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QuestionEstimate the mean survival time (in months) for 21 multiple myeloma patients treated with Thalidomide using the given frequency data.

Studdy Solution

STEP 1

Assumptions1. The class interval represents the survival time in months for a group of patients. . The frequency represents the number of patients that survived for the corresponding class interval.
3. The mean survival time is calculated as the sum of the product of each class interval and its corresponding frequency, divided by the total number of patients.

STEP 2

First, we need to calculate the product of each class interval and its corresponding frequency. This can be done using the formulaProduct=Class intervaltimesFrequencyProduct = Class\, interval \\times Frequency

STEP 3

Now, plug in the given values for the class intervals and frequencies to calculate the products.
For the first class intervalProduct=10timesProduct =10 \\timesFor the second class intervalProduct=20times8Product =20 \\times8For the third class intervalProduct=30timesProduct =30 \\timesFor the fourth class intervalProduct=40times3Product =40 \\times3For the fifth class intervalProduct=50times2Product =50 \\times2

STEP 4

Calculate the products for each class interval.
For the first class intervalProduct=10times4=40Product =10 \\times4 =40For the second class intervalProduct=20times8=160Product =20 \\times8 =160For the third class intervalProduct=30times4=120Product =30 \\times4 =120For the fourth class intervalProduct=40times3=120Product =40 \\times3 =120For the fifth class intervalProduct=50times2=100Product =50 \\times2 =100

STEP 5

Now that we have the products for each class interval, we can find the sum of these products. This can be done using the formulaSum of products=∑ProductSum\, of\, products = \sum Product

STEP 6

Calculate the sum of the products.
Sum of products=40+160+120+120+100Sum\, of\, products =40 +160 +120 +120 +100

STEP 7

Calculate the sum of the products.
Sum of products=40+160+120+120+100=540Sum\, of\, products =40 +160 +120 +120 +100 =540

STEP 8

Now that we have the sum of the products, we can find the total number of patients. This can be done by adding up the frequencies.
Total number of patients=∑FrequencyTotal\, number\, of\, patients = \sum Frequency

STEP 9

Calculate the total number of patients.
Total number of patients=4+8+4+3+2Total\, number\, of\, patients =4 +8 +4 +3 +2

STEP 10

Calculate the total number of patients.
Total number of patients=4+8+4+3+2=21Total\, number\, of\, patients =4 +8 +4 +3 +2 =21

STEP 11

Now that we have the sum of the products and the total number of patients, we can calculate the mean survival time. This can be done using the formulaMean survival time=Sum of productsTotal number of patientsMean\, survival\, time = \frac{Sum\, of\, products}{Total\, number\, of\, patients}

STEP 12

Plug in the values for the sum of the products and the total number of patients to calculate the mean survival time.
Mean survival time=54021Mean\, survival\, time = \frac{540}{21}

STEP 13

Calculate the mean survival time.
Mean survival time=54021=25.7143Mean\, survival\, time = \frac{540}{21} =25.7143The mean survival time for the patients in the clinical trial is approximately25.7 months, rounded to one decimal place.

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