Statistics Midterm
What is the difference between a frequency polygon and an ogive?
A frequency polygon shows relative frequency with each value connected to form a polygon. An ogive, shows cumulative frequency. Oh Come On (Ogive = cumulative frequency).
What is the level of measure of the following data sets: A list of birthdays: June 4, Feburary 18, August 15th
Nominal - there is no set order, qualitative, it is the "name" of a thing.
What is the level of measure of the following data sets: A list of movies by time: Star Wars VIII @ 8:00 pm, Star Trek XXII @ 8:30 pm, Rock IX @ 9:00 pm
Ordinal - there is an order to the qualitative data.
Describe the difference between the calculation of population standard deviation and that of sample standard deviation.
Sample standard deviation required (n-1) adjustment in the denominator. Population standard deviation = GO OVER WITH DAD
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. We can use Mrs. Miller's fourth grade participation rate of 72% to show that more than half of all fourth grade students in the school participated in the fundraising drive.
Statistic, because you are making generalizations about the entire population.
What is the difference between class limits and class boundaries?
Class limits show the lowest and highest values in a class. Class boundaries are not values in a class, but fall between classes.
Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem.
Empirical Rule: 68% of the data in the first quartile, 95% of the data is second quartile, and 99.7% in the third quartile. Chebychev's Theorem: at least 75% of data in second quartile, at least 88.9% of data + 3rd quartile used for all distributions. ASK DAD
Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 15.6 14.3 4.7 30.5 23.4 15.8 34.6 41.4 45.2 20.3 43.9 36.2 77.4 13.5 49.5 41.8 8.6 42.7 11.6 36.7 23.2 19.6 19.5 17.8 79.3 22.7 29.5 21.5 6.9 18.9 28.4 32.8 25.1 27.5 22.5 26.4 65.4 28.1 34.2 15.5
Find Q1= find the median, and then find the median for the first half of the data.. Find Q3= find the median, and then find the median for the second half of the data. Find the interquartile range = subtract Q3 - Q1. Identify outliers = IQR * 1.5 and then add this number to the Q3 OR = IQR * 1.5 and then subtract this from Q1.
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. (when finding the width, always remember to.....) Minimum=9 Maximum=94 Number of Classes=6
LL =(9.24,39,54,69,84) UL-(23, 38, 53, 68, 83, 98). You can find the width by subtracting the maximum by the minimum and then dividing by the number of classes and always remember to ROUND UP to the next whole number.
11. Draw an example of the following distributions: symmetric, uniform, skewed left, skewed right.
Make a drawing on a scratch piece of paper.
12. Find the mean, median, and mode of the data, if possible. If any of these measures cannot be found or a measure does not represent the center of the data, explain why. 11.5 10.2 10.7 10.6 11.2 9.6 8.9 9.7 11.3 10.8 10.6 11.6
Mean = 10.56 Median = 10.65 Mode=10.6
(a) Find the probability that a randomly selected student is male, given that the student is a journalism major. (b) Find the probability that a randomly selected student is a non-journalism major, given that the student is female. (c) Find the probability that a randomly selected student is journalism major and a male. (d) Find the probability that a randomly selected student is a female or a non-journalism major. (e) Find the probability that a randomly selected student is neither female nor a journalism student.
ASK DAD
10. Use the frequency table below to create an ogive. Use the ogive to answer parts a) through d). Weight (in pounds) of 6 month old puppies at a kennel 1.2 3.4 5.2 7.4 8.6 3.2 7.9 6.9 5.1 11.4 14.3 15.8 20.3 13.5 4.7 9.6 22.7 18.9 27.5 28.1 2.8 4.6 3.9 9.5 11.6 19.5 29.5 28.4 22.5 34.2 30.5 41.4 36.2 31.8 36.7 17.8 21.5 32.8 26.4 15.5 a) What is the cumulative frequency for a weight of 27.5 pounds? b) What is the weight for which the cumulative frequency is 60? c) How many puppies weigh between 22.5 and 29.5 pounds? d) How many puppies weigh more than 30.5 pounds?
ASK DAD
22. To the left is a box and whisker plot that shows the age children are identified with Attention Deficit Disorder. The median age is 8, with a 1st quartile of 4.7 and a 3rd quartile of 14.3 years old. The minimum age is 3.2 and the maximum age is 19.5. a) Find the probability that a child will be diagnosed before 14.3 years of age. b) Find the probability that a child will be diagnosed after 8 years of age. c) Find the probability that a child will be diagnosed below 4.7 years of age
ASK DAD
In a survey of a group of teenagers, the weights in the 12-14 age group were normally distributed, with a mean of 109 pounds and a standard deviation of 22 pounds. A study participant is randomly selected. (a) Find the probability that a study participant has a weight that is less than 110 pounds. (b) Find the probability that a study participant has a weight that is between 105 and 130 pounds. (c) Find the probability that a study participant has a weight that is more than 130 pounds. (d) Identify any unusual events. Explain your reasoning.
ASK DAD
Sample annual salaries (in thousands of dollars) for employees at a company are listed. 47 47 51 46 38 38 50 47 56 34 46 50 53 (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a 20% raise. Find the sample mean and sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?
ASK DAD
The data set in problem 19 represents the average rainfall in Johnsonville County in the month of June over a 40-year period. Find the percentile that corresponds to a rainfall of 42.7 inches.
ASK DAD
Use the probability distribution to find the (a) mean, (b) variance, (c) standard deviation, and (d) expected value of the probability distribution, and (e) interpret the results. The probability distribution shows the distribution of family sizes in country A for a recent year. 0.224 0.329 0.173 0.112 0.093 0.069 1 2 3 4 5 6
ASK DAD
What is an inherent zero? Which of the following has an inherent zero? - Football salaries in dollars. - Average snowfall in inches - Average temperature in Alaska in Fahrenheit - A measure of how much someone is loved on a scale of 0 to 10.
An inherent zero means there is literally nothing there... a true zero (i.e. the absence of something existing. - Football salaries in dollars = inherent zero. - average snowfall in inches = inherent zero - average temperature in Alaska in Ferenheit = no inherent zero. - A measure of how much someone is loved on a scale of 0 to 10= not an inherent zero.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. 54% of fourth grade white students scored below a proficient reading level in the US in 2017.
Parameter, because you are surveying a sample of the population.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. Mrs. Miller's fourth grade class had a 72% participation rate in the fundraising drive.
Parameter, because you are surveying a sample of the population.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. The average salary of the English department is $68,000.
Parameter, because you are surveying a sample of the population.
For the standard normal distribution, find the probability of z occurring in the indicated region of Z = -0.44 to Z = 0.09.
Practice in STATCRUNCH
Use the standard normal calculator to find the following z-scores to match the probabilities, or the probabilities to match the z-scores. a.) Find the probability that a randomly selected variable will fall within the region of the standard normal curve to the left of z=1.47 b.) Find the probability that a randomly selected variable will fall within the region of the standard normal curve between z=0 and z=1.99 c.) Find the probability that a randomly selected variable will fall within the region of the standard normal curve to the left of z= −2.62 and to the right of z=2.6
Practice in STATCRUNCH
Find the indicated z-score that equates to the given p-value. a) p = 0.997, z-score = b) p = 0.0215, z-score = c) p = 0.356, z-score = d) p = 0.749, z-score =
Practice in Stat Crunch
Use the standard normal table to find the z-score that corresponds to the given percentile. a) P17 = b) P82 = c) P97 = d) P08 =
Practice in Statcrunch
What is the level of measure of the following data sets: Rainfall by year: 1980 (34.5 in), 1985 (43.9 in), 1990 (29.4in)
Ratio - there is an absolute zero and data is quantitative
Define double blind
neither the subject nor the experimenter know who is in the treatment group.
Define control
used as a standard of comparison in an experiment
Identify six different sampling techniques and their potential biases:
1. Random: each subject has an equally likely chance of being chosen. 2. Systematic - select every nth subject susceptible to patterns. 3. Cluster - select 1 subgroup and conduct a census. 4. Stratefied - select n subjects from all subgroups. 5. Convenience - allow subjects to self-select. 6. Simple random- subjects are placed into groups and each group has an equally likely chance to be selected.
14. The mean scores for students in three elementary schools are shown below. What is the mean score all elementary schools in the district? Miller Elementary: 90 No. of student 109 South Poplar Elementary: 94 No. of students125 Van Buren Elementary: 76 No. of students 137
109(90) + 125 (94) + 137 (76)/ (109+ 125 + 137) = 86.2 mean for all elementary schools in the district.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. The average annual salary of 50 of a company's 1500 employees is $54,000.
Statistic, because you are surveying the entire company rather than a sample of the company.
Use the given frequency distribution to find the: (a) class width) (b) class midpoints (c) class boundaries [0,4] = 4 [5,9] = 7 [10,14] = 8 [15,19] = 6 [20,24] = 5 [25,29] = 3
The class width=5 (YOU CAN USE 0 AS A LOWER LIMIT). Class midpoints=2, 7, 12, 17, 22, 27 (add up lower and upper limits and then divide by 2) Class boundaries = -.5, 4.5, 9.5, 14.5, 19.5, 24.5, 29.5. This can be found by subtracting .5 from the lower limits for each frequency distribution class.
Explain how the inter-quartile range of a data set can be used to identify outliers.
To find outliers: IQR *1.5 and then add this number to Q3 OR IQR * 1.5 and then subtract this number from Q1.
Sampling Distribution: A population has a mean μ=61 and a standard deviation σ = 16. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 117.
To find the sampling distribution: - Divide the mean by the square root of the sample size Mean/Square root of sample size
Use the data here to create a probability distribution. [0,4] = 4 [5,9] = 7 [10,14] = 8 [15,19] = 6 [20,24] = 5 [25,29] = 3 a) Calculate the mean of the probability distribution. b) Calculate the variance of the probability distribution. c) Calculate the standard deviation of the probability distribution.
To make a probability distribution: - find the midpoints - add up the total sum (sample size) of the frequencies - divide the frequency by the total sample size - multiply the midpoint * the probability (Px). - Add up the sum and you get the mean. To calculate the variance: - (x - mean) 2; data point - mean and then squared... and then multiply by the probability. To calculate the standard deviation: take the square root of the variance
Define Symptom
a characteristic that is attributable to a disease. Treatment can be applied to remedy a symptom.
Define experimental unit
a member of a set of subjects being studied
Define treatment
a substance intentionally used to cause an experimental effect
Define placebo
a substance with no experimental effect