Statitics Homework

(10 QUESTIONS @ 0.8 = 8 PTS) MUST SHOW YOUR WORK, BUT POINTS AWARDED FOR CORRECT ANSWERS ONLY.

#1. Qualitative data “measured’ on which SCALE(S) can NOT provide valid statistics?

#2. A PIE CHART is a circle and a circle has 360 degrees (360o). If a family’s annual expenses were $ 15,000 for groceries, $ 4,000 for fuel, and $ 24,000 for rent, what PERCENT of the circle area (showing the sum of all 3 expenses) is each expense? THEN, for the pie chart, what are the three WEDGE ANGLES (in degrees) ? (Google “protractor”)

#3. ELEVEN DATA x-Values: 6, 1, 7, 13, 14, 9, 8, 31, 10 , 9, 15 What are the MEAN and STANDARD DEVIATION (HAND CALCULATE – NOT SOFTWARE (BUT YOU CAN USE SOFTWARE TO CHECK YOUR ANSWERS)?

#4. Same data set as in (#3) What are the Q1, Q2, Q3 and IQR ?

#5. DRAW A BOX PLOT and show where the values in #3 and #4 are AND tell which statistics are NOT shown in a box plot (if any). Can you think of anything else that a BOX PLOT does NOT tell us about our data?

#6. FOR #3 Using the TWO methods for determining OUTLIERS (mean + 2 SD’s and the Q3 + 1.5 * IQR AND Q1 – 1.5 * IQR) are there ANY outliers at either end? (SHOW YOUR WORK USING BOTH OUTLIER METHODS)

#7. What are the RANK AND ACTUAL DATA VALUE OF THE 55th PERCENTILE (USE FORMULA R = P/100 * (N+1) in the data list in #3

#8. READ CAREFULLY AND DO ALL PARTS. DELETE data point “31” from the list in problem #3, and recalculate the mean, standard deviation, Q1, Q2, Q3 and IQR. THEN, IDENTIFY HOW DELETING THAT “OUTLIER” AFFECTED WHICH STATISTICS AND HOW THIS COULD AFFECT ANY INTERPRETATION OF THOSE STATISTICS. DO YOU SEE WHY THE “MEDIAN” PRICE IS USED FOR HOUSES AND “MEDIAN” INCOME IS USED FOR SALARIES (RATHER THAN THE MEAN) ? BUT, SHOULD OUTLIERS ROUTINELY BE DELETED, FOR EXAMPLE THE “ONE DEATH IN A THOUSAND” FOR A PARTICULAR MEDICATION ? SO, WHAT EVIDENCE COULD JUSTIFY DELETING SUCH OUTLIERS?

#9. For the following data COMPUTE the (ƩX)2 and the ƩY2 (be careful)

#10. In this STEM & LEAF diagram how many numbers are between (a) 20 and 71 INCLUDING 20 and 71 if present AND

(b) BETWEEN 102 AND 114 (INCLUDING THOSE ENDS IF PRESENT) (c) DOES THIS DATA DISTRIBUTION LOOK “NORMAL” (BELL CURVE SHAPE)?

11| 4 4 9

10| 3 4 5 7 9

9| 3 5 8 8 8 9

8| 0 0 2 2 2 2 4 7

7| 1 1 1 3 4 6 6 8 8

6| 2 3 5 6 7 8 9

5| 4 5 5 6 6 9 9

4| 2 3 3 3 4 4

2| 0 0 1 3 5

1| 0 0 0 2

(STEMS TIMES 10: This means that the lowest number is 10 and the highest is 119)

NO CREDIT FOR SOFTWARE ANSWERS. MUST SHOW WORK (SET-UPS), BUT CREDIT FOR CORRECT ANSWERS ONLY