Question

The number of goals scored by Wayne Gretzky was recorded for seasons 1978-1999. 46, 51, 55, 92, 71, 87, 73, 52, 62, 40, 54, 40, 41, 31, 16, 38, 11, 23, 5, 23, 9 What is the average number of goals scored by Wayne Gretzky? What is the standard deviations of the number of goals? Draw a stem-and-leaf plot (by hand) Roughly, how would you describe the shape of the graph? Calculate the 3 quartiles (Q1, Q2 = median, Q3)? What is the proportion of the measurements in x 2s? Is this proportion close to what the empirical rule suggests? Why?

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The monthly utility bills for a household in Windsor, Ontario, were recorded for 12 consecutive months starting in January 2006: 204.94,180.00, 178.23, 176.43, 165.12, 236.72, 276.70, 309.70, 312.40, 238.66, 225.47, 222.23 25% of utility bills are smaller than what value? 50% of utility bills are greater than what value? 75% of utility bills are smaller than what value? Calculate the IQR (i.e. Inter-Quartile Range). Calculate the lower and upper fences. Construct a Boxplot (by hand). [2] Describe the distribution of the monthly utility bills and identify any outliers.

i need help with both but the most important one is the first i hope someone can answer both i will really appreciate it.

Answer 1

Following table shows the ordered data set and calculations for mean and SD:

Sample size: n=21

The mean is

The standard deviation is

Following is the stem and leaf plot:

Stem and leaf plot shows that distribution is almost symmetric.

There are 21 data values so median will be 11th data value. Therefore:

There are 10 data values in the first half so first quartile will be average of 5th and 6th data values. So first quartile is

There are 10 data values in the second half so third quartile will be average of 16th and 17th data values. So third quartile is

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The interval is

Out of 21 data values, all 21 data values lie in the above interval so the proportion of the measurements in x +/- 2s is

(21 /21) *100% = 100%

According to empirical rule, 95% data values lies within 2 standard deviations of mean. So proportion 100% is not close to 95%.