Problem 1 Please answer the below questions based on this data: 44, 20, 85, 68, 64, 83, 56, 70, 55, 78, 80,65,64,54,53, 85, 68, 50, 57, 61, 51, 94, 87, 25, 30, Compute: 1. Mean, Median, Mode 2. SD, Variance 3. Range

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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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12:54 D E
A ll 100%I
+ Assignment3.pdf
Problem 1
Please answer the below questions based on this data:
44, 20, 85, 68, 64, 83, 56, 70, 55, 78, 80,65,64,54,53, 85, 68, 50, 57, 61, 51, 94, 87, 25, 30,
Compute:
1. Mean, Median, Mode
2. SD, Variance
3. Range
4. The 75th percentile, the 25th percentile, the 55th percentile
5. Interquartile Range
6. Are 98 an outlier? Is 124 an extreme outlier?
7. Draw the frequency table of this data, mentioning only the frequency and the cumulative
frequency
8. Represent this data using a boxplot
9. Is this data symmetrical or skewed?
Problem 2
Table of results for survey of daycare status and ear infection by 6 months for 260 infants
Ear Infection by 6 Months
No
Daycare
Yes
Total
Yes
58
62
120
45
No
95
140
Total
103
157
260
Calculate the following from the table counts
1. Marginal probability that an infant had an ear infection by 6 months?
2. Marginal probability that an infant was in daycare?
3. Joint probability of being in daycare and having an ear infection by 6 months?
4. Joint probability of being in daycare and not having an ear infection by 6 months?
5. Conditional probability of having an ear infection by 6 months given that the infant is in daycare?
6. What is the conditional probability of having an ear infection given that the infant was not in
daycare?
7. What is the probability of having an ear infection or that the infant was not in daycare?
8. Are daycare status and ear infection status independent? Justify your answer.
Problem 3
A new test is developed for the detection of carcinoma of the prostate.(Foti et al. NEngl. J Med. 1977).
When it is tested in a group of 113 patients with prostatic cancer, 79 have a positive test.
In a group of 217 individuals without prostatic cancer, 10 have a positive test.
a) What is the specificity and sensitivity of the test?
b) Calculate FP rate and FN rate.
c) Calculate PPV and NPV.
d) In patients with palpable prostatic nodules, the prevalence of prostatic cancer is 0.5%. The test under
these conditions has a sensitivity of 80%. Assuming the specificity is 95%, what is the probability that a
patient with a positive test result having prostatic cancer?
Transcribed Image Text:12:54 D E A ll 100%I + Assignment3.pdf Problem 1 Please answer the below questions based on this data: 44, 20, 85, 68, 64, 83, 56, 70, 55, 78, 80,65,64,54,53, 85, 68, 50, 57, 61, 51, 94, 87, 25, 30, Compute: 1. Mean, Median, Mode 2. SD, Variance 3. Range 4. The 75th percentile, the 25th percentile, the 55th percentile 5. Interquartile Range 6. Are 98 an outlier? Is 124 an extreme outlier? 7. Draw the frequency table of this data, mentioning only the frequency and the cumulative frequency 8. Represent this data using a boxplot 9. Is this data symmetrical or skewed? Problem 2 Table of results for survey of daycare status and ear infection by 6 months for 260 infants Ear Infection by 6 Months No Daycare Yes Total Yes 58 62 120 45 No 95 140 Total 103 157 260 Calculate the following from the table counts 1. Marginal probability that an infant had an ear infection by 6 months? 2. Marginal probability that an infant was in daycare? 3. Joint probability of being in daycare and having an ear infection by 6 months? 4. Joint probability of being in daycare and not having an ear infection by 6 months? 5. Conditional probability of having an ear infection by 6 months given that the infant is in daycare? 6. What is the conditional probability of having an ear infection given that the infant was not in daycare? 7. What is the probability of having an ear infection or that the infant was not in daycare? 8. Are daycare status and ear infection status independent? Justify your answer. Problem 3 A new test is developed for the detection of carcinoma of the prostate.(Foti et al. NEngl. J Med. 1977). When it is tested in a group of 113 patients with prostatic cancer, 79 have a positive test. In a group of 217 individuals without prostatic cancer, 10 have a positive test. a) What is the specificity and sensitivity of the test? b) Calculate FP rate and FN rate. c) Calculate PPV and NPV. d) In patients with palpable prostatic nodules, the prevalence of prostatic cancer is 0.5%. The test under these conditions has a sensitivity of 80%. Assuming the specificity is 95%, what is the probability that a patient with a positive test result having prostatic cancer?
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