Question

5. 6) I am interested in the amount of $ my friends win or lose while playing blackjack at the casinos. So I go out and collect a sample of data an obtain the following distribution of data (negative numbers mean $ was lost)
   -13, -12, -8, -4, -3, 0, 2, 4, 6, 8, 12,14

   1. What is the Range? (2pts)

   2. What is the Mean? (3pts)

   3. What is the Median? (3pts)

   4. What is the standard deviation of your sample ‘s’ (6pts)

   5. Sketch an informative error-bar chart showing the mean with error

      bars showing one standard deviation away from the mean (5pts)

   6. What are the two Quartiles (3pts)

   7. What is the 5-number summary? (3pts)

   8. What is the Interquartile Range? (3pts)

6. According to the 1.5*IQR rule, are there any potential outliers? (10pts)

7. Sketch an informative Box Plot of the distribution. (5pts)

Answer 1

Range =maximum value - minimum value =14 - (-13) =$27​​​​​​

Mean, = =6/12 =$0.50

Median =the middle most value after arranging the data in an ascending order(if we get two middle values, we take average of such two values) =(0+2)/2 =$1

Sample std.deviation, s = =$8.84 (rounded to 2 decimal places).

The two Quartiles:

Lower quartile, Q1 = - 7 and Upper quartile, Q3 =7.5

Five number summary:

Median, Q2 =1

Minimum = -13

Maximum =14

First quartile(lower quartile), Q1 = -7

Third quartile(upper quartile), Q3 =7.5

IQR:

Interquartile Range, IQR =Q3-Q1 =14.5

Outliers:

Outliers: none

Values higher than Q3+1.5(IQR) or lower than Q1-1.5(IQR) are considered as outliers and are plotted above the top whisker or below the bottom whisker.

Box plot: