Stats Assignment

HOMEWORK SET # 2 Due Date: Sept 15, 2020
Name ____________________________ RUID ____________________

1.- Write any 5 numbers whose mean is 5:

2.- Write any 5 numbers whose median is 1:

3.- Write any 5 numbers whose mean is 3 and whose median is 6:

4.- Write any 5 numbers with mode equals 0:

5.- Write any 5 numbers with no mode:

6.- Calculate the mean, the median and the mode for the following numbers:
2, 3, 5, 3, 2, 3, 4, 3, 5, 1, 2, 3, 4

Answer: mean = median = the modes are:

7.- Calculate the range, the variance and the standard deviation for the following sample:
1, 6, 2, 2, 3, 0, 3
Answer: range = variance = standard deviation =

8.- Calculate the variance and standard deviation for the samples
a) n = 40, Σx2 = 380, Σx = 100 Answer: s2 = s =

b) n = 20, Σx2 = 18, Σx = 17 Answer: s2 = s =

9.- Consider the following sample of five measurements: 2, 1, 1, 0, 3.
a). Calculate the range, s2, and s.
Answer: range = variance = standard deviation =

b). Add 3 to each measurement and repeat part a.
Answer: range = variance = standard deviation =

c). Subtract 4 instead of adding 3 from each measurement and repeat part a).
Answer: range = variance = standard deviation =

d). Considering your answers to parts a, b, and c, what is your conclusion? (Circle your answer)
1) The variance increase when adding 3
2) The variance decrease when subtracting 4
3) The variance does not change

10.- Find the fraction or proportion of the data, according to Chebyshev’s rule, that is contained in the interval (x ̅ – 2.2s ; x ̅ + 2.2s)
Answer: ________

11.- Find the fraction or porportion of the data, according to the Empirical rule, that is contained in the interval (x ̅ – 2s ; x ̅ + s)
Answer: ________

12.- Using the relation of the range with standard deviation, give an estimate of s, the sample standard deviation when the value of the range is 24.
Answer: _________

13.- Give the percentage of measurements in a dataset that are above and below each of the following percentiles:
a. 71st percentile Answer: above is ____ below is ____

b. 59th percentile Answer: above is ____ below is ____

c. 2nd percentile Answer: above is ____ below is ____

14.- Compare the z-scores to decide which of the following xvalues lie the greatest distance above the mean and the greatest distance below the mean.

a).x = 100, µ = 50, σ = 25 then z-score =

b).x = 1, µ = 5, σ = 1 then z-score =

c).x = 0, µ = 200, σ = 100 then z=score =

d).x = 10, µ = 5, σ = 4 then z-score =

Answer: the x value at the greatest distance above the mean is ________
the x value at the greatest distance below the mean is ________

15.- In problem (14) above, are there outlier observations? [circle your answers]
Answer: a) b) c) d) e) none

16.- Consider the horizontal box-plot shown below

a. What is the median of the data set (approximately)? Answer: ________
b. What are the upper and lower quartiles of the data set (approximately)?
Answer: QU = _____ QL = ______
c. What is the interquartile range of the data set (approximately)? Answer: IQR = ______
d. Is the data set skewed to the left, skewed to the right, or symmetric? (circle your answer)
Answer: to the left to the right it is symmetric
e. What percentage of the data lie to the right of the median? Answer: ______
To the left of the upper quartile? Answer: ______
f. Identify any outliers in the data. Answer: ___________________________

18.Male pulses (n1 = 10; x1 = 62.4; s1 = 11.9) and female pulses (n2 = 8; x2 = 75; s2 = 13.6). Assume the population standard deviations are equal. Evaluate the claim that the pulse rate of women is higher than men: calculate the appropriate test statistic, specify the degrees of freedom of the test statistic and find the pvalue. State the conclusions of the test at the significance levels 1%, 5%, and 10%. Conclude by constructing a 99% confidence interval for the difference in mean pulse rates.