Data Analysis - ISEE Middle Level Quantitative Reasoning

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Question

Find the mode of this set of numbers:

Answer

Find the most recurring number:

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Question

Find the mode of the set of numbers:

Answer

The mode is the number that appears most frequently in the data set:

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Question

Patricia bought three candles for her home. The candles cost $2.78, $3.68, $1.58, respectively. What was the average price of the candles that Patricia bought?

Answer

First, add all the prices:

Then, divide that amount by 3:

$8.04\div 3=2.68$

Answer: The average price of a candle is $2.68

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Question

Find the mode in this set of numbers:

7435, 8976, 2784, 7435, 1289, 8976, 2110, 8992, 8976, 2784.

Answer

Find the most recurring number in the set.

The answer is

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Question

Find the mean in this set of numbers:

5570, 4886, 5226, 4120, 6561, 4120, 6008

Answer

First, add all the numbers in this set:

Then, divide that amount by the total number in the set:

$36491\div 7=5213$

Answer: The mean is 5213.

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Question

Find the mean in this set of numbers:

9078, 9008, 9800, 9099, 9009, 9090, 9008

Answer

First add all the numbers:

Then, divide that number by 7:

$64,092\div 7=9156$

Answer: The mean is 9156

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Question

Find the average of these amounts:

$34.78, $21. 69, $76.89, $47.88

Answer

First, add all the amounts:

Then, divide by 4:

$181.24\div 4=45.31$

Answer: The average is 45.31

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Question

Find the mean of the following set of numbers: 227, 215, 206, 238, 249

Answer

Add the numbers, and divide by 5:

$\frac{ 227 + 215 +206+238+ 249}{5} = \frac{1,135}{5} = 227$

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Question

Find the mean in this set of numbers:

210, 120, 110, 220, 120

Answer

First, add up all of the numbers in the set:

Then, divide: $780 \div 5=156$

Answer: The mean is 156.

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Question

Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?

Answer

The square with the diagonal line alternates between the square on the left and the square on the right. Therefore, the next figure in the sequence will have its diagonal line in the rightmost square, eliminating Figures (b) and (d) and leaving Figures (a) and (c).

Also, the shaded square moves one position to the right from figure to figure, so in the next figure, the shaded square must be the one at the extreme right. Figure (c) matches that description.

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Question

Patricia is shopping for a coat. She is considering three coats. Each costs $85.98, $93.29 and $88.99, respectively. What is the average price of a coat she is considering?

Answer

First, add up all of the prices:

Then, divide $268.26 \div 3= 89.42$ .

Answer: The average price of a coat is $89.42.

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Question

An arithmetic sequence begins:

Which is the greater quantity?

(a)

(b) The tenth term of the sequence

Answer

The common difference of the sequence is . The tenth term of the sequence is $100 + (10-1) (-11) = 100 + 9 \cdot (-11) = 100 - 99 = 1$ .

This makes (b) greater.

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Question

Find the range in this set of numbers:

9881, 9889, 9818, 9981, 9891, 9918, 9989, 9889, 9198

Answer

First, order the numbers from least to greatest:

Then, find the difference of the largest and smallest number:

Answer: The range is 791.

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Question

Find the mode in this set of numbers:

22, 24, 28, 23, 27, 24, 29, 35, 23, 42, 42, 24, 26, 25, 26.

Answer

Find the number that appears most frequently.

Answer: The mode is 24.

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Question

Find the mean of this set of numbers:

Answer

The mean is the average of the set.

First add up the numbers:

Then divide by the number of elements in the set:

$270\div 5=54$

Answer:

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Question

Define:

Universal set $U =\mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

Answer

The gray region is the region outside both and and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: $7,431 \div 3 = 2,477$ and $3,966 \div 3 = 1,322$ .

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as $7,916 \div 3 =2,638 ; R; 2$ . Therefore, it is the correct choice.

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Question

Define:

Universal set $U =\mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

Answer

The gray region is the region outside both and and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: $7,431 \div 3 = 2,477$ and $3,966 \div 3 = 1,322$ .

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as $7,916 \div 3 =2,638 ; R; 2$ . Therefore, it is the correct choice.

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Question

Set is defined as:

Set is made by doubling the values in set .

What is the range of values in set ?

Answer

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way of constructing set by doubling set 's values, the largest and smallest values in will directly correlate to the same in set :

Smallest:

Largest:

Therefore, the range is:

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Question

The members of set are defined as the values for:

For values of between and .

What is the range of set ?

Answer

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set from the function , we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be and the largest will be

Smallest:

Largest:

Therefore, the range is:

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Question

Set is defined as:

The members of set are defined by the function:

, where is a member of set .

So, for instance, set T contains because for , we get:

What is the range of set ?

Answer

We first need to determine the members of set . Using our function, we will get:

Our largest value is , and our smallest value is ; therefore, the range is

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