2E Review of Statistics

  1. The following data represents the Algebra test scores of 20 students:

29, 31, 67, 67, 69, 70, 71, 72, 75, 77, 78, 80,83,85, 87, 90,90,91,91,93

a)What is the mean, mode, and median?

Mean______Mode ______Median ______

b)Create a box-plot

c)What is the interquartile range?______

d)What is the standard deviation?______

e)Suppose that a 21st score of a 5 on a test is added. Which is likely to change the most; mean, median, or mode?______

Will the standard deviation increase or decrease?______

f)Describe the shape, center and spread of this data.

  1. Describe the shape of the following distributions. Use words like skewed to the left (less numbers on the left), skewed to the right (less numbers to the right), normal (evenly distributed).

Distribution A:Distribution B:Distribution C:

______

  1. Use the following box-plot of 120 bowlers to answer the questions

a)What is the interquartile range?

b)What is the maximum?

c)What is the minimum?

d)Draw a histogram that best models this box-plot

e)What is the range?

f)How many people got at most 95?

  1. A set of data has a mean of 56.7 and a standard deviation of 2.5.

What would the new mean and new standard deviation be if each of the data is increased by 5?

  1. The data below shows the ages of teachers: 23, 25, 25, 27, 29, 30,31,32,33,34,36,37,40,41,42,43,55

a)What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation?)

b)Describe the shape of this data

  1. A teacher interviewed 200 students and found the following results:

Male / Female
Sophomore / .2 / .1
Junior / .1 / .25
Senior / .25 / .1

a)How many senior males did the teacher interview?

b)If the student was a sophomore, what gender was it more likely to be?

c)How many more female juniors were there than male juniors?

  1. The following are test scores of a Biology test: 55, 59, 60, 61,65,65,65,70,72,73,74,76,77,78, 82, 88, 93,94,95

a)What is the mean, mode, and median?

Mean______Mode ______Median ______

b)Create a box-plot

c)What is the interquartile range?______

d)What is the standard deviation?______

e)Suppose that a 21st score of a 5 on a test is added. Which measure is likely to change the most; mean, median, or mode? Will the standard deviation increase or decrease?

  1. Use the following box-plot of answers to 80 people to answer the questions

a)What is the interquartile range?

b)What is the maximum and minimum?

c)How many people got at least 16?

  1. A set of data has a mean of 44.7 and a standard deviation of 1.3.

What would the new mean and new standard deviation be if each of the data is decreased by 3?

New Mean ______New Standard Deviation ______

  1. The data below shows the household income: 23500, 26000, 28000, 29000, 32500, 36500, 38500, 42200, 55000, 58500, 62000, 67000, 112200

a)What measure of spread is more appropriate for this data (mean, mode, median, or standard deviation)?

b)Are there any outliers? (Explain…)

c)Describe the shape of this data.

d)Suppose that a millionaire is added to the data set, which measure of spread will increase the most(mean, mode, median, or standard deviation)?

  1. 400 people were surveyed. Each person was asked whether he or she prefers Drama or Comedy movies. The results are shown in the relative frequency table below:

Age / Drama / Comedy / Total
21-30 / .25 / .30 / .55
31-40 / .15 / .06 / .21
>41 / .20 / .04 / .24
Total / .6 / .4 / 1

a)How many more people prefer drama than comedy?

b)How many more 21-30 year olds prefer comedy than drama?

c)How many total people prefer drama?

MULTIPLE CHOICE

  1. The following table shows the population of various towns:

City / Eastville / Northville / Southville / Westville / Centerville / Wayoutville / Salemville
Population (thousands) / 30 / 40 / 56 / 48 / 51 / 53 / 64

Suppose that Winstonville with a population of 26,000 is added to the data set.

Which of the following is true?

  1. The mean increasesB. The range remains the same

C. The standard deviation increases D. The interquartile-range increases

  1. A chair lift can hold a maximum of 40000 pounds and 200 people. A safety inspector is determining if the chair lift is safe or not. Which measure of central tendency of people’s weight would be most useful to determine if the chair lift is safe?
  1. MeanB. MedianC. ModeD. Standard Deviation
  1. The number of points scored by a football team in the first eight games of a season are: 10,14, 17, 20, 35,35,38,42. What would happen to the data distribution if the team scored 27,27, and 28 in the next three games?
  1. The standard deviation would increase
  2. The data distribution would become more peaked and more widely spread.
  3. The data distribution would become less peaked and less widely spread.
  4. The data distribution would become more peaked and less widely spread.
  1. Which of the following is most likely to have the highest standard deviation? To have the lowest interquartile-range?
  1. The average age of 100 people surveyed at the mall
  2. The average age of 100 people living in a retirement center
  3. The weight of 100 new-born babies.
  4. The amount of TV’s that 100 households have.
  1. Which of the following statements is true?
  1. A data set with high standard deviation means that there is low variability.
  2. A data set with low standard deviation means that the data is spread out.
  3. As the amount of data increases, the standard deviation usually increases.
  4. A data set with many outliers will have a high standard deviation.

Geometry / Algebra / Total
Underclassmen / .36 / .28 / .64
Upperclassmen / .04 / .32 / .36
Total / .4 / .6 / 1.00
  1. The math club has 50 members. Each member was asked if he preferred Algebra or Geometry. The results are shown in the relative frequency table below:
  1. The following table displays a group of students preference of pizza

Cheese / Pepperoni / Total
Males / 23 / 57 / 80
Females / 45 / 35 / 80
  1. What percentage of males prefers Pepperoni?
  2. What percentage of females prefers Cheese?
  3. Of the Cheese pizza lovers, what percentage are males?
  4. What is the total percentage of people that prefer Pepperoni?
  5. Make the Total relative frequency table with percentages.
  1. To the right is a box plot that shows the scores of two football teams, Team A and B.

a)Which team usually scored the most points?

b)Which team has a higher standard deviation?

c)Which team was more consistent with their scoring?

d)How much larger is the range of team B than of team A?

  1. Circle the graph with the lowest standard deviation. Put a box around the one that has the highest variability.
  1. Which of the following examples are most likely to have the largest interval ranges for a histogram and interquartile range for a boxplot? Which is most likely to have smallest intervals and interquartile range?

I: The weight (in pounds) of 30 people at the mall

II. The ages of 30 people at the mall

III. The amount of money in the wallet of 30 people at the mall.

IV. The shoe sizes of 30 people at the mall.

  1. The following are attendance for home football games: 287, 263, 286,286, 256, 70, 255, and 300. If the attendance for the 6th game (70) wasn’t included then which measure would increase the most: mean, mode, median, or standard deviation? Explain your reasoning.
  1. Rank the following from having the most likely lowest standard deviation to the most likely highest standard deviation. Explain your answers:

A: Finding the age (in years) of 50 dogs in the dog pound

B: Finding the age of 20 dogs in the dog pound

C: Randomly selecting 50 numbers from 1-1000

D: Randomly selecting 20 numbers from 1-1000

E: Randomly selecting 50 even numbers from 1-2000