Math - Basic Statistics

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?

Explanation

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

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?

Explanation

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.

Explanation

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

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

Explanation

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

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

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

$\frac{1}{30}$

$\frac{1}{6}$

$\frac{2}{5}$

$\frac{11}{15}$

$\frac{9}{20}$

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.

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

Explanation

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

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

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?

Explanation

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.

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?

Explanation

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.

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

Explanation

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

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

Explanation

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

Basic Statistics

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