Flashcard 37: What is the mean absolute deviation (MAD) from the mean for values $x_1,\dots,x_n$?

Answer: $\text{MAD}=\frac{|x_1-\bar{x}|+\cdots+|x_n-\bar{x}|}{n}$. Average distance of all values from the mean.

Flashcard 38: What is the mean of the data set $4,6,8,12$?

Answer: $\frac{4+6+8+12}{4}=7.5$. Sum is $30$, divided by $4$ values.

Flashcard 39: What is the mean of a data set in terms of $n$ values $x_1, x_2, \dots, x_n$?

Answer: $\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}$. Sum all values and divide by the count.

Flashcard 40: What is the median of an ordered data set with an odd number of values?

Answer: The middle value. With odd count, the median is the single center value.