Basic Statistics - High School Math

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Question

In a standard deck of cards, with replacement, what is the probability of drawing two Ace of Hearts?

Answer

Probability of drawing first ace of hearts:

Probability of drawing second ace of hearts:

Multiply both probabilities by each other:

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Question

In a standard deck of cards, without replacement, what is the probability of drawing three kings?

Answer

Start with 52 cards, probability of drawing first king:

Now you have 51 cards. Probability of drawing second king:

Now you have 50 cards. Probability of drawing third king:

Multiply all probabilities:

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Question

Using a standard deck of cards, what is the probability of choosing a single face card?

Answer

There are cards in a standard deck: cards in suits. There are face cards (King, Queen, Jack) in each suit, so there are total face cards.

Thus the probability of choosing a single face card is or .

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Question

With a standard deck of cards, what is the probability of picking a spade then a red card if there is no replacement?

Answer

In a standard deck of cards:

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Question

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

535

155

305

720

315

214

What is the mean value of the six homes?

Answer

The mean is calculated by adding all the values in a group together, then dividing the sum by the total number in the group. In this case, six homes are for sale. The six home values are added together , then that value is divided by six.

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Question

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

535

155

305

720

315

214

What is the median value of the six homes?

Answer

The median is determined by ordering the values in the group from least to greatest: 155, 214, 305, 315, 535, 720. The value directly in the middle is the median. For instance, if there are five numbers, the third is the median. Here, we have an even number of values so there is no value directly in the middle. To find the median when there is no middle-most value, find the average of the two middle values. The mean is determined by adding the two values and dividing by two (the number in the group):

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Question

A bird watcher observed how many birds came to her bird feeder for four days. These were the results:

Day 1: 15

Day 2: 12

Day 3: 10

Day 4: 13

What is the mean number of birds?

Answer

The mean is calculated by adding the values from the four days together, then dividing the sum by the total number of values. In this case, four values must be added:

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Question

What is the mode of the following list of numbers?

35, 17, 4, 25, 7, 4, 17, 26, 8, 17

Answer

The mode is the number that appears most frequently in a series of numbers. First, organize the numbers in order from least to greatest: 4, 4, 7, 8, 17, 17, 17, 25, 26, 35. The number 17 appears three times, more than any other number.

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Question

is the ____________ of the following dataset below.

Answer

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

The number in the middle is the median.

The most frequent numeral is the mode.

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

The mean is 15.

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

The range is 8.

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Question

For the following data set:

Which is the smallest?

Answer

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

or

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

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Question

Answer

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Question

Each student's grade in Becky's math class is determined using a weighted average. Exams comprise 50% of the grade, quizzes comprise 20%, and homework comprises the final 30%. Becky has an 87% average on tests, 82% on quizzes, and 97% on homework. What is her overall grade?

Answer

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

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Question

Find the median of the following number series:

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

Answer

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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Question

Find the mean and median of the following data set:

Answer

The mean is the sum of the numbers divided by their count:

To find the median, order the set from smallest to largest:

When there are two numbers in the middle, find the average of those numbers:

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Question

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

Answer

In a standard deck of playing cards we have:

So the probability of picking the first card red is .

Then the probability of picking the second card black is because this is without replacement.

They are independent events so the probabilities get multiplied together to give .

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Question

Which statement is true concerning the following data set:

Answer

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

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

So is the only true statement.

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Question

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 was the mean temperature for the week?

Answer

The mean is calculated by adding all the values in a group, then dividing the sum by the total number in the group.

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Question

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 mode of the temperatures?

Answer

The mode is the number that appears most frequently in a series of numbers. First, organize the numbers in order from least to greatest. Then, identify the value that is repeated most frequently.

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Question

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 median temperature?

Answer

The median is determined by ordering the values in the group from least to greatest and identifying the value directly in the middle. For instance, if five numbers are ordered from least to greatest, the third is the median.

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Question

What is the probability of rolling an odd sum less than seven when rolling two standard six-sided dice?

Answer

The sample space for rolling two six-sided dice is .

The odd numbers less than seven are one, three, and five.

The smallest sum you can get with two dice is .

sum of

sum of

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