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SAT Math : Statistics

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Example Questions

Example Question #61 : How To Find Arithmetic Mean

What is the average of the numbers: 12,17,22,11,14,23,17,16,18,10

Possible Answers:

Correct answer:

Explanation:

The mean of a set of numbers is the average of all the numbers in a given set.

Step 1: We will take the sum of all the numbers given. We will add each number together.

12+17+22+11+14+23+17+16+18+10=160

Step 2: To find the average of the numbers given in the question, we need to take the total sum of the numbers divided by how many numbers we have.

Sum= 160 , Numbers=

$\frac{Sum}{Numbers}=\frac{160}{10}$

Step 3: Simplify the fraction that we got in the second step:

$\frac {160}{10}=\frac {16}{1}=16 (average)$

The average of all numbers in the question is 16.

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Example Question #61 : Arithmetic Mean

Five athletes throw a javelin. The distances of their throws are shown here, measured in yards:

20, 40, 35, 2x, 3x

If the average of all of their throws is , then what is the median of the group?

Possible Answers:

Correct answer:

Explanation:

First, we need to find the value of with our given average. We know the average of the throws is and that there are throws total. Therefore:

$\frac{20+40+36+2x+3x}{5}=50$

Now we can solve for our unknown.

$\frac{20+40+36+2x+3x}{5}=50$

20+40+35+2x+3x = 250

95 + 5x = 250

5x = 155

x=31

Know that we know the value of our unknown, we can figure out the last two distances.

The fourth distance in the list is 2x = 2(31) = 62 .

The fifth distance is 3x = 3(31) = 93 .

To find the median of the group, let's write the distances in order from least to greatest and find the number that sits in the middle.

20, 35, 40, 62, 93

The median of our group is .

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Example Question #62 : Statistics

A set of four consecutive odd numbers has an average of 56. What is the smallest number in this set?

Possible Answers:

53.5

Correct answer:

Explanation:

You will want to define the smallest number as x and the other numbers as x+2, x+4, x+6.

Then enter those values in to the equation needed to find the mean.

$\frac{x +(x+2) + (x+4)+ (x+6)}{4}=56$

$\frac{4x+12}{4}=56$

x+3=56

x=53

53 is the smallest number in the set.

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Example Question #61 : How To Find Arithmetic Mean

44, 37, __, 73, 52, 43

If the arithmetic mean of the set above is 50, find the missing number in the set.

Possible Answers:

Correct answer:

Explanation:

$mean = \frac{sum of terms}{number of terms}$

$50=\frac{44+37+x+73+52+43}{6}$

$50=\frac{249+x}{6}$

300=249+x

x=51

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Example Question #61 : Statistics

Screen_shot_2013-05-17_at_12.12.58_am

What is the average number of apples a student has?

Possible Answers:

2.5

1.5

Correct answer:

2.5

Explanation:

To calculate the average number of apples a student has, the following formula is used.

$\text{Average } \# \text{of Apples }=\frac{\text{Sum of Apples}}{\text{Sum of Students}}$

First, calculate the total number of apples there are. To do this multiply the number of apples by the number of students that have that many apples.

Screen_shot_2013-05-17_at_12.12.58_am

$\\\text{Total Apples}=3(60)+2(30)+1(10) \\\text{Total Apples}=180+60+10 \\\text{Total Apples}=250$

This number divided by the total number of students.

$\text{Average } \# \text{of Apples }=\frac{\text{250}}{60+30+10}=\frac{250}{100}=2.5$

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Example Question #62 : Statistics

The histogram depicts the number of errors students missed on last week's homework assignment. Estimate the mean number of errors made. Screen shot 2016 02 10 at 10.32.20 am

Possible Answers:

4.615

6.741

4.012

5.623

2.876

Correct answer:

4.615

Explanation:

To estimate the mean number of errors made, first calculate the mean of each bar in the histogram.

Recall to calculate a mean of a histogram bar use the formula:

$\text{Mean}=\frac{\text{Largest Value }+\text{ Smallest Value}}{2}\times \text{Frequency}$

Screen shot 2016 02 10 at 10.32.20 am

The red bar's mean:

$M_R=\frac{2+0}{2}\times 6=1\times 6=6$

The yellow bar's mean:

$M_Y=\frac{4+2}{2}\times 6=3\times 6=18$

The green bar's mean:

$M_G=\frac{6+4}{2}\times 6=5\times 6=30$

The teal bar's mean:

$M_T=\frac{8+6}{2}\times 6=7\times 4=28$

The blue bar's mean:

$M_B=\frac{10+8}{2}\times 3=9\times 3=27$

The purple bar's mean:

$M_P=\frac{12+10}{2}\times 1=11\times 1=11$

Now to estimate the mean of the number of errors, add the means of the bars together and divide by the total number of frequencies.

$\\M=\frac{M_R+M_Y+M_G+M_T+M_B+M_P }{6+6+6+4+3+1} \\\\\\M=\frac{6+18+30+28+27+11 }{26} \\\\\\M=\frac{120}{26} \\\\M=4.615$

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Example Question #61 : Statistics

Screen shot 2016 02 11 at 1.26.48 pm

Calculate the mean from the above dot plot.

Possible Answers:

5.1

7.1

6.2

Correct answer:

7.1

Explanation:

To calculate the mean, we need to sum up every individual entry and divide it by the total number of entries. This looks like $\bar{x}=\frac{x_1+x_2+\cdots x_n}{n}$ , where is the total number of entries and $x_1,\cdots, x_n$ are the individual entries.

Here is the calculation of the mean,

$\bar{x}=\frac{3(4)+5(2)+6(2)+7(1)+8(3)+9(3)+10(5)}{20}$

$\bar{x}=\frac{12+10+12+7+24+27+50}{20}$

$\bar{x}=\frac{142}{20}=7.1$

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Example Question #62 : Statistics

Screen shot 2016 02 12 at 9.39.26 am

The bar chart shows the number of consecutive heads for a fair coin. How many more 4 Heads were there compared to 3 Heads?

Possible Answers:

Correct answer:

Explanation:

To figure this out, we need to go to the y-axis and find the number of 4 heads and 3 Heads there were. $4\: \text{Heads}=5$ , $3\:\text{Heads}=3$ . Now we find the difference between them, which is simply 5-3=2 .

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Example Question #63 : Statistics

Screen shot 2016 02 12 at 9.39.26 am

Find the average rate of change between 3 Heads and 5 Heads

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

The average rate of change is calculated by the following.

$\text{Average Rate of Change}=\frac{f(b)-f(a)}{b-a}$

So we simply do the following,

$\text{3\:Heads}=3$

$\text{5\:Heads}=6$

$\text{Average Rate of Change}=\frac{6-3}{5-3}=\frac{3}{2}=1.5$

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Example Question #64 : Statistics

Screen shot 2016 02 12 at 11.14.52 am

What is the interpretation of the y-intercept?

Possible Answers:

The model indicates that approximately $30\%$ of people weren't accepted into College in 1940 .

$45\%$ of people weren't accepted into College.

The model indicates that approximately $45\%$ of people weren't accepted into College in 1980 .

The model indicates that approximately $45\%$ of people weren't accepted into College in 1940 .

$30\%$ of people weren't accepted into College.

Correct answer:

The model indicates that approximately $45\%$ of people weren't accepted into College in 1940 .

Explanation:

They y-intercept is at x=0 . So at x=0 , is about . What this means is at the year 1940 , the Denial Rate of Getting into College was $45\%$ . So the correct answer would be, "the model indicates that approximately $45\%$ of people weren't accepted into College in 1940 ."

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SAT Math : Statistics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #61 : How To Find Arithmetic Mean

Example Question #61 : Arithmetic Mean

Example Question #62 : Statistics

Example Question #61 : How To Find Arithmetic Mean

Example Question #61 : Statistics

Example Question #62 : Statistics

Example Question #61 : Statistics

Example Question #62 : Statistics

Example Question #63 : Statistics

Example Question #64 : Statistics

All SAT Math Resources

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