Question

Information for Questions 3 and 4: In order to measure the effectiveness of their exercise plans, physical therapists collect data on their patients. Here are sets of three measurements of Left Hand Strength along with three measures of Right Hand Strength. The 6 measurements are taken on each day that the patient has physical therapy. The following data is for 10 different days. Right Hand Strength Median: Left Hand Median: Right Hand Day: 1 72 60 68 3 76 Left Hand Strength 52 50 48 42 54 50 | 62 54 | 47 44 59 58 5962 58 54 62 56 5 8 57 51 45 50 56 46 57 60 57 50 57 76 74 56 66 66 67 8277 66 69 74 65 70 60 68 67 67 59 67 63 7 82 | 74 74 67 67 10 To begin, find the Median value for each set of 3 hand strengths. In other words, find the median left hand strength for the 3 readings on Day 1, then find the median right hand strength for the 3 readings on Day 1. (Note: You do not need to enter these values into your calculator in order to find the medians! Simply look at the values and pick the middle value when the data is put in order. For example, Day 10 left hand, the median is 57 because when you put the data in order it is: 57 57 58.) Enter the Medians for the Left hand into L1 and the medians for the Right hand into L2. Then, using the Left hand medians as the base, calculate the percentage by which the right hand medians exceed the left hand medians using (L2-L1)/L1 *100 and store the results in L3. To do this, scroll to the top of L3. Highlight the heading 'L3" and press ENTER. At the bottom of the screen enter the formula for L3: (L2-L1)/L1 *100. Create two boxplots on your calculator using L1 and L2 by turning on Plot1 and Plot2. Which of the following statements is a true statement about the two Boxplots? (Note: Only one statement is true.) The maximum value in the left hand boxplot is significantly more than the minimum value in the right hand boxplot. a. There is much more variability in the right hand median data than in the left hand median data. b. The c. The maximum value in the left hand boxplot is about equal to the minimum value in the right hand boxplot. The maximum value in the left hand boxplot is significantly less than the minimum value in the right hand boxplot. O d. In the left hand median data there is one outlier, 45.

Answer 1

Q3:

Left hand strength	Median (L1)	Right hand strength	Median (L2)	L3=((L2-L1)/L1)*100
52	50	51	51	72	76	74	74	45.1
48	42	45	45	60	56	66	60	33.33
54	50	50	50	68	66	67	67	34
62	54	56	56	76	82	77	77	37.5
47	44	46	46	70	66	69	69	50
59	58	57	58	82	74	65	74	27.59
59	62	60	60	74	70	60	70	16.67
58	54	57	57	74	68	67	68	19.3
62	56	50	56	67	67	59	67	19.64
58	57	57	57	67	67	63	67	17.54

Boxplot of Median (L1), Median (L2) Data Median (L1) Median (L2)

Option a. The maximum value in the left hand boxplot is significantly more than the minimum value in the right hand boxplot.

Q4:

Boxplot of L3 L3

Five number summary:

Variable Minimum Q1 Median Q3 Maximum
L3 16.7 19.3 30.5 37.5 50.00

Option c. Five Number summary: 16.7, 19.3, 30.5, 37.5 and 50; No outliers.