Biostatistics Tutorial 3

Tutorial 3

Question 1

a) A company wishes to review its distribution operation and from its time sheet records it found that 144 vehicles were loaded in a 24 hour period. A frequency distribution table was prepared from the data as follows:

Time to load (minutes) Number of vehicles 40 up to 50 17 50 up to 60 61 60 up to 70 59 70 up to 80 7

From the above data construct : i) a frequency histogram. ii) a frequency polygon. iii) a cumulative frequency curve (ogive). iv) From your ogive estimate:

- the median loading time - the interquatile range and quartile deviation. - The number of vehicles loaded in under 52 minutes.

Question 2

The frequency distribution shows the times taken by 30 pupils to do their Mathematics homework. Times have been measured to the nearest minute.

Time (min) Frequency

14. 4 24. 8 34. 10 35-44 8

i) Construct a histogram of the data. ii) Construct a polygon. iii) Construct a less than cumulative frequency table and draw the corresponding curve. Use your curve to estimate: - the median, - the lower and upper quartile ages, inter quartile range and quartile deviation. - the percentage of pupil spending more than 30 minutes to do their homework

Question 3

On a certain day, 500 cars were park in the parking lots of a shopping complex. The parking duration of each car (to the nearest minute) is shown in the table below.

|Time |1-20 |21-30 |31-40 |41-50 |51-60 |61-80 |
|Frequency |62 |73 |90 |120 |110 |45 |

(a) Draw an ogive for the data.

(b) From the ogive, determine

i) The number of cars that park more than 45 minutes. ii) The percentage of cars that park less than 25 minutes.

Compare the variability of the total number of hours exercised between the men and the women.

Question 4 A hospital administrator is interested in the number of outpatients treated in the casualty section of a large hospital. The medical records officer is asked to record the number of outpatients for a period of 100 days. She presents the information to the administrator in the following form:

|Number of outpatients |Frequency (days) |
|Less than 10 |6 |
|10 to under 20 |12 |
|20 to under 30 |23 |
|30 to under 40 |31 |
|40 to under 50 |20 |
|50 to under 60 |8 |
|total |100 |

(a) Calculate the sample mean and sample standard deviation.
(b) Determine the mode by drawing a histogram. Comment on the shape of the distribution based on the histogram drawn.
(c) Use the median formula to find the median. Interpret the meaning of this value.
(d) Calculate the Pearson’s measure of skewness by using the median obtained in (c). Does it confirm the shape of the distribution based on the histogram?
(e) Construct a cumulative frequency table for the given grouped data and hence use it to draw an ogive for the data. From the ogive,
(f) estimate the number of days that the hospital will have more than 35 outpatients.
(g) find the median,
(h) find the interquartile range.