Statistics Questions With Tasks And Answers

• Frequency distribution table to represent the data is shown below.Histogram to represent the prices of the part Mean, median and mode of the data.

Sorted data

Sum of observation =12602

Number of observation = 60

Mean

Median of the even numbers is computed below.

Mode

Maximum frequency is observed for 140 and hence, the mode of the data would be 140. Number of flights at the airport and the baggage’s sold 

• The above is a sample since it relates to the data provided for 7 weeks only and does not consider the relevant data for the complete list of all the weeks for which the airport has been operational and data available. In this regards, it is imperative to note that population refers to the complete set of requisite observations while sample refers to a part of the observations drawn from population of interest (Flick, 2015).

• Standard deviation of flights at the airport is calculated as shown below.Inter quartile range (IQR) of the number of baggage’s sold is calculated as shown below.Sorted data

Third Quartile = 75^th percentile

First Quartile = 25^th percentile

IQR is more useful than standard deviation since it is less susceptible to being influenced by the extreme values present in the data along with the skewed nature of data (Hair et. al., 2015).

• Correlation coefficient (R) is calculated as shown below.

From the above value, it can be inferred that the linear relationship between the given variables is positive but moderate in strength (Hillier, 2016).

• Regression equationHence, Regression equation

• Coefficient of determination

The correlation coefficient indicates that only 20.57% variation in the number of baggage’s sold would be explained in the variation in the number of flights at the airport (Flick, 2015).The cross table for the data is highlighted below.

• Probability that a randomly selected player will be club members OR receiving Grassroots training.

Favourable cases

Total cases

Probability

• Probability that a randomly selected player will be external AND be in the scientific training.

Favourable cases

Total cases

Probability

• Probability that a randomly selected player will be from club and also be in the scientific training.

Favourable cases

Total cases

Probability

• Probability table is shown below.

	Scientific training	Grassroots training
Recruited from club members	=40/140 =0.2857	=100/140=0.7142
External recruitment	=50/70=0.7142	=20/70 =0.2857

The above probability computations clearly highlight that the two events i.e. training and recruitment are not independent as the underlying probabilities of receiving a particular training is contingent on the recruitment method (Hillier, 2016). the requisite probability is 0.580 that consumer comes from A segment and prefers TV over Radio.

Distribution of x is highlighted below.Mean of the amount won per ticket is E(x).Standard deviation of the amount won per ticket Therefore, the mean and standard deviation of the amount won per ticket is 0.61132 and 6.63 respectively.

Normal distribution

Average speed of passenger train = 250 km per hour

Standard deviation = 30 km per hour

1. Probability that train will average less than 200 km per hour

From standard normal table

Hence, there is a 0.0475 probability that train will average less than 200 km per hour.

1. Probability that train will average more than 300 km per hour From standard normal table Hence, there is a 0.0475 probability that train will average more than 300 km per hour.Probability that train will average between 210 and 280 km per hour

From standard normal table

Hence, there is a 0.7495 probability that train will average between 210 and 280 km per hour.

Average number of shoppers = 448 shoppers

Standard deviation = 21 shoppers

Random sample = 49

Probability that mean between 441 and 446 shoppers =?

Here,Therefore, the probability that mean between 441 and 446 shoppers 0.2415. 

References

Flick, U. (2015) Introducing research methodology: A beginner’s guide to doing a research project. 4th ed. New York: Sage Publications.

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods. 2nd ed. New York: Routledge.

Hillier, F. (2016) Introduction to Operations Research 6th ed. New York: McGraw Hill Publications.