Free

Frequency Distributions - Assignment Example

Summary
The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
…

Extract of sample "Frequency Distributions"

Case Assignment Answer the following problems showing your work and explaining (or analyzing) your results The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99   34   86   57   73   85    91   93   46    96   88   79    68   85   89
Ans: The mean is 77.93 and the Standard deviation is 18.38.
There were 12 observations within one Standard Dev of mean limits
There were 14 observations within two Standard Dev of mean limits

2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
Ans: Mean=74.8 and S.D= 7.57, then z= (85-74.8) / 7.57 i.e 1.3474
Cumulative area for z score 1.3474 is 0.911 i.e. cumulative area for z score>1.3474 is (1-0.911) = 0.089.
Therefore student scoring above 85% is 15*0.089 which is 1.335 or 1 (approx).
3. If you know the standard deviation, how do you find the variance? Ans: If we square the Standard Deviation we get Variance.
Variance= (Standard Deviation)^2
4. To get the best deal on a stereo system, Louis called eight appliance stores and asked for the cost of a specific model. The prices he was quoted are listed below:
\$216   \$135   \$281   \$189   \$218   \$193   \$299   \$235
Find the standard deviation.
Ans: Standard Deviation is 48.88
5. A company has 70 employees whose salaries are summarized in the frequency distribution below.
Salary
Number of Employees
5,001–10,000
8
10,001–15,000
12
15,001–20,000
20
20,001–25,000
17
25,001–30,000
13
a. Find the standard deviation.
b. Find the variance.
Ans: standard deviation is 1.252
Variance is 1.568
6.  Calculate the mean and variance of the data. Show and explain your steps. Round to the nearest tenth.
14,   16,   7,   9,   11,   13,   8,   10
Ans: Mean is 11 and Variance is 8.5.
The steps are shown below:
a) calculate the mean i.e sum(all obsv)/no.of obsv.
(14+16+7+9+11+13+8+10) / 8
b) calculate ( obsv-mean )^2 as shown below
c) Calculate sum of (obsv-mean) ^2 and divide it by no of obsv to get the variance. i.e. 68/8
7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)
3,   5,   1,   6,   1,   2,   2,   6,   3,   4,   5,   1,   1,   3,   4,   2,   1,   6,   5,   3,   4,   2,   1,   3,   2,   4,   6,   5,   3,   1
Ans: Frequency distribution is shown below:
8. Answer the following questions using the frequency distribution table you created in No. 7.
a. Which number(s) had the highest frequency?
b. How many times did a number of 4 or greater get thrown?
c. How many times was an odd number thrown?
d. How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
Ans: The table below gives the answer:

9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.
a. Range
b. Standard deviation
c. Variance
Lastly, compare the two sets of results.
Ans: The answer is given below in table:
Company
Wait times in seconds
Big Burger Company
105
67
78
120
175
115
120
59
The Cheesy Burger
133
124
200
79
101
147
118
125
10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?
Ans: A graph is said to be normally distributed if it is symmetric and bell shaped with a single peak. For any normal distribution two quantities must be defined, the mean “mu” where the peak of the curve occurs and standard deviation “sigma” which signifies the spread of the curve from its mean value.
68% of the observations fall within 1 standard deviation of the mean.
95% of the observations fall within 2 standard deviation of the mean.
99.7% of the observations fall within 3 standard deviation of the mean.
Reference
Das, N.G. (2006). Statistical Methods. Kolkata: Word Press Read More
Cite this document
• APA
• MLA
• CHICAGO
(“Frequency Distributions Assignment Example | Topics and Well Written Essays - 500 words”, n.d.)
Frequency Distributions Assignment Example | Topics and Well Written Essays - 500 words. Retrieved from https://studentshare.org/statistics/1657570-frequency-distributions
(Frequency Distributions Assignment Example | Topics and Well Written Essays - 500 Words)
Frequency Distributions Assignment Example | Topics and Well Written Essays - 500 Words. https://studentshare.org/statistics/1657570-frequency-distributions.
“Frequency Distributions Assignment Example | Topics and Well Written Essays - 500 Words”, n.d. https://studentshare.org/statistics/1657570-frequency-distributions.
Click to create a comment or rate a document

CHECK THESE SAMPLES OF Frequency Distributions

Frequency Distributions

...?Situation Imagine that you can predict the s scores on the Tests for Understanding in this In Week there was a bimodal distribution. In Week 2, there was a positive skew. In Week 3, there was a normal distribution. In Week 4, there was a negative skew.  Questions: 1. What do these different scores tell you about the tests in Weeks 1, 2, 3, and 4? What is happening to the students' scores over time?  From the given distributions, one can say that there is a distinct change in the pattern of student’s scores on understanding over the three weeks. Initially, there was a bimodal distribution, showing that students were grouped into those that understood better (scores that clustered around the top of the scale) and those that did... , and only...
2 Pages(500 words)Essay

Amplitude & Frequency Modulation Techniques

...Table of Contents Objectives………………………………………………………………. 2 2. Introduction ……………………………………………………………. 2 3. Amplitude Modulation………………………………………………….. 3 3.1 AM Mathematical Analysis……………………………………….. 3 3.2 AM Modulation Index…………………………………………….. 4 3.3 AM Spectrum and Bandwidth……………………………………. 5 3.4 AM Power Relations………………………………………………. 6 3.5 AM Demodulation Circuits……………………………………….. 7 3.6 Double Sideband Suppressed Carrier (DSBSC) and Single Sideband (SSB) AM……………………………………… 8 3.7 Practical AM Modulation and Demodulation Circuits…………. 9 3.8 Advantages and Disadvantages of AM Modulation…………… 10 3.9 MATLAB/ SIMULINK Simulation Results for AM……………… 11 4. Frequency...
12 Pages(3000 words)Essay

Frequency Distribution

...1. Based on the Frequency distribution and the Histogram chart, the frequency of the data is centered at 43 53 which is covers the statisticalmean of 1.48. The distribution looks a normal bell curve with high peak; however, the data has a longer tail starting from 2.03 up. The frequency distribution tells us that the nurses to bed ratio in the US is centered at 1.43-1.53 and a few 2.0 nurses to bed ratio. Bin Frequency 0.93 1 1.03 1 1.13 2 1.23 4 1.33 5 1.43 10 1.53 5 1.63 3 1.73 3 1.83 1 1.93 0 2.03 2 2.13 1 More 2 2. Based on the Frequency distribution and the Histogram chart, the...
5 Pages(1250 words)Essay

Frequency Distribution

...Statistics Inserts His/Her Inserts Grade Inserts 1st June, Overview Frequency distributionsare used in analyzing patterns in data that are measured in different tasks undertaken under project management. In cases where several people undertake similar tasks graphs can be used in measuring work output and quantity. In a project it might be difficult to measure the output of workers or employees generally. However, with the use of frequency distributions we can easily get exact figures for every task or data collected for each and every employee (Lewis, 2006). Making use of frequency distribution tools like graphs and tables we are able to measure and...
1 Pages(250 words)Assignment

Unit 2 IP/ Probability Distributions

... Lecturer The law court system and federal court system were both established under the United s of America’s Constitution. However, their jurisdiction to determine the cases differs as per the authorities given by the state. Federal court system, mostly handle the disputes involving the Constitutions and laws passed by the Congress. (Reed 1997) explains, the state law is broad and cover a wide jurisdiction and most likely involve in robberies, traffic violations, broken contracts and family disputes cases. The litigations against the United States and some cases that touches federal laws such as criminal, patent, same maritime cases, copyright, bankruptcy, and antitrust do not fall within the jurisdiction of state law courts... Lecturer The ...
1 Pages(250 words)Essay

Probability Distributions

...Probability Distributions This report contains the findings of a study done to determine the age, gender and crime distribution in various correctional facilities in the USA. It also includes the satisfaction scores for key components of criminal justice system and services. The research participants were 25 prisoners serving various jail terms in both the state and federal prisons. The survey established that four out of every five prisoners are males. Moreover, a person aged between 16 to 49 years is three times more likely to commit a crime than a person who is over 60 years old. Burglary topped the list of the most committed crime with 44%. On satisfaction, the criminal justice ranked first with 5.4...
6 Pages(1500 words)Assignment

Linux distributions

...the said goal, imparting adequate training to its employees or to hire trained professionals to apply the system for the optimum benefit of the organisation becomes inevitable. With a view to select appropriate software to suit the requirements, Red Hat, Ubuntu and Novell’s SUSE based OS are being taken into consideration. Indeed the training motivates the employees as well as raises their confidence in using the software to meet the requirements. RedHat: In terms of trained professionals and certified training program, Red hat tops other Linux distributions. RedHat training centers are spread across the globe and training programs on various specializations are available. They are also providing ‘on-site team...
9 Pages(2250 words)Essay

Frequency Distributions (mod 3 slp)

...From the data collected in Module a frequency distribution can be prepared as shown in Table Table Frequency Distribution Time (in Minutes) Frequency 81-100 1 101-120 3 121-140 0 141-160 3 161-180 8 181-200 3 201-220 2 Figure 1: Graph for Frequency Distribution The distribution resembles a normal distribution as evidenced by the bar and line graphs depicted in Figure 1. Now, to calculate standard deviation, the upper limit and lower limit of each salary range are listed. After this, the mid-point of each salary range is computed. The product of midpoint of the salary and the...
2 Pages(500 words)Essay

FREQUENCY DISTRIBUTIONS

...Introduction to Probability Brandon M. Blackmon Trident International Frequency distribution table Frequency distribution tables present data in the form of values and their frequencies. It helps in the calculation of, measures of central tendencies, for example, the mean, as well as, measures of variations including the range, standard deviation, and variance. To measure the standard deviation and the variance, one has to calculate the average of standard deviations of all the values from the mean. The below frequency distribution table shows the collected data relating to the amount of time spent on physical fitness...
3 Pages(750 words)Assignment