Question 1

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 46 km/h to 61 km/h with a mean speed of 56 km/h and a standard deviation of 8 km/h.The quartiles and median speeds were 49 km/h,58 km/h,and 53 km/h.Suppose during the month,one driver was clocked at 25 km/h.Which of the summary statistics might not change if that data value was added to the distribution?
A)Mean,IQR
B)Median,IQR
C)Range,SD
D)Median,range
E)Q1,Q3

Accepted Answer

The median and IQR (Interquartile Range) are resistant to extreme values, so adding a single outlier like 25 km/h is unlikely to change them.

Question 2

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000,mean salary = $35,000,median = $25,000,range = $60,000,IQR = $30,000,first quartile = $17,500,standard deviation = $20,000.
Between what two values are the middle 50% of the salaries found?
A)$15,000 and $75,000
B)$17,500 and $37,500
C)$17,500 and $30,000
D)$35,000 and $25,000
E)$17,500 and $47,500

Accepted Answer

The answer of Here are the summary statistics for the...

Question 3

A town's average snowfall is 40 cm per year with a standard deviation of 12 cm.How many standard deviations from the mean is a snowfall of 64 cm?
A)0.44 standard deviations below the mean
B)2.00 standard deviations above the mean
C)2.00 standard deviations below the mean
D)1.60 standard deviations above the mean
E)0.44 standard deviations above the mean

Accepted Answer

To find how many standard deviations from the mean a value is, you subtract the mean from the value and divide by the standard deviation: (64 cm - 40 cm) / 12 cm = 24 cm / 12 cm = 2.00 standard deviations above the mean.

Question 4

The freethrow percentages for the participants of a basketball tournament were compiled.The percents ranged from 39% to 99% with a mean of 50% and a standard deviation of 5%.The quartiles and median percentages were 49%,87%,and 50%.Suppose one participant did not make any of his attempted freethrows (0%).Which of the summary statistics might not change if that data value was added to the distribution?
A)Q1,Q3
B)Mean,IQR
C)Median,IQR
D)Range,SD
E)Median,range

Accepted Answer

The median and IQR only depend on the order and range of the data, not on the actual values in the data set. Adding a 0% value to the distribution will not affect the position of the median or the calculation of the IQR. The other summary statistics, such as mean, range, and standard deviation, are affected by the actual values in the data set and will change with the addition of a new data point.

Question 5

The average number of average number of hours per day a university student spends on homework is 5 hours with a standard deviation of 1.25 hours.How many standard deviations from the mean is 2 hours spent on homework?
A)2.40 standard deviations below the mean
B)1.20 standard deviations below the mean
C)2.50 standard deviations above the mean
D)1.20 standard deviations above the mean
E)2.40 standard deviations above the mean

Accepted Answer

To find how many standard deviations from the mean 2 hours is, use the formula: (X - μ) / σ, where X is 2 hours, μ (mean) is 5 hours, and σ (standard deviation) is 1.25 hours. This calculation gives (2 - 5) / 1.25 = -3 / 1.25 = -2.4, indicating 2.40 standard deviations below the mean.

Question 6

Mario's poker winnings average $319 per week with a standard deviation of $56.How many standard deviations from the mean is winning $195?
A)About 1.11 standard deviations below the mean
B)About 2.21 standard deviations above the mean
C)About 1.64 standard deviations below the mean
D)About 2.21 standard deviations below the mean
E)About 1.11 standard deviations above the mean

Accepted Answer

To find how many standard deviations from the mean $195 is, we use the formula: (X - μ) / σ, where X is the value ($195), μ is the mean ($319), and σ is the standard deviation ($56). So, (195 - 319) / 56 = -124 / 56 = -2.21. This means $195 is about 2.21 standard deviations below the mean.

Question 7

Here are some summary statistics for the size of forest fires last year: smallest fire = 72 acres,mean = 493 acres,median = 493 acres,range = 7,928 acres,IQR = 370,Q1 = 197,standard deviation = 59 acres.Between what two values are the middle 50% of fire sizes found?
A)123.25 and 369.75
B)98.6 and 394.4
C)197 and 567
D)72 and 8000
E)246.5 and 493

Accepted Answer

The middle 50% of fire sizes are found between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 197 and IQR = 370, Q3 can be calculated as Q1 + IQR = 197 + 370 = 567. Thus, the middle 50% of fire sizes are between 197 and 567 acres.

Question 8

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 67,median = 81.2,range = 79,IQR = 60,Q1 = 27,standard deviation = 8.6.Between what two values are the middle 50% of the scores found?
A)31 and 110
B)67 and 81.2
C)27 and 87
D)16.75 and 50.25
E)20.3 and 60.9

Accepted Answer

The middle 50% of scores are within the IQR, which is from Q1 (27) to Q3 (87). Therefore, the answer is C, which includes both Q1 and Q3 in the range.

Question 9

The setter on your school's volleyball team average 58 assists per match with a standard deviation of 6.How many standard deviations from the mean is an outing with 79 assists?
A)1.75 standard deviations below the mean
B)1.36 standard deviations below the mean
C)3.50 standard deviations below the mean
D)3.50 standard deviations above the mean
E)1.75 standard deviations above the mean

Accepted Answer

To find the number of standard deviations from the mean, use the formula: (observed value - mean) / standard deviation. Here, (79 - 58) / 6 = 21 / 6 = 3.50. Since 79 is greater than the mean, it is 3.50 standard deviations above the mean.

Question 10

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 207 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 154,252,and 202 grams.A customer makes a special order of a 16 ounce cone.Which of the summary statistics might not change if that data value was added to the distribution?
A)Range,SD
B)Median,IQR
C)Median,range
D)Mean,IQR
E)Q1,Q3

Accepted Answer

The median and IQR (Interquartile Range) are resistant to extreme values, so they might not change significantly with the addition of a new data point.

Question 11

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 97,median = 105,range = 92,IQR = 105,Q1 = 39,standard deviation = 16.Between what two values are the middle 50% of the scores found?
A)26.25 and 78.75
B)58 and 150
C)39 and 144
D)24.25 and 67.9
E)97 and 105

Accepted Answer

The middle 50% of the scores are represented by the IQR (the range between the 25th and 75th percentiles). We know that Q1 = 39 and IQR = 105. To find the 75th percentile, we can add 105 to Q1, giving us 144. Therefore, the middle 50% of scores are between 39 and 144, which corresponds to choice C.

Question 12

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 18 cm,mean = 49 cm,median = 42 cm,range = 82 cm,IQR = 50,Q1 = 20,standard deviation = 10 cm.Between what two values are the middle 50% of snowfall found?
A)20 and 70
B)12.25 and 36.75
C)49 and 42
D)10.5 and 31.5
E)18 and 100

Accepted Answer

The median is closer to the first quartile (Q1) than the third quartile (Q3), indicating a negatively skewed distribution. Therefore, we can estimate that the lower quartile (Q1) is around 20 cm and the upper quartile (Q3) is around 70 cm. The interquartile range (IQR) is the distance between Q1 and Q3, which is given as 50 cm. Thus, the middle 50% of snowfall is found between Q1 and Q3, or between 20 cm and 70 cm. Therefore, the answer is (A) 20 and 70.

Question 13

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 132 minutes,mean = 76 minutes,median = 76 minutes,range = 102 minutes,IQR = 62,Q1 = 30,standard deviation = 10 minutes.Between what two values are the middle 50% of times?
A)15.2 and 60.8
B)132 and 30
C)19 and 57
D)38 and 76
E)30 and 92

Accepted Answer

The middle 50% of times are between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 30 and IQR = 62, Q3 = Q1 + IQR = 30 + 62 = 92. Therefore, the middle 50% of times are between 30 and 92.

Question 14

Here are some summary statistics for last year's basketball team scoring output: lowest score = 23 points,mean = 53 points,median = 47 points,range = 92 points,IQR = 51,Q1 = 32,standard deviation = 5 points.Between what two values are the middle 50% of scores found?
A)53 and 47
B)23 and 115
C)13.25 and 3,975
D)32 and 83
E)11.75 and 35.25

Accepted Answer

The IQR is the range of the middle 50% of the data. Q1 is the 25th percentile and Q3 is the 75th percentile. From the given information, Q1 = 32 and IQR = 51. Therefore, Q3 = 32 + 51 = 83. The middle 50% of scores are between Q1 and Q3, which is 32 and 83. Thus, the correct answer is D.

Question 15

The average size of forest fires last year was 968 acres with a standard deviation of 182 acres.How many standard deviations from the mean is a forest fire consuming 245 acres?
A)About 3.97 standard deviations below the mean
B)About 1.35 standard deviations above the mean
C)About 3.97 standard deviations above the mean
D)About 1.99 standard deviations below the mean
E)About 1.99 standard deviations above the mean

Accepted Answer

To find how many standard deviations from the mean a value is, you subtract the mean from the value and divide by the standard deviation: (245 - 968) / 182 = -723 / 182 ≈ -3.97. This means the fire consuming 245 acres is about 3.97 standard deviations below the mean.

Question 16

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?
A)3.25 standard deviations below the mean
B)6.50 standard deviations above the mean
C)3.25 standard deviations above the mean
D)6.50 standard deviations below the mean
E)1.78 standard deviations above the mean

Accepted Answer

The answer of The average number of babies born in...

Question 17

The average number of days absent per student per year at West Valley School is 16 days with a standard deviation of 5 days.How many standard deviations from the mean is of 6 absent days?
A)0.83 standard deviations above the mean
B)1.83 standard deviations below the mean
C)2.00 standard deviations above the mean
D)2.00 standard deviations below the mean
E)1.83 standard deviations above the mean

Accepted Answer

To find how many standard deviations from the mean 6 absent days is, we use the formula: (X - μ) / σ, where X is the value (6 days), μ is the mean (16 days), and σ is the standard deviation (5 days). So, (6 - 16) / 5 = -10 / 5 = -2. This means 6 absent days is 2 standard deviations below the mean.

Question 18

Suppose that the average amount of sugar a person eats per year is 5 kg with a standard deviation of 1.7 kg.How many standard deviations from the mean is the consumption of 14 kg of sugar?
A)About 3.00 standard deviations above the mean
B)About 3.00 standard deviations below the mean
C)About 2.94 standard deviations above the mean
D)About 5.29 standard deviations above the mean
E)About 5.29 standard deviations below the mean

Accepted Answer

We can use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean (μ) that corresponds to a value x, given a standard deviation of σ.

Substituting the values given in the problem, we have:

z = (14 kg - 5 kg) / 1.7 kg
z ≈ 5.29

This means that a consumption of 14 kg of sugar is about 5.29 standard deviations above the mean.

Therefore, the best choice is D.

Question 19

The weights of children age two average 25 pounds with a standard deviation of 4 pounds.How many standard deviations from the mean is a weight of 15 pounds?
A)2.50 standard deviations below the mean
B)1.40 standard deviations above the mean
C)1.40 standard deviations below the mean
D)1.67 standard deviations above the mean
E)2.50 standard deviations above the mean

Accepted Answer

To find how many standard deviations a weight of 15 pounds is from the mean, use the formula: (X - μ) / σ. Here, X = 15, μ = 25, and σ = 4. So, (15 - 25) / 4 = -2.5, which means 15 pounds is 2.50 standard deviations below the mean.

Question 20

The mean test score on a statistics test was 72 with a standard deviation of 10.How many standard deviations from the mean is a test score of 90?
A)1.80 standard deviations above the mean
B)1.80 standard deviations below the mean
C)0.69 standard deviations above the mean
D)0.80 standard deviations above the mean
E)0.69 standard deviations below the mean

Accepted Answer

To find how many standard deviations a score is from the mean, subtract the mean from the score and divide by the standard deviation: (90 - 72) / 10 = 18 / 10 = 1.80 standard deviations above the mean.

Quiz 5: The Standard Deviation As a Ruler and the Normal Model

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000,mean salary = $35,000,median = $25,000,range = $60,000,IQR = $30,000,first quartile = $17,500,standard deviation = $20,000. Between what two values are the middle 50% of the salaries found?

A town's average snowfall is 40 cm per year with a standard deviation of 12 cm.How many standard deviations from the mean is a snowfall of 64 cm?

The average number of average number of hours per day a university student spends on homework is 5 hours with a standard deviation of 1.25 hours.How many standard deviations from the mean is 2 hours spent on homework?

Mario's poker winnings average $319 per week with a standard deviation of $56.How many standard deviations from the mean is winning $195?

Here are some summary statistics for the size of forest fires last year: smallest fire = 72 acres,mean = 493 acres,median = 493 acres,range = 7,928 acres,IQR = 370,Q1 = 197,standard deviation = 59 acres.Between what two values are the middle 50% of fire sizes found?

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 67,median = 81.2,range = 79,IQR = 60,Q1 = 27,standard deviation = 8.6.Between what two values are the middle 50% of the scores found?

The setter on your school's volleyball team average 58 assists per match with a standard deviation of 6.How many standard deviations from the mean is an outing with 79 assists?

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 97,median = 105,range = 92,IQR = 105,Q1 = 39,standard deviation = 16.Between what two values are the middle 50% of the scores found?

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 18 cm,mean = 49 cm,median = 42 cm,range = 82 cm,IQR = 50,Q1 = 20,standard deviation = 10 cm.Between what two values are the middle 50% of snowfall found?

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 132 minutes,mean = 76 minutes,median = 76 minutes,range = 102 minutes,IQR = 62,Q1 = 30,standard deviation = 10 minutes.Between what two values are the middle 50% of times?

Here are some summary statistics for last year's basketball team scoring output: lowest score = 23 points,mean = 53 points,median = 47 points,range = 92 points,IQR = 51,Q1 = 32,standard deviation = 5 points.Between what two values are the middle 50% of scores found?

The average size of forest fires last year was 968 acres with a standard deviation of 182 acres.How many standard deviations from the mean is a forest fire consuming 245 acres?

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?

The average number of days absent per student per year at West Valley School is 16 days with a standard deviation of 5 days.How many standard deviations from the mean is of 6 absent days?

Suppose that the average amount of sugar a person eats per year is 5 kg with a standard deviation of 1.7 kg.How many standard deviations from the mean is the consumption of 14 kg of sugar?

The weights of children age two average 25 pounds with a standard deviation of 4 pounds.How many standard deviations from the mean is a weight of 15 pounds?

The mean test score on a statistics test was 72 with a standard deviation of 10.How many standard deviations from the mean is a test score of 90?