Ivo Dinov
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STAT 13 (1a, 1b, 1c, 1d)

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 1
Due Date: Wednesday, Jan. 13, 2010

Please, submit your homework right before lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW_1.1) A dendritic tree is a branched structure that emanates from the body of a nerve cell. As part of a study of brain development, 36 nerve cells were taken from the brains of newborn guinea pigs. The investigators counted the number of dendritic branch segments emanating from each nerve cell. The numbers were as follows:
 DendriticSegments 33 30 54 28 31 29 34 35 28 27 21 43 51 35 51 49 35 27 26 29 21 29 37 27 28 33 33 31 37 17 20 48 41 20 30 55
• (HW_1.3) The histogram below (right) shows the same data that are shown in one of the four boxplots (left). Which boxplot goes with the histogram? Explain!

• (HW_1.4)  Dopamine is a chemical that plays a role in the transmission of signals in the brain. A pharmacologist measured the amount of dopamine in the brain of each of seven rats. The dopamine levels (nmol/g) were as follows:
 7.1 5.6 5.9 5.9 6.2 7.4 6.4
(a) Calculate the (sample) mean and standard deviation. Explain these 2 sample measures in the context of the data.
(b) Determine the median and the interquartile range.
(c) Calculate the coefficient of variation.
(d) Replace the observation 7.4 by 10.4 and repeat parts (a) and (b). Which of the descriptive (sample) measures above display resistance to this change and which do not?

• (HW_1.5) Here are the 20 measurements of preening time:
 PreeningTimes 27 21 10 16 62 76 33 31 46 24 8 26 57 32 25 48 22 48 29 39

(a) Determine the median and the quartiles.
(b) Determine the interquartile range.
(c) Construct a boxplot of the data, use SOCR Charts (Select Box-Plot).

• (HW_1.6)  A geneticist counted the number of bristles on a certain region of the abdomen of the fruitfly Drosophila melanogaster. The results for 119 individual fruitflies are shown in the table below.
•  Number_of_Bristles Number_of_Flies 29 1 30 0 31 1 32 2 33 2 34 6 35 9 36 11 37 12 38 18 39 13 40 10 41 15 42 10 43 2 44 2 45 3 46 2
(a) Find the Median  number of bristles.
(b) Find Q1 and Q3.
(c) Make a boxplot of the number of flies.
(d) The sample (number of bristles) mean is 38.45 and the sample SD is 3.20. What percentage of the observations fall within 1 SD of the mean?

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