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High School Math : Data Properties

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Example Question #1 : How To Find The Range For A Set Of Data

Six homes are for sale and have the following dollar values in thousands of dollars:

535

155

305

720

315

214

What is the range of the values of the six homes?

Possible Answers:

565

346

155

374

535

Correct answer:

565

Explanation:

The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720.

720 - 155 = 565

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Example Question #2 : How To Find The Range For A Set Of Data

Alice recorded the outside temperature at noon each day for one week. These were the results.

Monday: 78

Tuesday: 85

Wednesday: 82

Thursday: 84

Friday: 82

Saturday: 79

Sunday: 80

What is the range of temperatures?

Possible Answers:

81.4

83.7

570

Correct answer:

Explanation:

The range is the simplest measurement of the difference between values in a data set. To find the range, simply subtract the lowest value from the greatest value, ignoring the others.

85-78=7

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Example Question #1 : Understanding Range

You are given the following data:

3, 7, 2, 3, 9, 12, 2, 3, 9, 0, 1

What is the range?

Possible Answers:

5.5

Correct answer:

Explanation:

Recall that we find the range of a set of data by subtracting the smallest value from the largest value. In this case, the smallest value is and the largest value is . Thus, our range is 12 - 0 = 12 .

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Example Question #2 : Understanding Range

There are girls and boys running a race. What is the probability that only boys will finish in the top three places?

Possible Answers:

$\frac{1}{6}$

$\frac{1}{30}$

$\frac{9}{20}$

$\frac{2}{5}$

$\frac{11}{15}$

Correct answer:

$\frac{1}{30}$

Explanation:

Probability is a fraction between and . The numerator is the total number of ways to get what you want, or a subset of the sample space. The denominator is the total ways, or complete sample space.

The number of ways only boys would finsih in the top three places: $4\cdot 3\cdot 2= 24$

The number of ways all contestants can finish the race: $10\cdot 9\cdot 8=720$

So the probability of only boys finishing in the top three places is given by the fraction $\frac{24}{720}= \frac{1}{30}$ when simplified.

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Example Question #11 : Basic Statistics

is the ____________ of the following dataset below.

$\{20, 12, 17, 14, 12\}$

Possible Answers:

range

mean

median

mode

Correct answer:

median

Explanation:

Reorder the numerals in the set, from least to greatest.

$\{12, 12, 14, 17, 20\}$

The number in the middle is the median. $\{12, 12, \mathbf{14}, 17, 20\}$

The most frequent numeral is the mode. $\{\mathbf{12}, \mathbf{12}, 14, 17, 20\}$

The mean is the sum of the numerals divided by the number of data points.

$\frac{12+12+14+17+20}{5}=15$

The mean is 15.

The range is the difference between the maximum and the minimum.

20-12=8

The range is 8.

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Example Question #11 : Basic Statistics

For the following data set:

$2,\; 5,\; 9,\; 3,\; 7,\; 12,\; 15,\; \; 10,\; 9$

Which is the smallest?

Possible Answers:

Mode

None of the answers

Median

Mean

Range

Correct answer:

Mean

Explanation:

Put the data in order from smallest to largest and then calculate each stastic: mean, mode, median, range

$2,\;3,\;5,\;7,\;9,\;9,\;10,\;12,\;15$

Range = Max - Min or 15-2=13

Mode is the most often repeated number or

Median is the number in the middle or

Mean is the sum of the data divided by the number of data points or $\frac{\sum x}{n}= \frac{72}{9}=8$

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Example Question #1 : Understanding Mean, Median, And Mode

1,1,2,3,6,8,10,11,12,15, 30

$\textup{What is the median of the above number set?}$

Possible Answers:

Correct answer:

Explanation:

$\textup{As the numbers are already listed in increasing order, the median is simply}$

$\textup{the one in the middle. In this case 8 is the 6th term counted from either side..}$

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Example Question #1 : Data Properties

Find the median of the following number series:

3, 6, 27, 19, 8, 11, 30, 42, 7, 39

Possible Answers:

19.2

Correct answer:

Explanation:

The first step to finding the median is always to put the numbers in the proper order:

3, 6, 7, 8, 11, 19, 27, 30, 39, 42

When we have an even amount of numbers, we find the average (or mean) of the middle two to get the median:

11 + 19 = 30/2 = 15

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Example Question #15 : Basic Statistics

With a standard deck of playing cards, what is the probability of picking one red card followed by one black card, without replacement?

Possible Answers:

$\frac{13}{51}$

$\frac{1}{26}$

$\frac{1}{4}$

$\frac{17}{25}$

$\frac{17}{52}$

Correct answer:

$\frac{13}{51}$

Explanation:

In a standard deck of playing cards we have:

$26\; red+26\; black=52\; cards$

So the probability of picking the first card red is $\frac{26}{52}=\frac{1}{2}$ .

Then the probability of picking the second card black is $\frac{26}{51}$ because this is without replacement.

They are independent events so the probabilities get multiplied together to give $\frac{13}{51}$ .

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Example Question #1 : Understanding Mean, Median, And Mode

Which statement is true concerning the following data set:

2,5,9,3,4,7,3,8,11,15,10

Possible Answers:

range - mode = mean

mode+mean = median

mode+median> range

mode> mean

mean=median

mode+mean = median

Correct answer:

mean=median

Explanation:

First, put the data in order, smallest to largest:

2,3,3,4,5,7,8,9,10,11,15

$mean = \frac{\sum x}{n}=\frac{77}{11}=7$

mode=3

median = 7

range=max-min=15-2=13

Note, the mode is the number most often repeated in the data set and the median is the middle number.

So mean=median is the only true statement.

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High School Math : Data Properties

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Range For A Set Of Data

Example Question #2 : How To Find The Range For A Set Of Data

Example Question #1 : Understanding Range

Example Question #2 : Understanding Range

Example Question #11 : Basic Statistics

Example Question #11 : Basic Statistics

Example Question #1 : Understanding Mean, Median, And Mode

Example Question #1 : Data Properties

Example Question #15 : Basic Statistics

Example Question #1 : Understanding Mean, Median, And Mode

All High School Math Resources

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