Data Analysis - SSAT Middle Level Quantitative

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Question

Give the mean of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

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Answer

Since there are 16 elements, divide their sum by 16 to get the mean:

$(1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$

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Question

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

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Answer

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

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Question

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

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Answer

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

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Question

Consider the data set: $\left \{ 13, 18, 20, 22, 24, 29, 30, 36\right \}$

What is the difference between the mean of this set and the median of this set?

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Answer

To get the mean, add the numbers and divide by 8:

$\left ( 13+ 18+ 20+ 22+ 24+ 29+ 30+ 36 \right )\div 8 = 192 \div 8 = 24$

To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle):

$(22 + 24) \div 2 = 46 \div 2 = 23$

The difference is

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Question

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

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Answer

By dividing the numerator of each fraction by its denominator, each fraction can be rewritten as its decimal equivalent:

$\frac{1}{3} = 1 \div 3 = 0.333...$

$\frac{2}{5} = 2 \div 5 = 0.4$

$\frac{3}{8} = 0.375$

$\frac{5}{13} = 5 \div 13 = 0.384615...$

All fractions except can be seen to fall between 0.3 and 0.4, exclusive. Three is the correct answer.

Note that $\frac{2}{5}$ is equal to 0.4, so we don't include it. The criterion requires strict inequality.

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Question

Give the mean of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

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Answer

Since there are 16 elements, divide their sum by 16 to get the mean:

$(1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$

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Question

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Tap to reveal answer

Answer

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

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Question

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

Tap to reveal answer

Answer

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

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Question

Consider the data set: $\left \{ 13, 18, 20, 22, 24, 29, 30, 36\right \}$

What is the difference between the mean of this set and the median of this set?

Tap to reveal answer

Answer

To get the mean, add the numbers and divide by 8:

$\left ( 13+ 18+ 20+ 22+ 24+ 29+ 30+ 36 \right )\div 8 = 192 \div 8 = 24$

To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle):

$(22 + 24) \div 2 = 46 \div 2 = 23$

The difference is

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Question

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Tap to reveal answer

Answer

By dividing the numerator of each fraction by its denominator, each fraction can be rewritten as its decimal equivalent:

$\frac{1}{3} = 1 \div 3 = 0.333...$

$\frac{2}{5} = 2 \div 5 = 0.4$

$\frac{3}{8} = 0.375$

$\frac{5}{13} = 5 \div 13 = 0.384615...$

All fractions except can be seen to fall between 0.3 and 0.4, exclusive. Three is the correct answer.

Note that $\frac{2}{5}$ is equal to 0.4, so we don't include it. The criterion requires strict inequality.

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Question

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Tap to reveal answer

Answer

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

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Question

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Tap to reveal answer

Answer

By dividing the numerator of each fraction by its denominator, each fraction can be rewritten as its decimal equivalent:

$\frac{1}{3} = 1 \div 3 = 0.333...$

$\frac{2}{5} = 2 \div 5 = 0.4$

$\frac{3}{8} = 0.375$

$\frac{5}{13} = 5 \div 13 = 0.384615...$

All fractions except can be seen to fall between 0.3 and 0.4, exclusive. Three is the correct answer.

Note that $\frac{2}{5}$ is equal to 0.4, so we don't include it. The criterion requires strict inequality.

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Question

Give the mean of the data set (nearest tenth, if applicable):

$\left \{ 56,78,98,85,77,73 \right \}$

Tap to reveal answer

Answer

Add the six elements and divide the sum by 6:

$467 \div 6 \approx 77.8$

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Question

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

Tap to reveal answer

Answer

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

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Question

Give the median of the following nine scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$

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Answer

Arrange the scores from least to greatest.

$\left \{ 61, 67, 68, 70, 72, 73, 76, 80, 90 \right \}$

There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.

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Question

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Tap to reveal answer

Answer

By dividing the numerator of each fraction by its denominator, each fraction can be rewritten as its decimal equivalent:

$\frac{1}{3} = 1 \div 3 = 0.333...$

$\frac{2}{5} = 2 \div 5 = 0.4$

$\frac{3}{8} = 0.375$

$\frac{5}{13} = 5 \div 13 = 0.384615...$

All fractions except can be seen to fall between 0.3 and 0.4, exclusive. Three is the correct answer.

Note that $\frac{2}{5}$ is equal to 0.4, so we don't include it. The criterion requires strict inequality.

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Question

$\left \{ 2,4,6,8,10,x,14,y,18,20\right \}$ What are the two missing values in the following set?

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Answer

The pattern for the set is all even numbers up until . The missing even number between and would be and the missing number between and would be .

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Question

Give the mean of the data set (nearest tenth, if applicable):

$\left \{ 56,78,98,85,77,73 \right \}$

Tap to reveal answer

Answer

Add the six elements and divide the sum by 6:

$467 \div 6 \approx 77.8$

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Question

Give the mean of the following nine scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$

Tap to reveal answer

Answer

Divide the sum of the scores by nine:

$\frac{ 61 + 67+ 80+ 72+ 76+73+90+68+70}{9} = \frac{ 657}{9} = 73$

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Question

Give the mode of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

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Answer

The element 6 appears four times, more frequently than any other element, and is therefore the (only) mode.

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Knew It

Data Analysis - SSAT Middle Level Quantitative

Give the mean of the following data set:

Since there are 16 elements, divide their sum by 16 to get the mean:

Give the mean of the following eight scores:

Divide the sum of the scores by eight:

Give the median of the data set:

9 being an odd number, the median of a set with nine elements is the highest element when the elements are arranged in order. This fifth-highest element is 59.

Consider the data set: What is the difference between the mean of this set and the median of this set?

To get the mean, add the numbers and divide by 8: To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle): The difference is

How many of the following four numbers are elements of the set ? (A) (B) (C) (D)

Give the mean of the following data set:

Since there are 16 elements, divide their sum by 16 to get the mean:

Give the mean of the following eight scores:

Divide the sum of the scores by eight:

Give the median of the data set:

9 being an odd number, the median of a set with nine elements is the highest element when the elements are arranged in order. This fifth-highest element is 59.

Consider the data set: What is the difference between the mean of this set and the median of this set?

To get the mean, add the numbers and divide by 8: To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle): The difference is

How many of the following four numbers are elements of the set ? (A) (B) (C) (D)

Give the mean of the following eight scores:

Divide the sum of the scores by eight:

How many of the following four numbers are elements of the set ? (A) (B) (C) (D)

Give the mean of the data set (nearest tenth, if applicable):

Add the six elements and divide the sum by 6:

Give the median of the data set:

9 being an odd number, the median of a set with nine elements is the highest element when the elements are arranged in order. This fifth-highest element is 59.

Give the median of the following nine scores:

Arrange the scores from least to greatest. There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.

How many of the following four numbers are elements of the set ? (A) (B) (C) (D)

What are the two missing values in the following set?

The pattern for the set is all even numbers up until . The missing even number between and would be and the missing number between and would be .

Give the mean of the data set (nearest tenth, if applicable):

Add the six elements and divide the sum by 6:

Give the mean of the following nine scores:

Divide the sum of the scores by nine:

Give the mode of the following data set:

The element 6 appears four times, more frequently than any other element, and is therefore the (only) mode.

Give the mean of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

Since there are 16 elements, divide their sum by 16 to get the mean:

$(1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

Consider the data set: $\left \{ 13, 18, 20, 22, 24, 29, 30, 36\right \}$

What is the difference between the mean of this set and the median of this set?

To get the mean, add the numbers and divide by 8:

$\left ( 13+ 18+ 20+ 22+ 24+ 29+ 30+ 36 \right )\div 8 = 192 \div 8 = 24$

To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle):

$(22 + 24) \div 2 = 46 \div 2 = 23$

The difference is

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Give the mean of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

Since there are 16 elements, divide their sum by 16 to get the mean:

$(1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

Consider the data set: $\left \{ 13, 18, 20, 22, 24, 29, 30, 36\right \}$

What is the difference between the mean of this set and the median of this set?

To get the mean, add the numbers and divide by 8:

$\left ( 13+ 18+ 20+ 22+ 24+ 29+ 30+ 36 \right )\div 8 = 192 \div 8 = 24$

To get the median, find the mean of the fourth- and fifth-highest elements (the ones in the middle):

$(22 + 24) \div 2 = 46 \div 2 = 23$

The difference is

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

Give the mean of the data set (nearest tenth, if applicable):

$\left \{ 56,78,98,85,77,73 \right \}$

Add the six elements and divide the sum by 6:

$467 \div 6 \approx 77.8$

Give the median of the data set:

$\left \{ 45, 48, 49, 49, 59, 60, 66, 68, 77 \right \}$

9 being an odd number, the median of a set with nine elements is the $\frac{9+1}{2} = 5 \textrm{th}$ highest element when the elements are arranged in order. This fifth-highest element is 59.

Give the median of the following nine scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$

Arrange the scores from least to greatest.

$\left \{ 61, 67, 68, 70, 72, 73, 76, 80, 90 \right \}$

There are an odd number (nine) of scores, so the median of the scores is the one that falls in the center - namely, 72.

How many of the following four numbers are elements of the set

$\left \{ x ; | ; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(C) $\frac{3}{8}$

(D) $\frac{5}{13}$

$\left \{ 2,4,6,8,10,x,14,y,18,20\right \}$ What are the two missing values in the following set?

Give the mean of the data set (nearest tenth, if applicable):

$\left \{ 56,78,98,85,77,73 \right \}$

Add the six elements and divide the sum by 6:

$467 \div 6 \approx 77.8$

Give the mean of the following nine scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$

Divide the sum of the scores by nine:

$\frac{ 61 + 67+ 80+ 72+ 76+73+90+68+70}{9} = \frac{ 657}{9} = 73$

Give the mode of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$