Ivo Dinov
UCLA Statistics, Neurology, LONI
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STAT 13 (1a, 1b, 1c)

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

Instructor: Ivo Dinov

Homework 1
Due Date: Monday, Oct. 06, 2008

Please, submit your homework right beofre 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:

•  23 30 54 28 31 29 34 35 30 27 21 43 51 35 51 49 35 24 26 29 21 29 37 27 28 33 33 23 37 27 40 48 41 20 30 57

(a) Construct a stem-and-leaf diagram of the data by hand.
(b) Construct a dotplot of the data, using SOCR Charts (Select Dot-Plot).
• (HW_1.3) The histogram below shows the same data that are shown in one of the four boxplots. 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:
 6.8 5.3 6 5.9 6.8 7.4 6.2
(a) Calculate the mean and standard deviation.
(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 measures display resistance and which do not?

• (HW_1.5) Here are the 20 measurements of preening time:
 34 24 10 16 52 76 33 31 46 24 18 26 57 32 25 48 22 48 29 19
(a) Determine the median and the quartiles.
(b) Determine the interquartile range.
(c) Construct a (modified) 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 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Number_of_Flies 1 0 1 2 2 6 9 11 12 18 13 10 15 10 2 2 3 2
(a) Find the Median  number of bristles.
(b) Find Q1 and Q3.
(c) Make a boxplot of the data.
(d) The smaple 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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